Research ArticleQuality Visibility Improvement with Effort Alignment andCost-Sharing Policies in a Food Supply Chain

Wenbo Zhang 123 and Qin Su 123

1School of Management Xirsquoan Jiaotong University Xirsquoan 710049 China2State Key Laboratory for Manufacturing Systems Engineering Xirsquoan 710054 China3Key Laboratory of Process Control and Efficiency Engineering (Xirsquoan Jiaotong University) Ministry of EducationXirsquoan 710049 China

Correspondence should be addressed to Qin Su qinsumailxjtueducn

Received 3 June 2020 Revised 13 August 2020 Accepted 18 August 2020 Published 1 September 2020

Academic Editor Sri Sridharan

Copyright copy 2020Wenbo Zhang and Qin Suis is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

Improving quality visibility along a food supply chain has been considered as a critical driver of quality risk mitigation safety andsecurity assurance and performance sustainability is paper explores the coordination mechanisms in a food supply chainwhere the demand and costs are sensitive to the supply chain quality visibility that depends on an upstream supplier and adownstream retailer jointly and the effort to improve quality visibility is increasingly expensive After comparing the centralizedand decentralized supply chain models to discover an opportunity for Pareto improvement it is proved that a pure revenue-sharing contract fails to coordinate the supply chain while the price discount contract with effort alignment policy or effort cost-sharing policy works e two coordinating contractsrsquo boundary conditions of excluding deviated actions are presented It isshown that the contract with effort alignment policy is cheaper but more rigid whereas the cost-sharing one allows us to arbitrarilyallocate the supply chainrsquos profits despite more information being collectedemodels are applied to a fresh chicken supply chainin order to verify their effectiveness and robustness in realitye impacts of several specific parameters on supply chain decisionsand performances are analyzed and the results reveal some meaningful managerial implications regarding supply chainquality visibility

1 Introduction

A series of food recalls and destructions worldwide due topoor quality or safety and security have aroused intensiveattention on supply chain vulnerability versus sustainabilityin food industry and academia Recently in July ChinaCustoms detected the novel coronavirus that causesCOVID-19 on the packages of frozen South American whiteshrimp produced by Ecuadorian enterprises and returned ordestroyed the batches of risky food soon afterward Unclearcontamination source is attributed to the inadequate qualitymanagement and visibility in the producerrsquos supply chainwhich brings huge health threats and market losses Globalsourcing and outsourcing stretch supply chains wherequality information becomes opaque leading to unexpected

supply chain disasters even if one plant is contaminated[1ndash3] Fortunately it is possible to make supply chainsmore visible given the prevalence of information tech-nologies such as radio frequency identification (RFID)technology global positioning system (GPS) quick re-sponse (QR) code and blockchain technology Increasinglymore enterprises consider supply chain visibility as acritical solution to assure product quality and safety reducefood spoilage and waste [4] enhance operations efficiencyand mitigate supply chain risks [5] Walmart developed afood traceability initiative with IBMrsquos Food Trust Platformbased on blockchain technology and required all his leafy-greens suppliers to use this system starting in September2019 It allows one to trace a food product back to the farmwithin seconds rather than days as before which will help

HindawiMathematical Problems in EngineeringVolume 2020 Article ID 8918139 17 pageshttpsdoiorg10115520208918139

Walmart confirm that products are certified in every ex-change thus mitigating the propagation risk of food-bornediseases along the supply chain and avoiding the losses thathe and his partners may suffer in food recalls (sourcehttpswwwnasdaqcomarticleswalmart-embraces-ibms-blockchain-tech-2018-09-25) e 2017 Supply ChainWorldwide Survey conducted by GEODIS reveals thatldquoImprove end-to-end Supply Chain visibilityrdquo has becomethe third most important supply chain objective behindonly two delivery indices [6]

Another stimulus for supply chain quality visibilitycomes from consumers e anxiety for quality conditionsto be inspected anytime and anywhere via the ubiquitousmobile network and the awareness of sustainable con-sumption responding to environmental preservation andhumanitarian production induce people to request com-plete quality and health information in order to make sureit meets their exceptions [7] Specifically one reviewsingredients production and expiration dates on foodlabels and further wants to know where and how theproduct was planted or fed whether the materials involvedare organic or environmentally friendly whether therelevant companies have quality certifications andwhether the product was transported in an uninterruptedcold chain When it is easy to track these data withinseconds for example by just scanning the QR code on thepackage using a smartphone consumers are willing to buysuch high-visibility products with traceable codes or PDO(EUrsquos Protected Designation of Origin) labels and even paya considerable premium [8]

In addition there are pressures from regulation and thepublic Food visibility that proves good quality and safety hasbeen a legal requirement or best practice in many regionsreferring to US Quality System Regulation (see FDA 21 CFRPart 820 at httpswwwaccessdatafdagovscriptscdrhcfdocscfcfrCFRSearchcfmCFRPart820) EUrsquos GeneralFood Law (see Regulation (EC) No 1782002 at httpseur-lexeuropaeulegal-contentENTXTuricelex32002R0178)Chinarsquos Food Safety Law (see the original version (inChinese) at httpwwwgovcnzhengce2015-0425content_2853643htm For an unofficial translation version (in En-glish) from the United States Department of Agriculture(USDA) see httpsappsfasusdagovnewgainapiapireportdownloadreportbyfilenamefilenameAmended20Food20Safety20Law20of20China_Beijing_China20-20Peoples20Republic20of_5-18-2015pdf) etc Commentsand complaints about food quality on social networks andthe media sometimes not sent by the target consumerslead companies to invest more in quality visibility topromote public trust and confidence not merely legalcompliance More and more food companies are inte-grating with Alibaba Healthrsquos ldquoTrust on the Coderdquo plat-form under the guidance of the local government isplatform helps regulators and consumers to identify theauthenticity of the provenance and quality of importedfoods (see ldquoTrust on the Coderdquo website (httpswwwmashangfangxincom) which is initially designed forpharmaceutical traceability but now also available for foodtraceability)

Although supply chain quality visibility benefits com-panies in proactive quality risk control operations efficiencyand consumer trust the motivation to improve qualityvisibility is still scant GEODIS reports that 77 percent ofsupply chain companies have no or very restricted visibility[6] e few visibility examples at present mostly appear inapparel companies like HampM and Swiss Heidi who havedisclosed their entire supply chain information from thecotton source to the distribution center through the label ofeach garment [5] However in the food domain there arenot so many examples as we might think even it should bemore reasonable to disclosure information tightly related tohealth

Two reasons may explain the status quo First technicaldifficulties and expensive costs of building quality visibilityare growing exponentially in food supply chains often af-fordable for only large-scale companies It requires access tomore subjects processes and items following the ldquowaterfallflowrdquo from farm to table [5] and needs more hard work tocollect standardize communicate analyze store and vi-sualize quality data as compared with well-quantified in-formation such as price demand and inventory Besides thequality of food especially fresh or perishable food is alwaysin continuous degradation between two adjacent processing[9] so periodic or real-time monitoring of quality changes isnecessary in food supply chains and of course quite ex-pensive In contrast product quality is generally constantduring each company who gathers quality information onlyonce with a quality inspection in other supply chainsSecond companiesrsquo quality visibility decisions are trapped inldquodouble marginalizationrdquo and lack an overall coordinationCompanies keep the inertia of saving the expense andprotecting private information with the expectation of anadvantage in competition or games and they fail to balanceinformation cost information confidentiality and infor-mation value eir decisions tend to maximize onersquos owninterest which makes supply chain revenue and qualityvisibility suboptimal

eoretical works surrounding supply chain qualityvisibility are mostly conceptual technical or empirical atpresent and the model research ignores the expensive cost ofbuilding quality visibility and consumer sensitivity to qualityvisibility in food supply chains erefore it is quite nec-essary to further explore the impacts of quality visibility inthe food supply chain and use the approach of coordinatingsupply chain to reduce companiesrsquo cost pressure in qualityvisibility investment thus achieving multi-win outcomes forthe whole supply chain including the consumer

is paper seeks to answer the following researchquestions

(1) What are the optimal strategies in the centralizedand decentralized food supply chains with demandand cost dependent on quality visibility Whetherthe cooperative decision-making benefits the supplychain profit and quality visibility

(2) What kind of contracts can coordinate the supplychain What are their conditions strengths andlimitations

2 Mathematical Problems in Engineering

(3) How do the key parameters such as consumersrsquosensitivity to quality visibility affect the supply chaindecisions and performances What are the effectivemoves of the managers to improve their profits andquality visibility

To address these research questions this study con-structs models to investigate the centralized and decen-tralized decision-making scenarios and the feasibility of acommon revenue-sharing contract Based on that twomodified contracts with effort alignment and cost-sharingpolicies that coordinate the supply chain with quality visi-bility effort are proposed Next the effectiveness and ro-bustness of the contracts in reality are verified with apractical chicken supply chain case Finally suggestions forperformance improvement and managerial insights areoffered

e contributions of this paper are mainly manifested inthree aspects (i) We build an analytical model assumingdemand and cost are sensitive to quality visibility of theupstream and downstream companies and provide a usefulway to capture the optimal price and quality visibilitystrategies in the food supply chain (ii) e positive impactsof food quality visibility spectrum on supply chain playersare quantitatively demonstrated and the opportunity forPareto improvement is revealed theoretically enablingcompanies to improve their quality visibility (iii) Twocontract mechanisms based on the price discount contractare designed to address the coordination problem with dualquality visibility efforts Both contracts align the decisionmotivations of the supply chain players and show a strongrobustness To the best of our knowledge there are no othercoordination research studies about quality visibility in thesupply chain context

e rest of the paper is arranged as follows e secondsection reviews the relevant literature Afterward the thirdsection describes the basic model and compares the cen-tralized decision-making supply chain with the decentral-ized one In the fourth section several contracts arediscussed to coordinate the supply chain which is followedby a practical case that applies the model in the fifth sectionFinally this paper concludes with the research limitationsand future directions

2 Literature Review

21 Supply Chain Quality Visibility Concept Althoughscholars have focused on supply chain visibility for yearsthere seems no clear consensus on its definition and position[10] It is early viewed as the extent of information sharing inthe supply chain based on the transparency concept(Lamming et al [11] and Bartlett et al [12]) and later de-scribed as something similar to traceability based on RFIDtechnology (Holmstrom et al [13]) the capacity of thesupply chain to have a view of the product life cycle (Musaet al [14]) or the lower uncertainty of the companyrsquos socialresponsibility effort outcomes based on a CSR perspective(Kraft et al [15]) In contrast the definition proposed byBarratt and Oke [16] is more widely accepted the extent to

which supply chain actors have access to or share key oruseful information with mutual benefits to their operations

It is still necessary to distinguish ldquosupply chain visibilityrdquofrom several intertwined concepts before we discuss itsderivative ldquosupply chain quality visibilityrdquo Based on theexisting discussions we contend that information sharingamong the related companies is a prerequisite for supplychain visibility and traceability means a visibility of in-formation provenance and dissemination process Supplychain visibility is considered to meet the information needsof stakeholders internal to the supply chain and it is namedmostly from the perspective of the information user whilesupply chain transparency from the information providerrsquosperspective comes up only when supply chain companiesshare or disclose visibility to the external stakeholders [5]When the consumer is treated as an outsider of the tradi-tional supply chain supply chain transparency perceived bythem can be understood as the minimum of supply chainvisibility in terms of information transferred However theconsumer has been an insider of the modern supply networkwith engaging more and more in product design qualitysupervision and brand advocacy etc erefore from theperspective of the whole supply chain we can use ldquosupplychain visibilityrdquo and ldquosupply chain transparencyrdquo inter-changeably to describe the extent to which the consumer getsthe desired information from the upstream supply chain

Supply chain quality visibility then can be conciselydefined as the extent to which supply chain actors haveaccess to high-quality information related to product (ser-vice) quality High-quality information means the infor-mation rich in ldquoinformation qualityrdquo ie accuracytimeliness completeness trustworthy usefulness and easeof use Information quality represents the level of supplychain visibility [17] and depends on the efforts to collect andintegrate relevant information from the upstream anddownstream supply chain [5] Quality information ofproduct or service involves not only inherent characteristicsof the product or contents of the service but also all theprocesses operations and factors that may have an impactTraceability systems that aim to provide such quality visi-bility have gradually been opened up to consumers especiallyin food supply chains Similar to supply chain transparency[18] supply chain visibility can be categorized into pricedemand quality cost inventory and process visibility byinformation element It is noticeable that some processinformation may contribute to both quality and processvisibility but process visibility prefers information aboutproduction transaction and management processes foroperational or strategic considerations which is differentfrom quality visibility

As for measuring supply chain quality visibility Caridiet al [19 20] suggest a structured assessment model ofsupply chain visibility using a weighted sum of all the nodecompaniesrsquo visibility which is calculated by the geometricmean of three scales information type information quantity(which can be regarded as the completeness dimension ofinformation quality) and information quality Bartlett et al[12] link information type to the following quality criteriascrap levels rework levels process repeatability supplier

Mathematical Problems in Engineering 3

quality quality system audit and continuous improvementTse and Tan [17] believe that product quality (risk) visibilitycomes from the number of product transitions and thedisclosure level of suppliersrsquo information that refers tosuppliersrsquo conformity reliability safety and quality stan-dards For the sake of usefulness to the consumer wesummarize and refine the following types (i) productprovenance (ii) supplier quality about quality details inproduction process (iii) transport conditions (iv) retailerquality about quality details in selling process (v) qualityaudit and certification about third-party or self-certificationof food and companies and (vi) product quality aboutdetails on food labels as regulated en their informationquality ratings are processed to get the supply chain qualityvisibility referring to Caridi et al [19]

22 Supply Chain Quality Visibility Effect Studies about theimpacts of supply chain quality visibility (or supply chainvisibility) on the decisions and performances of supply chaincompanies are relevant Delen et al [21] explore the extent ofthe logistics performance improvement in a supply chaininfluenced by visibility expressed as RFID data and theyassert that the supply chain visibility could make a companydistinctive just as quality was once the differentiator Basedon the theory of organizational information processingWilliams et al [22] verify that internal integration canpositively regulate the relationship between supply chainvisibility (demand supply and market visibility) and supplychain responsiveness Tse and Tan [23] provide qualitycriteria and a multi-outsourcing decision path for focalcompanies in supply chains using a marginal incrementalanalysis (MIA) method Guo [24] discuss the impact ofquality information disclosure on companiesrsquo profits in abilateral monopoly and find that indirect disclosure throughthe retailer is the optimal form of quality informationdisclosure Zhao et al [25] extend Guorsquos research to thecompetitive market and the results indicate that at equi-librium the high-quality supply chain chooses not to dis-close quality while the low-quality one chooses to disclosequality through the retailer Wu et al [26] investigate thequality information-sharing problems in a dual-sourcingsupply chain and demonstrate that quality informationvisibility always benefits the cost-disadvantaged suppliersand the downstream retailer From a ldquonegative qualityrdquoperspective Piramuthu et al [27] compare the marginaldifferences of recall costs at different visibility levels based onthe accuracy of contamination source identification anddetermine the best timing of recall polices in a multistageperishable food supply network

For consumers supply chain quality visibility is good up tonow Granados and Gupta [7] elucidate the benefits of quality-and price-related visibility (transparency) to consumers withdifferent product features industry competition and regulatoryintensity through examples Ghosh andGalbreth [28] find that agreater proportion of partially informed consumers who capturedisclosed quality information can decrease their search be-haviour and help companies save disclosure cost and increaseprofit Both external visibility initiatives (such as proactive

labelling strategies of voluntary certification and ingredientreplacement [29]) and internal visibility initiatives (such asimproving environmentally sustainablemanufacturing [30]) canspur consumers to purchase products El Benni et alrsquos [8] surveystudy indicates that affected by the 2008 melamine incidentChinese consumers are willing to pay an extra CNY 69sim109(equivalent to 30sim40 of the retail price) for a 900 g can ofinfantmilk formula with a PDO label as well as a high premiumfor anticounterfeiting packaging and a QR traceable code

We summarize the related literature in Table 1 esestudies confirm that supply chain quality visibility can bebeneficial to the entire supply chain downstream companiesand consumers while the impact on upstream companies isnot quite clear [7 24 26] It is because that quality visibility inthese studies is provided mainly by suppliers who thus bearquality visibility cost and information leakage risk alone emismatch between these disadvantages and slashed revenueshanded by downstream companies discourages upstreamcompanies and makes outcomes uncertain Furthermore mostof the model research studies focus on the informationstructure transformed by quality information disclosurestrategies also named transparency strategies [18] ey as-sume quality information is always ready to be shared or notignoring the previous processing cost and few of them arespecific to the food supply chain In fact every companycontributes to the supply chain quality visibility and everyoneneeds to pay for it in food supply chains We thus assumecompaniesrsquo respective quality visibility levels that jointly makeup the overall visibility determine their costs and explore theimpacts on supply chain players

23 Supply Chain Coordination Contracts Asymmetric in-formation in a supply chain often traps the upstream anddownstream companies into a double marginalizationwhich can be dramatically mitigated by supply chain co-ordination contracts maximizing supply chain profits[31 32] is field has accumulated extensive literature ispaper involves several relevant streams including supplychain coordination with a revenue-sharing contract or aprice discount contract and coordination policies for thesupply chain with effort decisions

e revenue-sharing contract is one of the most com-mon supply chain coordination mechanisms Cachon andLariviere [33] conduct a comprehensive analysis of it andillustrate its broad applicability with a single retailer indemand or price certaintyuncertainty settings or withcompeting retailers in quantity competition However itstops functioning when the supply chain needs to deal withthe retailerrsquos costly effort Xiao et al [34] examine the im-pacts of product quality and service quality on demand andobtain the optimal decisions and Pareto conditions of thecoordination mechanism using a revenue-sharing contractKong et al [35] discuss the information leakage problemfrom a supplier in a supply chain where the retailerscompete and their results show that a revenue-sharingcontract aligns the motivations of suppliers and retailersbetter and mitigates the supplierrsquos disclosure risk Bernsteinand Federgruen [36] propose a wholesale price contract with

4 Mathematical Problems in Engineering

a buyback rate ie a price discount contract that can co-ordinate the supply chain with uncertain demand which isproven to be equivalent to a revenue-sharing contract in theprice-setting model [33] Cai et al [37] demonstrate that inthe dual-channel supply chain competition the price dis-count contract reduces channel conflict and helps achievecoordination by distributing more profit to the retailer

To coordinate the supply chain with costly effortBhaskaran and Krishnan [38] respectively assess revenueinvestment and innovation sharing policies in an innova-tion supply chain Product innovation revenue only derivesfrom the quality improvement that depends on the inno-vation effort of both the focal company and the partnercompanye results show that although the proposed threemechanisms fail to coordinate the supply chain they im-prove supply chain profits compared with the decentralizedsupply chain when specific conditions are realized Krishnanet al [39] pointed out that a single-parameter contract couldnot correct the distortion caused by the pricing and effortdecisions and they propose effort cost-sharing unilateralmarkdown allowances and constrained buyback mecha-nisms to address it Cachon and Lariviere [33] also offer asimple coordinating quantity discount contract based onrevenue-sharing Lambertini [40] extends the traditionaltwo-part tariff contract for quality improvement using avariable linear tariff according to the RampD effort or productquality For fresh products Cai et al [9] consider the impactof distributorrsquos fresh-keeping effort on product freshnessand thus on product quality and quantity and develop a pricediscount sharing contract with compensation contract tomake the supply chain coordinated Extending Cai et alrsquos [9]study to the online situation Gu et al [41] characterize theonline retailerrsquos strategy of fresh-keeping effort under aconsumer full-refund policy and present a buyback contract

and a revenue- and cost-sharing contract to achieve thecooperative optimization

Table 2 provides an overview of the related literatureomitting the wholesale price contract that cannot coordinatethe supply chain in each row of the last column Most of theeffort-related studies deal with the single effort of thedownstream company and the revenue-sharing contract orprice discount contract works well by extending with anadditional parameter However when there are multipledecision variables linked to the efforts of the upstream anddownstream more than one parameter needs to be intro-duced into simple supply chain contracts [38 40] Fur-thermore there is no model research where the consumerdemand is influenced by quality visibility leaving a missinglink between visibility effort and market revenue In thispaper we consider the demand dependent on supply chainquality visibility and address the coordination problem withdual quality visibility efforts

3 The Basic Model

31 Model Settings We examine a two-tier food supplychain consisting of a supplier and a retailer who faces aconsumer market At the start of a selling season thesupplier sets a wholesale price w and its own quality visibilitylevel vs en the supplier invests in quality visibility as itclaims and begins to produce after receiving the retailerrsquosorder Once the delivery is ready the retailer determines aretail price p and its own quality visibility level vr Subse-quently the retailer invests in quality visibility and sells thefood e consumer observes the price and the overallquality visibility provided by both companies and decides tobuy or not finally making revenue realize e timeline ofevents is outlined in Figure 1

Table 1 Literature related to the effects of supply chain quality visibility

Literature Visibility focused Objectives Methods SC typesDelen et al [21] RFID data Logistical performance Case study Retail

Williams et al [22] Demand supply and marketvisibility Supply chain responsiveness Empirical study Various

including food

Tse and Tan [23] Quality risk visibility Multi-outsourcing decision Marginal incrementalanalysis (MIA) Common

Guo [24] Quality information disclosure Company pricing and profit Mathematical modelling CommonZhao et al [25] Quality information disclosure Company pricing and profit Mathematical modelling Common

Wu et al [26] Quality information sharing ornot Company profit and market share Mathematical modelling Common

Piramuthu et al[27]

Accuracy of contaminationsource identification Liability cost recall timing Mathematical modelling Food

Granados andGupta [7]

Quality price and featurestransparency etc

Buyerrsquos purchase decision businessinformation and IT strategies eoretical development Common

Ghosh andGalbreth [28] Quality information disclosure Consumer search and purchase

company pricing and profit Mathematical modelling Common

Riganelli andMarchini [29] Labelling strategies Consumer demand company

performance Empirical study Food

Buell and Kalkanci[30]

Internal and externaloperational transparency Consumer purchase Field experiment Apparel and

foodEl Benni et al [8] Authenticity cues Consumer choice Survey Food

is paper Supply chain quality visibility Company pricing visibility decisionand SC performance Mathematical modelling Food

Mathematical Problems in Engineering 5

311 Demand Function with Quality VisibilityConsumers are assumed sensitive to food price and supplychain quality visibility d(p vsc) θ minus λp + αvsc where θ isthe largest potential demand λ and α are sensitivity coef-ficients λ αgt 0 and θgt λpgt 0 Refer to the supply chainvisibility assessment method of [19] vsc 1113936ωivi(i s r)where the weight ωi measures the importance of the qualityvisibility provided by company i to consumers We supposeωs ωr (12) indicating equal importance e demandsensitive to quality visibility is reasonable mostly in foodsupply chains where consumers are willing to pay a sig-nificant premium [8]

312 Cost Function with Quality Visibility e visibilityeffort cost of the upstream or downstream company isc(vi) βiv

2i a most widely used effort cost function

[33 38 40] where βi gt 0e square reflects the diseconomy of

visibility systems due to the increased information capacityefficacy requirement and management complexity brought bya higher visibility level [42] e diseconomy occurs in everycompany no matter upstream and downstream characterizingthe food supply chain In contrast except for the focal com-pany quality visibility cost of the partner company is generallyfixed or linear in other types of supply chains For example aquality inspection instruction is usually enough for mobilephone components and the mobile phone retailer rarely needsto invest in quality visibility

e related notations and variables are defined as fol-lows i sc s r are the subscripts that represent the wholesupply chain the supplier and the retailer respectively j

C D R E B are the subscripts that represent scenarios ofcentralized decision-making decentralized decision-mak-ing a revenue-sharing contract a price discount contractwith effort alignment and a price discount contract withcost-sharing respectively

Table 2 Literature related to supply chain coordination contracts

Literature Demand (or other) depends on Main decision variable Contract types (coordination or not)Cachon andLariviere [33] (Inverse demand) quantity Price order quantity Revenue-sharing (Y) buyback (Y) quantity

flexibility (Y) sales rebate (Y) etc

Xiao et al [34] Price product quality servicequality Price service quality Revenue-sharing (Y)

Kong et al [35] (Inverse demand) quantity Price order quantity leakagedecision Revenue-sharing (Y)

Bernstein andFedergruen [36] Price Price order quantity Price discount (Y)

Cai et al [37] Price Price Price discount (Y)Supply chain with costly effortCachon andLariviere [33]

(Inverse demand) quantity retailereffort Retail effort order quantity Revenue-sharing (N) quantity discount

with revenue-sharing (Y)Bhaskaran andKrishnan [38]

(Quality depends on) innovationeffort of focal and partner firms

Innovation level of focal firm andpartner firm

Revenue-sharing (N) investment sharing(N) innovation sharing (N)

Krishnan et al [39] Promotional effort Price order quantity retailerpromotional effort

Buyback (N) buyback with threemechanisms (Y)

Lambertini [40] Price quality Price RampD effort of the upstreamand downstream

Two-part tariff (N) control-linear two-parttariff (Y) state-linear two-part tariff (Y)

Cai et al [9] Price freshness Price order quantity distributorrsquosfresh-keeping effort

Price discount sharing with compensation(Y)

Gu et al [41] Customer returns Price order quantity fresh-keeping effort

Buyback (Y) revenue-sharing (N)revenue- and cost-sharing (Y)

is paper Price SC quality visibility Price quality visibility (effort) ofthe upstream and downstream

Revenue-sharing (N) price discount witheffort alignment (Y) with cost-sharing (Y)

Supplier determineswholesale price and

quality visibility level

Retailer determinesquality visibility level

and retail price

Retailerorders

Supplierproduces

Retailersells

Demandand revenue

realize

Supply chainquality visibility

observed

Figure 1 Timeline of events under consideration

6 Mathematical Problems in Engineering

w is the wholesale price of a food unitp is the retail price of a food unitvi is the food quality visibility provided by the supplychain or company i

d is the market demandθ is the largest potential demandλ is the price sensitivity coefficient of demandα is the quality visibility sensitivity coefficient ofdemandβi is company irsquos cost coefficient of the quality visibilityeffort

In this supply chain setting the supplierrsquos profit is asfollows

πs w θ minus λp + αvsc( 1113857 minus βsv2s (1)

e retailerrsquos profit is given by

πr (p minus w) θ minus λp + αvsc( 1113857 minus βrv2r (2)

and the profit of the whole supply chain is given by

πsc πs + πr p θ minus λp + αvsc( 1113857 minus βsv2s + βrv

2r1113872 1113873 (3)

e channel costs of the supplier and the retailer areomitted however by replacing w and p with w minus cs andp minus cr respectively we have the intact costs where cs is thesupplierrsquos production cost per unit and cr is the retailerrsquosretail cost per unit

32 Centralized Supply Chain e supplier and the retailerare integrated when making decisions in the centralizedsupply chain Although their own visibility systems are alsoexpected to be integrated into one the system integrationcosts and benefits are quite slight compared to the visibilityinput cost namely the effort cost is is partly because theamounts and types of quality metadata collected from theupstream and the downstream are rarely the same and thusthe two parts of the integrated visibility system are regardedas still working separately e profit function of the cen-tralized supply chain is obtained from equation (3)

πscC pC vsC vrC1113872 1113873 pC θ minus λpC +α vsC + vrC1113872 1113873

2⎡⎣ ⎤⎦

minus βsv2sC minus βrv

2rC

(4)

e profit function (4) always has second continuouspartial derivatives In order to avoid not making sense thefunction is assumed to have a maximum value in its defi-nition domain θλgtpC gt 0 and viC gt 0 erefore its Hesse

matrix H

minus 2λ α2 α2α2 minus 2βs 0α2 0 minus 2βr

⎡⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎦ is set to be negative definite

Let Δ1 16λβsβr minus α2βs minus α2βr and then we have Δ1

minus 2|H|gt 0 and 16λβi minus α2 gt 16λβi minus α2 minus α2(βiβj)gt0(i j isin s r and ine j)

Proposition 1 Given the assumption 8λβsβr minus α2βs minus

α2βr gt 0 in the centralized supply chain the optimal retailprice is plowastC (8βsβrθΔ1) and the quality visibility levelsoffered by the supply chain are vlowastsC (2αβrθΔ1)vlowastrC (2αβsθΔ1) and vlowastscC (αθ(βs + βr)Δ1) the supplychain realizes the maximum profit πlowastscC (4βsβrθ

2Δ1)

Proof Solve three first-order conditions of equation (4)jointly as follows

zπscCzpC

minus 2λpC + θ +12α vsC + vrC1113872 1113873 0

zπscCzvsC

minus 2βsvsC +12αpC 0

zπscCzvrC

minus 2βrvrC +12αpC 0

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(5)

e optimal retail price plowastC (8βsβrθΔ1) the optimalquality visibility level of the upstream vlowastsC (2αβrθΔ1) andthe optimal quality visibility level of the downstream vlowastrC

(2αβsθΔ1) can be easily derived en substituting theminto equation (4) and vsc 1113936ωivi simultaneously we havethe optimal supply chain profit vlowastscC (αθ(βs + βr)Δ1) andmaximal supply chain quality visibility πlowastscC (4βsβrθ

2Δ1)in the centralized supply chain

e assumption 8λβsβr minus α2βs minus α2βr gt 0 ensures thatthe optimal price exists in the domain byθ minus λplowastC ((8λβsβr minus α2βs minus α2βr)θΔ1)gt 0 and it is morestrict than the negative definite assumption of Hessematrix

Corollary 1 (zKzλ)lt 0 (zKzα)gt 0 (zKzβs)lt 0 and(zKzβr)lt 0 where K isin plowastC vlowastsC vlowastrC vlowastscC πlowastscC1113966 1113967

From Corollary 1 we can find that the more sensitiveconsumers are to quality visibility the greater the incentivesthat supply chain companies have to improve their qualityvisibility related to the foods in each stage so that the supplychain can charge a higher retail price and gain a biggersupply chain profit Conversely more price-sensitive con-sumers and a greater marginal cost of the visibility systemprevent the previous process

33Decentralized SupplyChain In a decentralized decision-making supply chain the supplier firstly determines its ownquality visibility level and supplies the retailer at a wholesaleprice according to the pure wholesale price contract eretailer then decides its own quality visibility level afterreceiving the delivery and sells foods at a retail price

e profit function of the retailer is given by

πrD pD vrD1113872 1113873 pD minus wD( 1113857 θ minus λpD +α vsD + vrD1113872 1113873

2⎡⎣ ⎤⎦ minus βrv

2rD

(6)

and the profit function of the supplier is as follows

Mathematical Problems in Engineering 7

πsD wD vsD pD vrD1113872 1113873 wD θ minus λpD +α vsD + vrD1113872 1113873

2⎡⎣ ⎤⎦ minus βsv

2sD

(7)

Let Δ2 32λβsβr minus 2α2βs minus α2βr rough the backwardinduction of a Stackelberg game it is easy to find that theHessian matrixes of equations (6) and (7) are negativedefinite with 16λβr minus α2 gt 0 and Δ2 2Δ1 + α2βr gt 0 whichreveals that there exists a maximum solution set of thedecentralized supply chain

Proposition 2 In the decentralized supply chain the optimalwholesale price of the supplier is wlowastD (βsθ(16λβr minus α2)λΔ2) the optimal quality visibility is vlowastsD (2αβrθΔ2) andthe optimal profit is πlowastsD (4βsβrθ

2Δ2) Ee optimal retailprice of the retailer is plowastD (βsθ(24λβr minus α2)λΔ2) the op-timal quality visibility is vlowastrD (2αβsθΔ2) and the optimalprofit is πlowastrD (4β2sβrθ

2(16λβr minus α2)Δ22) Furthermore the

supply chain realizes the optimal quality visibilityvlowastscD (αθ(βs + βr)Δ2) and the optimal profit πlowastscD

(4βsβrθ2(48λβsβr minus 3α2βs minus α2βr)Δ

22)

Proof Given wD and vs the retailerrsquos optimal retail priceand quality visibility are acquired by the first-order con-ditions of equation (6) as follows

plowastD wD vsD1113872 1113873

8βrθ + 8λβrwD + 4αβrvsD minus α2wD

16λβr minus α2

vlowastrD wD vsD1113872 1113873

2αθ + α2vsD minus 2αλwD

16λβr minus α2

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(8)

We substitute them into equation (7)

πsD wD vsD1113872 1113873 4βrλwD αvsD + 2θ minus 2λwD1113872 1113873

16λβr minus α2minus βsv

2sD

(9)

and similarly obtain the supplierrsquos optimal wholesale pricewlowastD and quality visibility vlowastsD by solving the first-orderconditions of equation (9) en it is easy to get plowastD and vlowastrD

by a substitution into equation (8) and thus the optimalperformance variables by a few further substitutions

Corollary 2

(i) πlowastscC minus πlowastscD (4β3sβrθ2(16λβr minus α2)2Δ1Δ2

2)gt 0(ii) πlowastsD minus πlowastrD (4βsβrθ

2Δ1Δ22)gt 0

(iii) vlowastscC minus vlowastscD (αβsθ(16λβr minus α2)(βs + βr)Δ1Δ2)gt 0(iv) plowastC minus plowastD minus ((βsθ(16λβr minus α2)(8λβsβr minus α2βs minus

α2βr))λΔ1Δ2)lt 0

Under the optimal equilibriums by comparing theoverall supply chain profits in the two decision-making

contexts Corollary 2 (i) indicates that the overall profit ofthe decentralized supply chain is strictly less than those ofthe centralized supply chain Since the supply chainrsquos rev-enue completely comes from the retailer to coordinate thesupply chain the optimal solution plowastC vlowastrC1113966 1113967 of integrateddecisions should be optimal for the retailer and it mustsatisfy

zπrD plowastC vlowastrC1113872 1113873

zpD

0

zπrD plowastC vlowastrC1113872 1113873

zvrD

0

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(10)

en we have wD 0 and vsD vlowastsC which mean thatthe supplier receives nothing from charging a productioncost but bears its own quality visibility cost erefore thesimple wholesale price contract cannot coordinate thesupply chain which is consistent with many previous re-searches From Corollary 2 (ii) the supplierrsquos profit is largerthan the retailerrsquos which verifies the supplierrsquos great first-move advantage in the Stackelberg game

In addition Corollary 2 (iii) and (iv) show that theoverall quality visibility level in the decentralized supplychain is lower than that in the centralized one but theformer retail price is higher than the latter It implies that thecentralized supply chain realizes not only greater profit andhigher food quality visibility but also greater consumersurplus which leads to more social welfare thus realizing awin-win between the supply chain and consumers

Corollary 3 (zKzλ)lt 0 (zKzα)gt 0 (zKzβs)lt 0 and(zKzβr)lt 0 where K isin wlowastD plowastD vlowastiD πlowastiD1113966 1113967(i s r sc)

e inspirations from Corollary 3 are similar to thosefrom Corollary 1 ie consumersrsquo sensitivity to qualityvisibility positively influences the prices and performances ofthe decentralized supply chain as opposed to the pricesensitivity and visibility cost coefficients Nevertheless itseems that the extent of the influences they have is lesssignificant than that in the centralized supply chain due tothe double marginalization which will be recognized moreintuitively in the subsequent practical case is findingindicates that a centralized or coordinated food supply chainis more efficient than a decentralized one in performanceimprovement erefore it is necessary to explore a coor-dination contract if there is no chance to integrate this foodsupply chain to a centralized one

4 Supply Chain Coordination

41 Revenue-Sharing Contract e revenue-sharing con-tract is one of the most used coordination contracts Supposethat the supplier and the retailer agree on the following ex-ante revenue-sharing contract the supplier charges a lowerwholesale price wR and receives 1 minus φ(0ltφlt 1) percent of

8 Mathematical Problems in Engineering

the retailerrsquos revenue Assuming φ 1 the contract becomesa pure wholesale price contract and ifwR 0 it is equivalentto a price discount contract with w (1 minus φ)p ereforefor a crisp wholesale price contract and a price discountcontract there is always an equivalent revenue-sharingcontract

e retailerrsquos profit function is given by

πrR pR vrR1113872 1113873 φpR minus wR( 1113857 θ minus λpR +α vsR + vrR1113872 1113873

2⎡⎣ ⎤⎦ minus βrv

2rR

(11)

Similarly by solving the first-order conditions

zπrR plowastC vlowastrC1113872 1113873

zpR

0

zπrR plowastC vlowastrC1113872 1113873

zvrR

0

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(12)

we have wR (φ minus 1)plowastC lt 0 and vsR vlowastsC is means thatif the supply chain is coordinated the supplier needs tosubsidize the retailer (1 minus φ)plowastC for each unit of foodhowever the revenue that the supplier receives from theretailer is equal to the total subsidy Just like in thewholesale price contract the supplier in the revenue-sharing contract does not realize any revenue but experi-ences the losses due to his own quality visibility cost erevenue-sharing contract as Cachon and Lariviere [33]assert cannot coordinate the supply chain with costly effortdecisions

42 Effort Alignment Policy e contracts with a singleparameter could correct the distortion in the pricing deci-sions of the upstream and downstream supply chain butthey do not address the dual-effort and pricing decisionsTwo or more parameters need to be included to align therelevant decision variables making the profit function of thelast-move decision-maker an affine transformation of theprofit function of the whole supply chain In this paper theprofit function of the retailer who plays as the last-moverdepends on the effort decisions that is the quality visibilitydecisions of both the supplier and the retailer Given thateffort can be observed it is feasible to align the supplierrsquoseffort with the retailerrsquos similar to the wholesale pricealigned with the retail price in a pure price discount contract

Theorem 1 Ee following price discount contract with effortalignment (E) can coordinate the supply chain the suppliercharges a wholesale price wE (βr(βs + βr))pE and offersquality visibility vsE (βrβs)vrE Een the retailerrsquos profitfunction is πrE φπscC and the supplierrsquos profit function isπsE (1 minus φ)πscC wlowastE (1 minus φ)plowastC vlowastsC plowastC vlowastrC1113966 1113967 is theoptimal solution set of the supply chain whereφ (βs(βs + βr))

Proof Substitute wE (βr(βs + βr))pE and vsE (βrβs)

vrE into the retailerrsquos profit function (2)

πrE pE vrE1113872 1113873 pE minus (1 minus φ)pE1113858 1113859 θ minus λpE +α vsE + vrE1113872 1113873

2⎡⎣ ⎤⎦

minus βrv2rE middot

φ βs + βr( 1113857

βs

φpE θ minus λpE +α vsE + vrE1113872 1113873

2⎡⎣ ⎤⎦

minus φ βrv2rE + βsv

2sE1113872 1113873

(13)

ie πrE(pE vrE) φπscC(pE vsE vrE) and then plowastE plowastCvlowastsE vlowastsC vlowastrE vlowastrC and wlowastE (1 minus φ)plowastC e supplierrsquosprofit function is πsE πscC minus πrE (1 minus φ)πscC

eorem 1 shows that the price discount contract al-locates the supply chain profit to the supplier and theretailer at proportions of 1 minus φ and φ respectively andcoordinates the supply chain e proportion φ is a fixedvalue dependent on the quality visibility cost coefficients ofboth sides Since the quality visibility cost function isnonlinear φ has a unique value in order to ensure alinearly affine transform of the profit functions in a three-parameter contract (w vsφ) According to the contractthe supplier loses his decision autonomy on quality visi-bility which is anchored to that of the retailer via a fixedrate (βrβs) e bigger the rate is the greater the gapbetween the supplier and retailer regarding price qualityvisibility and profit Although the contract does not allowthem to freely negotiate on the profit allocation rate it ischeaper and less tedious under specified conditions due toa reduction of one contract parameter in thedetermination

Proposition 3 Ee incentive compatibility conditions of thecontract (E) are 16λβ2r minus 16λβsβr + α2βs ge 0 for the supplierand (3βs minus βr)Δ

22 + (βs + βr)α4β

2r ge 0 for the retailer when

there is an alternative opportunity profit by a pure wholesaleprice contract

Proof In order to avoid any deviated actions it must satisfyπlowastsE (1 minus φ)πlowastscC ge πlowastsD for the supplier andπlowastrE φπlowastscC ge πlowastrD for the retailer Simplifying them theconditions are given by

φ isin φminφmax1113858 1113859 (14)

where φmax (βs(16λβr minus α2)Δ2) and φmin (βs(16λβr minus

α2)Δ1Δ22)We substitute φ (βs(βs + βr)) into equation (14) and

simplify it to 16λβ2r minus 16λβsβr + α2βs ge 0 for the supplier and(3βs minus βr)Δ22 + (βs + βr)α4β

2r ge 0 for the retailer

e two inequations in Proposition 3 guarantee that theeffort alignment policy is Pareto superior to the decen-tralized decision-making and thus it can strictly coordinatethe supply chain coordination

Mathematical Problems in Engineering 9

43 Effort Cost-Sharing Policy e price discount contractwith an effort alignment policy may not always match thenegotiation power and profit appeal of the two supply chainplayers because it is unable to arbitrarily allocate supplychain profit and whether its rigid incentive compatibilityconditions could be realized with extreme parameters isdoubtful In order to relax these restrictions and thus en-hance companiesrsquo motivations for quality visibility effortcost-sharing is introduced into the price discount contractwhere the supplier and retailer proportionately share thetotal costs of quality visibility

Theorem 2 A price discount contract with cost-sharing (B)

can coordinate the supply chain the retailer pays the suppliera wholesale price wB (1 minus φ)pB and shares the total qualityvisibility cost of the supply chain at a proportion φ (thesupplier shares 1 minus φ and 0ltφlt 1) Een the retailerrsquos profitfunction is πrB φπscC and the supplierrsquos profit function isπsB (1 minus φ)πscC Furthermore wlowastB (1 minus φ)plowastC vlowastsC1113966

plowastC vlowastrC1113967 is the optimal decision set of the supply chain

Proof With cost-sharing the retailerrsquos profit function is

πrB pB vrB1113872 1113873 pB minus wB( 1113857 θ minus λpB + αvscB1113872 1113873 minus φ βrv2rB + βsv

2sB1113872 1113873

(15)

We substitute wB (1 minus φ)pB into it to get πrB(pBvrB)

φπscC(pBvsBvrB) and πsB (1 minus φ)πscC

Compared with contract (E) the feasible range of φunder contract (B) covers the whole interval (0 1) and it isdetermined by the bargaining power of the supplier and theretailere stronger the retailerrsquos power is the greater the φWhen φ equals 0 or 1 the supply chain turns into a cen-tralized one Similarly the incentive compatibility condi-tions (14) must be satisfied when a wholesale price contract isan option In addition the information of both contracts (B)

and (E) need to include the retail price and the retailerrsquosquality visibility level while contract (B) needs to includethe supplierrsquos quality visibility level as well e difference inthe required information sets dominates the applicability ofthe two contracts and the higher information cost ofcontract (B) contributes to the arbitrarily profit allocation tosome extent

5 Practical Case

51 Data Collection We collect data from a practical freshchicken supply chain where a fresh retailer orders to itspartner farm base Fresh chicken is not the dominant meat inthe local market and its demand is elastic e retailersubmits the order plan to the farm base regularly Afterreceiving the plan the farm base slaughters all the plannedchickens and cools them to 0 to 4 degree centigrade inpackages for chilled freshness e fresh retailer is in chargeof the delivery using its own whole-process cold chainsystem from the farm base to all its fresh supermarkets

Consumers can scan the QR traceable code on the package toobtain the quality visibility from the chicken feeding to theshelf reported by the farm base and the fresh supermarketand the completeness and accuracy of the available qualityinformation depend on the visibility systems of the twocompanies Figure 2 shows the quality visibility displayed ona type of packaging for fresh chicken

First we operationalize the supply chain quality visibilityassessment model suggested by Caridi et al [19] We ignorethe mandatory information such as ingredients productdate shelf life and quality certification as shown in Figure 2and focus on the changing quality information linked to QRcode and sale scene instead ie the four information typeslisted at the end of Section 21 except the fifth one Infor-mation quality is rated and quality visibility is calculated in(0 5) e 5 of quality visibility represents that consumerscould get all the quality-related knowledge if they want andthis knowledge has an almost perfect quality e 0 indicatesconsumers hardly get any additional information exceptwhat is on the package

Second the value of each parameter is derived based onthe sales statistics of the fresh retailer during a quarter in2019 When the price remains the same for a few days andthere is a change in the information system we obtain thesensitivity coefficient of the demand to quality visibility andthe potential market demand using linear fitting similarlythe sensitivity coefficient of demand to price is obtainedwhen the information system is constant and the pricefluctuates Two sensitivity coefficients of cost to qualityvisibility are derived by quadratic fitting Historical recordsof several other quarters are used as a reference forcorrection

For simplicity we use the integers close to these pa-rameters for case analysis and the sensitivity analysis inSection 53 proves that a slight parameter deviation does notaffect the validity of the results Finally we have the potentialmarket demand θ 5000 in the quarter the sensitivitycoefficient of demand to price λ 100 the sensitivity co-efficient of demand to quality visibility α 700 the sup-plierrsquos quality visibility cost coefficient βs 1900 and theretailerrsquos quality visibility cost coefficient βr 2500

52 Contract Discussion e optimal decisions and per-formances of the supply chain in different scenarios arepresented in Table 3 In this case it is obvious that the pricediscount contract with effort alignment (E) or cost-sharing(B) coordinates the supply chain to an integrated one Incontrast the total quality visibility and profit of the supplychain in the decentralized supply chain (D) are far lowerthan those in the other scenarios because of severe doublemarginalization It is presumed a higher revenue per unitwith an increased retail price and a lower visibility cost witha decreased visibility effort in (D) however they inhibitconsumersrsquo demand which dominates both companiesrsquoprofit functions erefore there are strong practical in-terests for both the farm base and fresh retailer driving them

10 Mathematical Problems in Engineering

to seek supply chain integration or coordinated decision-making

e outcomes under contract (E) are as good as acentralized supply chain but the contract distributes supplychain profit at a fixed proportion because it requires acorrelation of the visibility efforts between the supplier andthe retailer similar to the pricing It applies to two com-panies of similar size with stable partnership since it doesnot require integrating the visibility systems of the twocompanies leaving them largely independent insteadHowever contract (B) applies to a closer partnership be-cause it requires upstream and downstream firms to inte-grate visibility systems and share effort costs In this sensethe two contracts are in the middle of the vertical integrationspectrum where the decentralized and centralized scenariosare at opposite ends

Further consider that when the profit allocation rate φ isslightly lower than the lower threshold 025 (or slightlyhigher than the upper threshold 055) the fresh retailer (orthe farm base) obtains a slightly smaller profit under con-tract (B) than that under contract (D) It seems that there isno reason for the fresh retailer (or the farm base) to deviatefrom contract (D) in terms of profit but his and hispartnerrsquos quality visibility levels would be significantly im-proved if they used contract (B) Furthermore the reducedretail price and higher supply chain visibility offered by

contract (B) lead to increased food sales and consumerwelfare as well as predictable improvements in businessmanagement and goodwill which to some extent spur thefresh retailer and the farm base to change their minds Weconclude that there is a strong stability with contract (B)ere are some existing practices in which retailers or brandowners ally with suppliers to jointly bear the costs of visi-bility systems As mentioned earlier Walmart is believed toaccept a large part of the RampD costs of the Food TrustPlatform in cooperation with IBM while the leafy-greenssuppliers just pay a service fee of 100sim10000 dollars monthlyaccording to their scales

53 Sensitivity Analysis Figures 3ndash6 show the influence ofprice sensitivity quality visibility sensitivity and visibilitycost coefficients on supply chain performances and contractparameters e shadow in each figure represents the Paretoimprovement space in the decentralized supply chain

It is easy to find that increased quality visibility sensi-tivity leads to a higher price (in Figure 4(a)) higher qualityvisibility (in Figure 4(b)) and greater profit (in Figure 4(c))regardless of the supply chain or the companies in it whilethe other three parameters have the opposite effect (inFigures 3 5 and 6)erefore when the negotiating cost of acoordination contract is too high or the supply chain has

Trademark

Category

Quarantinepassedmark QR code

EAN-13 codeProduction dateand check digit

Contents and ingredientsdiced chicken leg

Storage condition0~4degC

Shelf life7 days

Qualityhighlights

Figure 2 Quality visibility about the fresh chicken on shelf

Table 3 Optimal solution sets in different scenarios

j vlowasts vlowastr vlowastsc wlowast plowast πlowasts πlowastr φ πlowastscC 321 244 283 mdash 3490 mdash mdash mdash 8725202D 144 110 127 2753 4321 3921407 2158991 036 6080398E 321 244 283 1983 3490 4957501 3767701 043 8725202B 321 244 283 2626sim1569 3490 6566211sim3921407 2158991sim4803795 025sim055 8725202

Mathematical Problems in Engineering 11

been coordinated for more profits and quality visibilitythe companies may consider (i) promoting food posi-tioning and acquiring more price-insensitive consumerssuch as by launching ldquoorganic chickenrdquo or minipackagingfor one meal by the farm base and locating in luxurycommunities or office buildings for the fresh retailer (ii)advocating for the traceable and trackable whole-chainquality and safety from farm to table in order to attractconsumers focused on quality visibility and (iii) pur-chasing or renting a more popular cost-effective visibilitysystem and improving the interfaces and compatibility ofvisibility systems

As shown in Figures 4(a)ndash4(c) when consumers paymore attention to quality visibility the companyrsquos visibilityinvestment increases demand which compensates for thedemand reduction caused by price inflation In this respecthigher quality visibility sensitivity rapidly increases theoptimal retail price in the supply chain that is consumersrsquowillingness to pay for a high-quality visibility food In thiscase for a unit increase in quality visibility consumers arewilling to pay an extra 7 CNY (αλ) as the food premium forhigh-quality visibility

e increased quality visibility sensitivity also leads toa broader range of the profit allocation rate (increased

90 100 110 12080λ

20

30

40

50

pCwD

pDwE

(a)

90 100 110 12080λ

1

2

3

4

5

vscCvsCvrC

vscDvsDvrD

(b)

90 100 110 12080λ

120000

100000

80000

60000

40000

20000

πCπsD πscD

πrD

(c)

90 100 110 12080λ

025

030

035

040

045

050

055

φEφminφmax

(d)

Figure 3 e impacts of price sensitivity (a) Prices (b) Quality visibility (c) Profits (d) Allocation rates

12 Mathematical Problems in Engineering

φmax and decreased φmin) from Figure 4(d) while theother three parameters still have the opposite effect andnarrow the range erefore it is easier to realize supplychain coordination with a high visibility sensitivity lowprice sensibility or low-quality visibility cost coefficient

In addition a significant impact of the visibility costcoefficient on the contract (E) is observed in Figures 5(d)and 6(d) e fresh retailer (or the farm base) seizes a largershare of the supply chain profit with its own lower cost

coefficient or a higher cost coefficient of the other partyMoreover a large part of the φE curve is below 05 (byβs βr) which suggests that it is prone to contract (E) whenthe visibility cost coefficient of the fresh retailer is far beyondthat of the farm base according to incentive compatibilityconditions in Section 42 Indeed more and more retailerssource directly from farms and transport using self-builtlogistics to mitigate supply risk and quality risk whichmakes the retailerrsquos visibility cost coefficient often greater

20

30

40

50

600 650 700 750 800 850550α

pCwD

pDwE

(a)

1

2

3

4

5

600 650 700 750 800 850550α

vscCvsCvrC

vscDvsDvrD

(b)

20000

40000

60000

80000

100000

600 650 700 750 800 850550α

πCπsD πscD

πrD

(c)

025

030

035

040

045

050

055

600 650 700 750 800 850550α

φEφminφmax

(d)

Figure 4 e impacts of quality visibility sensitivity (a) Prices (b) Quality visibility (c) Profits (d) Allocation rates

Mathematical Problems in Engineering 13

than the supplierrsquos and thus it is more likely to coordinatethe supply chain with contract (E)

It is also meaningful to examine the sensitivity of eachconstraint condition to each parameter e assumption inProposition 1 is the condition to ensure a profitable supplychain coordination denoting as Cdt1 while the incentivecompatibility conditions in Proposition 3 guarantees thecompaniesrsquo participation denoting as Cdt2 for the supplierand Cdt3 for the retailer respectively We can get the in-terval of each parameter with other parameters fixed (thestrictest condition where the number is derived is in theparentheses) λgt5674(Cdt1) (Cdt1)92932gtαgt0 (Cdt2)

284900gtβsgt81126(Cdt1) (Cdt3)567735gtβrgt90388(Cdt1) e result shows that as long as Cdt1 is met what

stops the company is its own cost coefficient of qualityvisibility erefore it could be the most important thing toreduce the unit cost of visibility efforts and a number ofcompanies good at information systems are working on thatFor example Frigga launches a low-cost real-time and anultra-low-cost USB temperature recorder for cold chainlogistics and both of them are disposable and can be used formore than 90 days (see its website httpswwwfriggatechcom)

Finally from the perspective of the overall supplychain or the regulators it is good for improving qualityvisibility to promote IT innovation upgrade industriesand consumption and create a conducive environmentfor sign a contract

20

30

40

50

1700 1900 2100 23001500βs

pCwD

pDwE

(a)

1

2

3

4

5

1700 1900 2100 23001500βs

vscCvsCvrC

vscDvsDvrD

(b)

1700 1900 2100 23001500βs

20000

40000

60000

80000

100000

πCπsD πscD

πrD

(c)

1700 1900 2100 23001500βs

03

04

05

06

φEφminφmax

(d)

Figure 5 e impacts of the supplierrsquos visibility cost coefficient (a) Prices (b) Quality visibility (c) Profits (d) Allocation rates

14 Mathematical Problems in Engineering

quality quality system audit and continuous improvementTse and Tan [17] believe that product quality (risk) visibilitycomes from the number of product transitions and thedisclosure level of suppliersrsquo information that refers tosuppliersrsquo conformity reliability safety and quality stan-dards For the sake of usefulness to the consumer wesummarize and refine the following types (i) productprovenance (ii) supplier quality about quality details inproduction process (iii) transport conditions (iv) retailerquality about quality details in selling process (v) qualityaudit and certification about third-party or self-certificationof food and companies and (vi) product quality aboutdetails on food labels as regulated en their informationquality ratings are processed to get the supply chain qualityvisibility referring to Caridi et al [19]

22 Supply Chain Quality Visibility Effect Studies about theimpacts of supply chain quality visibility (or supply chainvisibility) on the decisions and performances of supply chaincompanies are relevant Delen et al [21] explore the extent ofthe logistics performance improvement in a supply chaininfluenced by visibility expressed as RFID data and theyassert that the supply chain visibility could make a companydistinctive just as quality was once the differentiator Basedon the theory of organizational information processingWilliams et al [22] verify that internal integration canpositively regulate the relationship between supply chainvisibility (demand supply and market visibility) and supplychain responsiveness Tse and Tan [23] provide qualitycriteria and a multi-outsourcing decision path for focalcompanies in supply chains using a marginal incrementalanalysis (MIA) method Guo [24] discuss the impact ofquality information disclosure on companiesrsquo profits in abilateral monopoly and find that indirect disclosure throughthe retailer is the optimal form of quality informationdisclosure Zhao et al [25] extend Guorsquos research to thecompetitive market and the results indicate that at equi-librium the high-quality supply chain chooses not to dis-close quality while the low-quality one chooses to disclosequality through the retailer Wu et al [26] investigate thequality information-sharing problems in a dual-sourcingsupply chain and demonstrate that quality informationvisibility always benefits the cost-disadvantaged suppliersand the downstream retailer From a ldquonegative qualityrdquoperspective Piramuthu et al [27] compare the marginaldifferences of recall costs at different visibility levels based onthe accuracy of contamination source identification anddetermine the best timing of recall polices in a multistageperishable food supply network

For consumers supply chain quality visibility is good up tonow Granados and Gupta [7] elucidate the benefits of quality-and price-related visibility (transparency) to consumers withdifferent product features industry competition and regulatoryintensity through examples Ghosh andGalbreth [28] find that agreater proportion of partially informed consumers who capturedisclosed quality information can decrease their search be-haviour and help companies save disclosure cost and increaseprofit Both external visibility initiatives (such as proactive

labelling strategies of voluntary certification and ingredientreplacement [29]) and internal visibility initiatives (such asimproving environmentally sustainablemanufacturing [30]) canspur consumers to purchase products El Benni et alrsquos [8] surveystudy indicates that affected by the 2008 melamine incidentChinese consumers are willing to pay an extra CNY 69sim109(equivalent to 30sim40 of the retail price) for a 900 g can ofinfantmilk formula with a PDO label as well as a high premiumfor anticounterfeiting packaging and a QR traceable code

We summarize the related literature in Table 1 esestudies confirm that supply chain quality visibility can bebeneficial to the entire supply chain downstream companiesand consumers while the impact on upstream companies isnot quite clear [7 24 26] It is because that quality visibility inthese studies is provided mainly by suppliers who thus bearquality visibility cost and information leakage risk alone emismatch between these disadvantages and slashed revenueshanded by downstream companies discourages upstreamcompanies and makes outcomes uncertain Furthermore mostof the model research studies focus on the informationstructure transformed by quality information disclosurestrategies also named transparency strategies [18] ey as-sume quality information is always ready to be shared or notignoring the previous processing cost and few of them arespecific to the food supply chain In fact every companycontributes to the supply chain quality visibility and everyoneneeds to pay for it in food supply chains We thus assumecompaniesrsquo respective quality visibility levels that jointly makeup the overall visibility determine their costs and explore theimpacts on supply chain players

23 Supply Chain Coordination Contracts Asymmetric in-formation in a supply chain often traps the upstream anddownstream companies into a double marginalizationwhich can be dramatically mitigated by supply chain co-ordination contracts maximizing supply chain profits[31 32] is field has accumulated extensive literature ispaper involves several relevant streams including supplychain coordination with a revenue-sharing contract or aprice discount contract and coordination policies for thesupply chain with effort decisions

e revenue-sharing contract is one of the most com-mon supply chain coordination mechanisms Cachon andLariviere [33] conduct a comprehensive analysis of it andillustrate its broad applicability with a single retailer indemand or price certaintyuncertainty settings or withcompeting retailers in quantity competition However itstops functioning when the supply chain needs to deal withthe retailerrsquos costly effort Xiao et al [34] examine the im-pacts of product quality and service quality on demand andobtain the optimal decisions and Pareto conditions of thecoordination mechanism using a revenue-sharing contractKong et al [35] discuss the information leakage problemfrom a supplier in a supply chain where the retailerscompete and their results show that a revenue-sharingcontract aligns the motivations of suppliers and retailersbetter and mitigates the supplierrsquos disclosure risk Bernsteinand Federgruen [36] propose a wholesale price contract with

4 Mathematical Problems in Engineering

a buyback rate ie a price discount contract that can co-ordinate the supply chain with uncertain demand which isproven to be equivalent to a revenue-sharing contract in theprice-setting model [33] Cai et al [37] demonstrate that inthe dual-channel supply chain competition the price dis-count contract reduces channel conflict and helps achievecoordination by distributing more profit to the retailer

To coordinate the supply chain with costly effortBhaskaran and Krishnan [38] respectively assess revenueinvestment and innovation sharing policies in an innova-tion supply chain Product innovation revenue only derivesfrom the quality improvement that depends on the inno-vation effort of both the focal company and the partnercompanye results show that although the proposed threemechanisms fail to coordinate the supply chain they im-prove supply chain profits compared with the decentralizedsupply chain when specific conditions are realized Krishnanet al [39] pointed out that a single-parameter contract couldnot correct the distortion caused by the pricing and effortdecisions and they propose effort cost-sharing unilateralmarkdown allowances and constrained buyback mecha-nisms to address it Cachon and Lariviere [33] also offer asimple coordinating quantity discount contract based onrevenue-sharing Lambertini [40] extends the traditionaltwo-part tariff contract for quality improvement using avariable linear tariff according to the RampD effort or productquality For fresh products Cai et al [9] consider the impactof distributorrsquos fresh-keeping effort on product freshnessand thus on product quality and quantity and develop a pricediscount sharing contract with compensation contract tomake the supply chain coordinated Extending Cai et alrsquos [9]study to the online situation Gu et al [41] characterize theonline retailerrsquos strategy of fresh-keeping effort under aconsumer full-refund policy and present a buyback contract

and a revenue- and cost-sharing contract to achieve thecooperative optimization

Table 2 provides an overview of the related literatureomitting the wholesale price contract that cannot coordinatethe supply chain in each row of the last column Most of theeffort-related studies deal with the single effort of thedownstream company and the revenue-sharing contract orprice discount contract works well by extending with anadditional parameter However when there are multipledecision variables linked to the efforts of the upstream anddownstream more than one parameter needs to be intro-duced into simple supply chain contracts [38 40] Fur-thermore there is no model research where the consumerdemand is influenced by quality visibility leaving a missinglink between visibility effort and market revenue In thispaper we consider the demand dependent on supply chainquality visibility and address the coordination problem withdual quality visibility efforts

3 The Basic Model

31 Model Settings We examine a two-tier food supplychain consisting of a supplier and a retailer who faces aconsumer market At the start of a selling season thesupplier sets a wholesale price w and its own quality visibilitylevel vs en the supplier invests in quality visibility as itclaims and begins to produce after receiving the retailerrsquosorder Once the delivery is ready the retailer determines aretail price p and its own quality visibility level vr Subse-quently the retailer invests in quality visibility and sells thefood e consumer observes the price and the overallquality visibility provided by both companies and decides tobuy or not finally making revenue realize e timeline ofevents is outlined in Figure 1

Table 1 Literature related to the effects of supply chain quality visibility

Literature Visibility focused Objectives Methods SC typesDelen et al [21] RFID data Logistical performance Case study Retail

Williams et al [22] Demand supply and marketvisibility Supply chain responsiveness Empirical study Various

including food

Tse and Tan [23] Quality risk visibility Multi-outsourcing decision Marginal incrementalanalysis (MIA) Common

Guo [24] Quality information disclosure Company pricing and profit Mathematical modelling CommonZhao et al [25] Quality information disclosure Company pricing and profit Mathematical modelling Common

Wu et al [26] Quality information sharing ornot Company profit and market share Mathematical modelling Common

Piramuthu et al[27]

Accuracy of contaminationsource identification Liability cost recall timing Mathematical modelling Food

Granados andGupta [7]

Quality price and featurestransparency etc

Buyerrsquos purchase decision businessinformation and IT strategies eoretical development Common

Ghosh andGalbreth [28] Quality information disclosure Consumer search and purchase

company pricing and profit Mathematical modelling Common

Riganelli andMarchini [29] Labelling strategies Consumer demand company

performance Empirical study Food

Buell and Kalkanci[30]

Internal and externaloperational transparency Consumer purchase Field experiment Apparel and

foodEl Benni et al [8] Authenticity cues Consumer choice Survey Food

is paper Supply chain quality visibility Company pricing visibility decisionand SC performance Mathematical modelling Food

Mathematical Problems in Engineering 5

311 Demand Function with Quality VisibilityConsumers are assumed sensitive to food price and supplychain quality visibility d(p vsc) θ minus λp + αvsc where θ isthe largest potential demand λ and α are sensitivity coef-ficients λ αgt 0 and θgt λpgt 0 Refer to the supply chainvisibility assessment method of [19] vsc 1113936ωivi(i s r)where the weight ωi measures the importance of the qualityvisibility provided by company i to consumers We supposeωs ωr (12) indicating equal importance e demandsensitive to quality visibility is reasonable mostly in foodsupply chains where consumers are willing to pay a sig-nificant premium [8]

312 Cost Function with Quality Visibility e visibilityeffort cost of the upstream or downstream company isc(vi) βiv

2i a most widely used effort cost function

[33 38 40] where βi gt 0e square reflects the diseconomy of

visibility systems due to the increased information capacityefficacy requirement and management complexity brought bya higher visibility level [42] e diseconomy occurs in everycompany no matter upstream and downstream characterizingthe food supply chain In contrast except for the focal com-pany quality visibility cost of the partner company is generallyfixed or linear in other types of supply chains For example aquality inspection instruction is usually enough for mobilephone components and the mobile phone retailer rarely needsto invest in quality visibility

e related notations and variables are defined as fol-lows i sc s r are the subscripts that represent the wholesupply chain the supplier and the retailer respectively j

C D R E B are the subscripts that represent scenarios ofcentralized decision-making decentralized decision-mak-ing a revenue-sharing contract a price discount contractwith effort alignment and a price discount contract withcost-sharing respectively

Table 2 Literature related to supply chain coordination contracts

Literature Demand (or other) depends on Main decision variable Contract types (coordination or not)Cachon andLariviere [33] (Inverse demand) quantity Price order quantity Revenue-sharing (Y) buyback (Y) quantity

flexibility (Y) sales rebate (Y) etc

Xiao et al [34] Price product quality servicequality Price service quality Revenue-sharing (Y)

Kong et al [35] (Inverse demand) quantity Price order quantity leakagedecision Revenue-sharing (Y)

Bernstein andFedergruen [36] Price Price order quantity Price discount (Y)

Cai et al [37] Price Price Price discount (Y)Supply chain with costly effortCachon andLariviere [33]

(Inverse demand) quantity retailereffort Retail effort order quantity Revenue-sharing (N) quantity discount

with revenue-sharing (Y)Bhaskaran andKrishnan [38]

(Quality depends on) innovationeffort of focal and partner firms

Innovation level of focal firm andpartner firm

Revenue-sharing (N) investment sharing(N) innovation sharing (N)

Krishnan et al [39] Promotional effort Price order quantity retailerpromotional effort

Buyback (N) buyback with threemechanisms (Y)

Lambertini [40] Price quality Price RampD effort of the upstreamand downstream

Two-part tariff (N) control-linear two-parttariff (Y) state-linear two-part tariff (Y)

Cai et al [9] Price freshness Price order quantity distributorrsquosfresh-keeping effort

Price discount sharing with compensation(Y)

Gu et al [41] Customer returns Price order quantity fresh-keeping effort

Buyback (Y) revenue-sharing (N)revenue- and cost-sharing (Y)

is paper Price SC quality visibility Price quality visibility (effort) ofthe upstream and downstream

Revenue-sharing (N) price discount witheffort alignment (Y) with cost-sharing (Y)

Supplier determineswholesale price and

quality visibility level

Retailer determinesquality visibility level

and retail price

Retailerorders

Supplierproduces

Retailersells

Demandand revenue

realize

Supply chainquality visibility

observed

Figure 1 Timeline of events under consideration

6 Mathematical Problems in Engineering

w is the wholesale price of a food unitp is the retail price of a food unitvi is the food quality visibility provided by the supplychain or company i

d is the market demandθ is the largest potential demandλ is the price sensitivity coefficient of demandα is the quality visibility sensitivity coefficient ofdemandβi is company irsquos cost coefficient of the quality visibilityeffort

In this supply chain setting the supplierrsquos profit is asfollows

πs w θ minus λp + αvsc( 1113857 minus βsv2s (1)

e retailerrsquos profit is given by

πr (p minus w) θ minus λp + αvsc( 1113857 minus βrv2r (2)

and the profit of the whole supply chain is given by

πsc πs + πr p θ minus λp + αvsc( 1113857 minus βsv2s + βrv

2r1113872 1113873 (3)

e channel costs of the supplier and the retailer areomitted however by replacing w and p with w minus cs andp minus cr respectively we have the intact costs where cs is thesupplierrsquos production cost per unit and cr is the retailerrsquosretail cost per unit

32 Centralized Supply Chain e supplier and the retailerare integrated when making decisions in the centralizedsupply chain Although their own visibility systems are alsoexpected to be integrated into one the system integrationcosts and benefits are quite slight compared to the visibilityinput cost namely the effort cost is is partly because theamounts and types of quality metadata collected from theupstream and the downstream are rarely the same and thusthe two parts of the integrated visibility system are regardedas still working separately e profit function of the cen-tralized supply chain is obtained from equation (3)

πscC pC vsC vrC1113872 1113873 pC θ minus λpC +α vsC + vrC1113872 1113873

2⎡⎣ ⎤⎦

minus βsv2sC minus βrv

2rC

(4)

e profit function (4) always has second continuouspartial derivatives In order to avoid not making sense thefunction is assumed to have a maximum value in its defi-nition domain θλgtpC gt 0 and viC gt 0 erefore its Hesse

matrix H

minus 2λ α2 α2α2 minus 2βs 0α2 0 minus 2βr

⎡⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎦ is set to be negative definite

Let Δ1 16λβsβr minus α2βs minus α2βr and then we have Δ1

minus 2|H|gt 0 and 16λβi minus α2 gt 16λβi minus α2 minus α2(βiβj)gt0(i j isin s r and ine j)

Proposition 1 Given the assumption 8λβsβr minus α2βs minus

α2βr gt 0 in the centralized supply chain the optimal retailprice is plowastC (8βsβrθΔ1) and the quality visibility levelsoffered by the supply chain are vlowastsC (2αβrθΔ1)vlowastrC (2αβsθΔ1) and vlowastscC (αθ(βs + βr)Δ1) the supplychain realizes the maximum profit πlowastscC (4βsβrθ

2Δ1)

Proof Solve three first-order conditions of equation (4)jointly as follows

zπscCzpC

minus 2λpC + θ +12α vsC + vrC1113872 1113873 0

zπscCzvsC

minus 2βsvsC +12αpC 0

zπscCzvrC

minus 2βrvrC +12αpC 0

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(5)

e optimal retail price plowastC (8βsβrθΔ1) the optimalquality visibility level of the upstream vlowastsC (2αβrθΔ1) andthe optimal quality visibility level of the downstream vlowastrC

(2αβsθΔ1) can be easily derived en substituting theminto equation (4) and vsc 1113936ωivi simultaneously we havethe optimal supply chain profit vlowastscC (αθ(βs + βr)Δ1) andmaximal supply chain quality visibility πlowastscC (4βsβrθ

2Δ1)in the centralized supply chain

e assumption 8λβsβr minus α2βs minus α2βr gt 0 ensures thatthe optimal price exists in the domain byθ minus λplowastC ((8λβsβr minus α2βs minus α2βr)θΔ1)gt 0 and it is morestrict than the negative definite assumption of Hessematrix

Corollary 1 (zKzλ)lt 0 (zKzα)gt 0 (zKzβs)lt 0 and(zKzβr)lt 0 where K isin plowastC vlowastsC vlowastrC vlowastscC πlowastscC1113966 1113967

From Corollary 1 we can find that the more sensitiveconsumers are to quality visibility the greater the incentivesthat supply chain companies have to improve their qualityvisibility related to the foods in each stage so that the supplychain can charge a higher retail price and gain a biggersupply chain profit Conversely more price-sensitive con-sumers and a greater marginal cost of the visibility systemprevent the previous process

33Decentralized SupplyChain In a decentralized decision-making supply chain the supplier firstly determines its ownquality visibility level and supplies the retailer at a wholesaleprice according to the pure wholesale price contract eretailer then decides its own quality visibility level afterreceiving the delivery and sells foods at a retail price

e profit function of the retailer is given by

πrD pD vrD1113872 1113873 pD minus wD( 1113857 θ minus λpD +α vsD + vrD1113872 1113873

2⎡⎣ ⎤⎦ minus βrv

2rD

(6)

and the profit function of the supplier is as follows

Mathematical Problems in Engineering 7

πsD wD vsD pD vrD1113872 1113873 wD θ minus λpD +α vsD + vrD1113872 1113873

2⎡⎣ ⎤⎦ minus βsv

2sD

(7)

Let Δ2 32λβsβr minus 2α2βs minus α2βr rough the backwardinduction of a Stackelberg game it is easy to find that theHessian matrixes of equations (6) and (7) are negativedefinite with 16λβr minus α2 gt 0 and Δ2 2Δ1 + α2βr gt 0 whichreveals that there exists a maximum solution set of thedecentralized supply chain

Proposition 2 In the decentralized supply chain the optimalwholesale price of the supplier is wlowastD (βsθ(16λβr minus α2)λΔ2) the optimal quality visibility is vlowastsD (2αβrθΔ2) andthe optimal profit is πlowastsD (4βsβrθ

2Δ2) Ee optimal retailprice of the retailer is plowastD (βsθ(24λβr minus α2)λΔ2) the op-timal quality visibility is vlowastrD (2αβsθΔ2) and the optimalprofit is πlowastrD (4β2sβrθ

2(16λβr minus α2)Δ22) Furthermore the

supply chain realizes the optimal quality visibilityvlowastscD (αθ(βs + βr)Δ2) and the optimal profit πlowastscD

(4βsβrθ2(48λβsβr minus 3α2βs minus α2βr)Δ

22)

Proof Given wD and vs the retailerrsquos optimal retail priceand quality visibility are acquired by the first-order con-ditions of equation (6) as follows

plowastD wD vsD1113872 1113873

8βrθ + 8λβrwD + 4αβrvsD minus α2wD

16λβr minus α2

vlowastrD wD vsD1113872 1113873

2αθ + α2vsD minus 2αλwD

16λβr minus α2

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(8)

We substitute them into equation (7)

πsD wD vsD1113872 1113873 4βrλwD αvsD + 2θ minus 2λwD1113872 1113873

16λβr minus α2minus βsv

2sD

(9)

and similarly obtain the supplierrsquos optimal wholesale pricewlowastD and quality visibility vlowastsD by solving the first-orderconditions of equation (9) en it is easy to get plowastD and vlowastrD

by a substitution into equation (8) and thus the optimalperformance variables by a few further substitutions

Corollary 2

(i) πlowastscC minus πlowastscD (4β3sβrθ2(16λβr minus α2)2Δ1Δ2

2)gt 0(ii) πlowastsD minus πlowastrD (4βsβrθ

2Δ1Δ22)gt 0

(iii) vlowastscC minus vlowastscD (αβsθ(16λβr minus α2)(βs + βr)Δ1Δ2)gt 0(iv) plowastC minus plowastD minus ((βsθ(16λβr minus α2)(8λβsβr minus α2βs minus

α2βr))λΔ1Δ2)lt 0

Under the optimal equilibriums by comparing theoverall supply chain profits in the two decision-making

contexts Corollary 2 (i) indicates that the overall profit ofthe decentralized supply chain is strictly less than those ofthe centralized supply chain Since the supply chainrsquos rev-enue completely comes from the retailer to coordinate thesupply chain the optimal solution plowastC vlowastrC1113966 1113967 of integrateddecisions should be optimal for the retailer and it mustsatisfy

zπrD plowastC vlowastrC1113872 1113873

zpD

0

zπrD plowastC vlowastrC1113872 1113873

zvrD

0

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(10)

en we have wD 0 and vsD vlowastsC which mean thatthe supplier receives nothing from charging a productioncost but bears its own quality visibility cost erefore thesimple wholesale price contract cannot coordinate thesupply chain which is consistent with many previous re-searches From Corollary 2 (ii) the supplierrsquos profit is largerthan the retailerrsquos which verifies the supplierrsquos great first-move advantage in the Stackelberg game

In addition Corollary 2 (iii) and (iv) show that theoverall quality visibility level in the decentralized supplychain is lower than that in the centralized one but theformer retail price is higher than the latter It implies that thecentralized supply chain realizes not only greater profit andhigher food quality visibility but also greater consumersurplus which leads to more social welfare thus realizing awin-win between the supply chain and consumers

Corollary 3 (zKzλ)lt 0 (zKzα)gt 0 (zKzβs)lt 0 and(zKzβr)lt 0 where K isin wlowastD plowastD vlowastiD πlowastiD1113966 1113967(i s r sc)

e inspirations from Corollary 3 are similar to thosefrom Corollary 1 ie consumersrsquo sensitivity to qualityvisibility positively influences the prices and performances ofthe decentralized supply chain as opposed to the pricesensitivity and visibility cost coefficients Nevertheless itseems that the extent of the influences they have is lesssignificant than that in the centralized supply chain due tothe double marginalization which will be recognized moreintuitively in the subsequent practical case is findingindicates that a centralized or coordinated food supply chainis more efficient than a decentralized one in performanceimprovement erefore it is necessary to explore a coor-dination contract if there is no chance to integrate this foodsupply chain to a centralized one

4 Supply Chain Coordination

41 Revenue-Sharing Contract e revenue-sharing con-tract is one of the most used coordination contracts Supposethat the supplier and the retailer agree on the following ex-ante revenue-sharing contract the supplier charges a lowerwholesale price wR and receives 1 minus φ(0ltφlt 1) percent of

8 Mathematical Problems in Engineering

the retailerrsquos revenue Assuming φ 1 the contract becomesa pure wholesale price contract and ifwR 0 it is equivalentto a price discount contract with w (1 minus φ)p ereforefor a crisp wholesale price contract and a price discountcontract there is always an equivalent revenue-sharingcontract

e retailerrsquos profit function is given by

πrR pR vrR1113872 1113873 φpR minus wR( 1113857 θ minus λpR +α vsR + vrR1113872 1113873

2⎡⎣ ⎤⎦ minus βrv

2rR

(11)

Similarly by solving the first-order conditions

zπrR plowastC vlowastrC1113872 1113873

zpR

0

zπrR plowastC vlowastrC1113872 1113873

zvrR

0

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(12)

we have wR (φ minus 1)plowastC lt 0 and vsR vlowastsC is means thatif the supply chain is coordinated the supplier needs tosubsidize the retailer (1 minus φ)plowastC for each unit of foodhowever the revenue that the supplier receives from theretailer is equal to the total subsidy Just like in thewholesale price contract the supplier in the revenue-sharing contract does not realize any revenue but experi-ences the losses due to his own quality visibility cost erevenue-sharing contract as Cachon and Lariviere [33]assert cannot coordinate the supply chain with costly effortdecisions

42 Effort Alignment Policy e contracts with a singleparameter could correct the distortion in the pricing deci-sions of the upstream and downstream supply chain butthey do not address the dual-effort and pricing decisionsTwo or more parameters need to be included to align therelevant decision variables making the profit function of thelast-move decision-maker an affine transformation of theprofit function of the whole supply chain In this paper theprofit function of the retailer who plays as the last-moverdepends on the effort decisions that is the quality visibilitydecisions of both the supplier and the retailer Given thateffort can be observed it is feasible to align the supplierrsquoseffort with the retailerrsquos similar to the wholesale pricealigned with the retail price in a pure price discount contract

Theorem 1 Ee following price discount contract with effortalignment (E) can coordinate the supply chain the suppliercharges a wholesale price wE (βr(βs + βr))pE and offersquality visibility vsE (βrβs)vrE Een the retailerrsquos profitfunction is πrE φπscC and the supplierrsquos profit function isπsE (1 minus φ)πscC wlowastE (1 minus φ)plowastC vlowastsC plowastC vlowastrC1113966 1113967 is theoptimal solution set of the supply chain whereφ (βs(βs + βr))

Proof Substitute wE (βr(βs + βr))pE and vsE (βrβs)

vrE into the retailerrsquos profit function (2)

πrE pE vrE1113872 1113873 pE minus (1 minus φ)pE1113858 1113859 θ minus λpE +α vsE + vrE1113872 1113873

2⎡⎣ ⎤⎦

minus βrv2rE middot

φ βs + βr( 1113857

βs

φpE θ minus λpE +α vsE + vrE1113872 1113873

2⎡⎣ ⎤⎦

minus φ βrv2rE + βsv

2sE1113872 1113873

(13)

ie πrE(pE vrE) φπscC(pE vsE vrE) and then plowastE plowastCvlowastsE vlowastsC vlowastrE vlowastrC and wlowastE (1 minus φ)plowastC e supplierrsquosprofit function is πsE πscC minus πrE (1 minus φ)πscC

eorem 1 shows that the price discount contract al-locates the supply chain profit to the supplier and theretailer at proportions of 1 minus φ and φ respectively andcoordinates the supply chain e proportion φ is a fixedvalue dependent on the quality visibility cost coefficients ofboth sides Since the quality visibility cost function isnonlinear φ has a unique value in order to ensure alinearly affine transform of the profit functions in a three-parameter contract (w vsφ) According to the contractthe supplier loses his decision autonomy on quality visi-bility which is anchored to that of the retailer via a fixedrate (βrβs) e bigger the rate is the greater the gapbetween the supplier and retailer regarding price qualityvisibility and profit Although the contract does not allowthem to freely negotiate on the profit allocation rate it ischeaper and less tedious under specified conditions due toa reduction of one contract parameter in thedetermination

Proposition 3 Ee incentive compatibility conditions of thecontract (E) are 16λβ2r minus 16λβsβr + α2βs ge 0 for the supplierand (3βs minus βr)Δ

22 + (βs + βr)α4β

2r ge 0 for the retailer when

there is an alternative opportunity profit by a pure wholesaleprice contract

Proof In order to avoid any deviated actions it must satisfyπlowastsE (1 minus φ)πlowastscC ge πlowastsD for the supplier andπlowastrE φπlowastscC ge πlowastrD for the retailer Simplifying them theconditions are given by

φ isin φminφmax1113858 1113859 (14)

where φmax (βs(16λβr minus α2)Δ2) and φmin (βs(16λβr minus

α2)Δ1Δ22)We substitute φ (βs(βs + βr)) into equation (14) and

simplify it to 16λβ2r minus 16λβsβr + α2βs ge 0 for the supplier and(3βs minus βr)Δ22 + (βs + βr)α4β

2r ge 0 for the retailer

e two inequations in Proposition 3 guarantee that theeffort alignment policy is Pareto superior to the decen-tralized decision-making and thus it can strictly coordinatethe supply chain coordination

Mathematical Problems in Engineering 9

43 Effort Cost-Sharing Policy e price discount contractwith an effort alignment policy may not always match thenegotiation power and profit appeal of the two supply chainplayers because it is unable to arbitrarily allocate supplychain profit and whether its rigid incentive compatibilityconditions could be realized with extreme parameters isdoubtful In order to relax these restrictions and thus en-hance companiesrsquo motivations for quality visibility effortcost-sharing is introduced into the price discount contractwhere the supplier and retailer proportionately share thetotal costs of quality visibility

Theorem 2 A price discount contract with cost-sharing (B)

can coordinate the supply chain the retailer pays the suppliera wholesale price wB (1 minus φ)pB and shares the total qualityvisibility cost of the supply chain at a proportion φ (thesupplier shares 1 minus φ and 0ltφlt 1) Een the retailerrsquos profitfunction is πrB φπscC and the supplierrsquos profit function isπsB (1 minus φ)πscC Furthermore wlowastB (1 minus φ)plowastC vlowastsC1113966

plowastC vlowastrC1113967 is the optimal decision set of the supply chain

Proof With cost-sharing the retailerrsquos profit function is

πrB pB vrB1113872 1113873 pB minus wB( 1113857 θ minus λpB + αvscB1113872 1113873 minus φ βrv2rB + βsv

2sB1113872 1113873

(15)

We substitute wB (1 minus φ)pB into it to get πrB(pBvrB)

φπscC(pBvsBvrB) and πsB (1 minus φ)πscC

Compared with contract (E) the feasible range of φunder contract (B) covers the whole interval (0 1) and it isdetermined by the bargaining power of the supplier and theretailere stronger the retailerrsquos power is the greater the φWhen φ equals 0 or 1 the supply chain turns into a cen-tralized one Similarly the incentive compatibility condi-tions (14) must be satisfied when a wholesale price contract isan option In addition the information of both contracts (B)

and (E) need to include the retail price and the retailerrsquosquality visibility level while contract (B) needs to includethe supplierrsquos quality visibility level as well e difference inthe required information sets dominates the applicability ofthe two contracts and the higher information cost ofcontract (B) contributes to the arbitrarily profit allocation tosome extent

5 Practical Case

51 Data Collection We collect data from a practical freshchicken supply chain where a fresh retailer orders to itspartner farm base Fresh chicken is not the dominant meat inthe local market and its demand is elastic e retailersubmits the order plan to the farm base regularly Afterreceiving the plan the farm base slaughters all the plannedchickens and cools them to 0 to 4 degree centigrade inpackages for chilled freshness e fresh retailer is in chargeof the delivery using its own whole-process cold chainsystem from the farm base to all its fresh supermarkets

Consumers can scan the QR traceable code on the package toobtain the quality visibility from the chicken feeding to theshelf reported by the farm base and the fresh supermarketand the completeness and accuracy of the available qualityinformation depend on the visibility systems of the twocompanies Figure 2 shows the quality visibility displayed ona type of packaging for fresh chicken

First we operationalize the supply chain quality visibilityassessment model suggested by Caridi et al [19] We ignorethe mandatory information such as ingredients productdate shelf life and quality certification as shown in Figure 2and focus on the changing quality information linked to QRcode and sale scene instead ie the four information typeslisted at the end of Section 21 except the fifth one Infor-mation quality is rated and quality visibility is calculated in(0 5) e 5 of quality visibility represents that consumerscould get all the quality-related knowledge if they want andthis knowledge has an almost perfect quality e 0 indicatesconsumers hardly get any additional information exceptwhat is on the package

Second the value of each parameter is derived based onthe sales statistics of the fresh retailer during a quarter in2019 When the price remains the same for a few days andthere is a change in the information system we obtain thesensitivity coefficient of the demand to quality visibility andthe potential market demand using linear fitting similarlythe sensitivity coefficient of demand to price is obtainedwhen the information system is constant and the pricefluctuates Two sensitivity coefficients of cost to qualityvisibility are derived by quadratic fitting Historical recordsof several other quarters are used as a reference forcorrection

For simplicity we use the integers close to these pa-rameters for case analysis and the sensitivity analysis inSection 53 proves that a slight parameter deviation does notaffect the validity of the results Finally we have the potentialmarket demand θ 5000 in the quarter the sensitivitycoefficient of demand to price λ 100 the sensitivity co-efficient of demand to quality visibility α 700 the sup-plierrsquos quality visibility cost coefficient βs 1900 and theretailerrsquos quality visibility cost coefficient βr 2500

52 Contract Discussion e optimal decisions and per-formances of the supply chain in different scenarios arepresented in Table 3 In this case it is obvious that the pricediscount contract with effort alignment (E) or cost-sharing(B) coordinates the supply chain to an integrated one Incontrast the total quality visibility and profit of the supplychain in the decentralized supply chain (D) are far lowerthan those in the other scenarios because of severe doublemarginalization It is presumed a higher revenue per unitwith an increased retail price and a lower visibility cost witha decreased visibility effort in (D) however they inhibitconsumersrsquo demand which dominates both companiesrsquoprofit functions erefore there are strong practical in-terests for both the farm base and fresh retailer driving them

10 Mathematical Problems in Engineering

to seek supply chain integration or coordinated decision-making

e outcomes under contract (E) are as good as acentralized supply chain but the contract distributes supplychain profit at a fixed proportion because it requires acorrelation of the visibility efforts between the supplier andthe retailer similar to the pricing It applies to two com-panies of similar size with stable partnership since it doesnot require integrating the visibility systems of the twocompanies leaving them largely independent insteadHowever contract (B) applies to a closer partnership be-cause it requires upstream and downstream firms to inte-grate visibility systems and share effort costs In this sensethe two contracts are in the middle of the vertical integrationspectrum where the decentralized and centralized scenariosare at opposite ends

Further consider that when the profit allocation rate φ isslightly lower than the lower threshold 025 (or slightlyhigher than the upper threshold 055) the fresh retailer (orthe farm base) obtains a slightly smaller profit under con-tract (B) than that under contract (D) It seems that there isno reason for the fresh retailer (or the farm base) to deviatefrom contract (D) in terms of profit but his and hispartnerrsquos quality visibility levels would be significantly im-proved if they used contract (B) Furthermore the reducedretail price and higher supply chain visibility offered by

contract (B) lead to increased food sales and consumerwelfare as well as predictable improvements in businessmanagement and goodwill which to some extent spur thefresh retailer and the farm base to change their minds Weconclude that there is a strong stability with contract (B)ere are some existing practices in which retailers or brandowners ally with suppliers to jointly bear the costs of visi-bility systems As mentioned earlier Walmart is believed toaccept a large part of the RampD costs of the Food TrustPlatform in cooperation with IBM while the leafy-greenssuppliers just pay a service fee of 100sim10000 dollars monthlyaccording to their scales

53 Sensitivity Analysis Figures 3ndash6 show the influence ofprice sensitivity quality visibility sensitivity and visibilitycost coefficients on supply chain performances and contractparameters e shadow in each figure represents the Paretoimprovement space in the decentralized supply chain

It is easy to find that increased quality visibility sensi-tivity leads to a higher price (in Figure 4(a)) higher qualityvisibility (in Figure 4(b)) and greater profit (in Figure 4(c))regardless of the supply chain or the companies in it whilethe other three parameters have the opposite effect (inFigures 3 5 and 6)erefore when the negotiating cost of acoordination contract is too high or the supply chain has

Trademark

Category

Quarantinepassedmark QR code

EAN-13 codeProduction dateand check digit

Contents and ingredientsdiced chicken leg

Storage condition0~4degC

Shelf life7 days

Qualityhighlights

Figure 2 Quality visibility about the fresh chicken on shelf

Table 3 Optimal solution sets in different scenarios

j vlowasts vlowastr vlowastsc wlowast plowast πlowasts πlowastr φ πlowastscC 321 244 283 mdash 3490 mdash mdash mdash 8725202D 144 110 127 2753 4321 3921407 2158991 036 6080398E 321 244 283 1983 3490 4957501 3767701 043 8725202B 321 244 283 2626sim1569 3490 6566211sim3921407 2158991sim4803795 025sim055 8725202

Mathematical Problems in Engineering 11

been coordinated for more profits and quality visibilitythe companies may consider (i) promoting food posi-tioning and acquiring more price-insensitive consumerssuch as by launching ldquoorganic chickenrdquo or minipackagingfor one meal by the farm base and locating in luxurycommunities or office buildings for the fresh retailer (ii)advocating for the traceable and trackable whole-chainquality and safety from farm to table in order to attractconsumers focused on quality visibility and (iii) pur-chasing or renting a more popular cost-effective visibilitysystem and improving the interfaces and compatibility ofvisibility systems

As shown in Figures 4(a)ndash4(c) when consumers paymore attention to quality visibility the companyrsquos visibilityinvestment increases demand which compensates for thedemand reduction caused by price inflation In this respecthigher quality visibility sensitivity rapidly increases theoptimal retail price in the supply chain that is consumersrsquowillingness to pay for a high-quality visibility food In thiscase for a unit increase in quality visibility consumers arewilling to pay an extra 7 CNY (αλ) as the food premium forhigh-quality visibility

e increased quality visibility sensitivity also leads toa broader range of the profit allocation rate (increased

90 100 110 12080λ

20

30

40

50

pCwD

pDwE

(a)

90 100 110 12080λ

1

2

3

4

5

vscCvsCvrC

vscDvsDvrD

(b)

90 100 110 12080λ

120000

100000

80000

60000

40000

20000

πCπsD πscD

πrD

(c)

90 100 110 12080λ

025

030

035

040

045

050

055

φEφminφmax

(d)

Figure 3 e impacts of price sensitivity (a) Prices (b) Quality visibility (c) Profits (d) Allocation rates

12 Mathematical Problems in Engineering

φmax and decreased φmin) from Figure 4(d) while theother three parameters still have the opposite effect andnarrow the range erefore it is easier to realize supplychain coordination with a high visibility sensitivity lowprice sensibility or low-quality visibility cost coefficient

In addition a significant impact of the visibility costcoefficient on the contract (E) is observed in Figures 5(d)and 6(d) e fresh retailer (or the farm base) seizes a largershare of the supply chain profit with its own lower cost

coefficient or a higher cost coefficient of the other partyMoreover a large part of the φE curve is below 05 (byβs βr) which suggests that it is prone to contract (E) whenthe visibility cost coefficient of the fresh retailer is far beyondthat of the farm base according to incentive compatibilityconditions in Section 42 Indeed more and more retailerssource directly from farms and transport using self-builtlogistics to mitigate supply risk and quality risk whichmakes the retailerrsquos visibility cost coefficient often greater

20

30

40

50

600 650 700 750 800 850550α

pCwD

pDwE

(a)

1

2

3

4

5

600 650 700 750 800 850550α

vscCvsCvrC

vscDvsDvrD

(b)

20000

40000

60000

80000

100000

600 650 700 750 800 850550α

πCπsD πscD

πrD

(c)

025

030

035

040

045

050

055

600 650 700 750 800 850550α

φEφminφmax

(d)

Figure 4 e impacts of quality visibility sensitivity (a) Prices (b) Quality visibility (c) Profits (d) Allocation rates

Mathematical Problems in Engineering 13

than the supplierrsquos and thus it is more likely to coordinatethe supply chain with contract (E)

It is also meaningful to examine the sensitivity of eachconstraint condition to each parameter e assumption inProposition 1 is the condition to ensure a profitable supplychain coordination denoting as Cdt1 while the incentivecompatibility conditions in Proposition 3 guarantees thecompaniesrsquo participation denoting as Cdt2 for the supplierand Cdt3 for the retailer respectively We can get the in-terval of each parameter with other parameters fixed (thestrictest condition where the number is derived is in theparentheses) λgt5674(Cdt1) (Cdt1)92932gtαgt0 (Cdt2)

284900gtβsgt81126(Cdt1) (Cdt3)567735gtβrgt90388(Cdt1) e result shows that as long as Cdt1 is met what

stops the company is its own cost coefficient of qualityvisibility erefore it could be the most important thing toreduce the unit cost of visibility efforts and a number ofcompanies good at information systems are working on thatFor example Frigga launches a low-cost real-time and anultra-low-cost USB temperature recorder for cold chainlogistics and both of them are disposable and can be used formore than 90 days (see its website httpswwwfriggatechcom)

Finally from the perspective of the overall supplychain or the regulators it is good for improving qualityvisibility to promote IT innovation upgrade industriesand consumption and create a conducive environmentfor sign a contract

20

30

40

50

1700 1900 2100 23001500βs

pCwD

pDwE

(a)

1

2

3

4

5

1700 1900 2100 23001500βs

vscCvsCvrC

vscDvsDvrD

(b)

1700 1900 2100 23001500βs

20000

40000

60000

80000

100000

πCπsD πscD

πrD

(c)

1700 1900 2100 23001500βs

03

04

05

06

φEφminφmax

(d)

Figure 5 e impacts of the supplierrsquos visibility cost coefficient (a) Prices (b) Quality visibility (c) Profits (d) Allocation rates

14 Mathematical Problems in Engineering

a buyback rate ie a price discount contract that can co-ordinate the supply chain with uncertain demand which isproven to be equivalent to a revenue-sharing contract in theprice-setting model [33] Cai et al [37] demonstrate that inthe dual-channel supply chain competition the price dis-count contract reduces channel conflict and helps achievecoordination by distributing more profit to the retailer

To coordinate the supply chain with costly effortBhaskaran and Krishnan [38] respectively assess revenueinvestment and innovation sharing policies in an innova-tion supply chain Product innovation revenue only derivesfrom the quality improvement that depends on the inno-vation effort of both the focal company and the partnercompanye results show that although the proposed threemechanisms fail to coordinate the supply chain they im-prove supply chain profits compared with the decentralizedsupply chain when specific conditions are realized Krishnanet al [39] pointed out that a single-parameter contract couldnot correct the distortion caused by the pricing and effortdecisions and they propose effort cost-sharing unilateralmarkdown allowances and constrained buyback mecha-nisms to address it Cachon and Lariviere [33] also offer asimple coordinating quantity discount contract based onrevenue-sharing Lambertini [40] extends the traditionaltwo-part tariff contract for quality improvement using avariable linear tariff according to the RampD effort or productquality For fresh products Cai et al [9] consider the impactof distributorrsquos fresh-keeping effort on product freshnessand thus on product quality and quantity and develop a pricediscount sharing contract with compensation contract tomake the supply chain coordinated Extending Cai et alrsquos [9]study to the online situation Gu et al [41] characterize theonline retailerrsquos strategy of fresh-keeping effort under aconsumer full-refund policy and present a buyback contract

and a revenue- and cost-sharing contract to achieve thecooperative optimization

Table 2 provides an overview of the related literatureomitting the wholesale price contract that cannot coordinatethe supply chain in each row of the last column Most of theeffort-related studies deal with the single effort of thedownstream company and the revenue-sharing contract orprice discount contract works well by extending with anadditional parameter However when there are multipledecision variables linked to the efforts of the upstream anddownstream more than one parameter needs to be intro-duced into simple supply chain contracts [38 40] Fur-thermore there is no model research where the consumerdemand is influenced by quality visibility leaving a missinglink between visibility effort and market revenue In thispaper we consider the demand dependent on supply chainquality visibility and address the coordination problem withdual quality visibility efforts

3 The Basic Model

31 Model Settings We examine a two-tier food supplychain consisting of a supplier and a retailer who faces aconsumer market At the start of a selling season thesupplier sets a wholesale price w and its own quality visibilitylevel vs en the supplier invests in quality visibility as itclaims and begins to produce after receiving the retailerrsquosorder Once the delivery is ready the retailer determines aretail price p and its own quality visibility level vr Subse-quently the retailer invests in quality visibility and sells thefood e consumer observes the price and the overallquality visibility provided by both companies and decides tobuy or not finally making revenue realize e timeline ofevents is outlined in Figure 1

Table 1 Literature related to the effects of supply chain quality visibility

Literature Visibility focused Objectives Methods SC typesDelen et al [21] RFID data Logistical performance Case study Retail

Williams et al [22] Demand supply and marketvisibility Supply chain responsiveness Empirical study Various

including food

Tse and Tan [23] Quality risk visibility Multi-outsourcing decision Marginal incrementalanalysis (MIA) Common

Guo [24] Quality information disclosure Company pricing and profit Mathematical modelling CommonZhao et al [25] Quality information disclosure Company pricing and profit Mathematical modelling Common

Wu et al [26] Quality information sharing ornot Company profit and market share Mathematical modelling Common

Piramuthu et al[27]

Accuracy of contaminationsource identification Liability cost recall timing Mathematical modelling Food

Granados andGupta [7]

Quality price and featurestransparency etc

Buyerrsquos purchase decision businessinformation and IT strategies eoretical development Common

Ghosh andGalbreth [28] Quality information disclosure Consumer search and purchase

company pricing and profit Mathematical modelling Common

Riganelli andMarchini [29] Labelling strategies Consumer demand company

performance Empirical study Food

Buell and Kalkanci[30]

Internal and externaloperational transparency Consumer purchase Field experiment Apparel and

foodEl Benni et al [8] Authenticity cues Consumer choice Survey Food

is paper Supply chain quality visibility Company pricing visibility decisionand SC performance Mathematical modelling Food

Mathematical Problems in Engineering 5

311 Demand Function with Quality VisibilityConsumers are assumed sensitive to food price and supplychain quality visibility d(p vsc) θ minus λp + αvsc where θ isthe largest potential demand λ and α are sensitivity coef-ficients λ αgt 0 and θgt λpgt 0 Refer to the supply chainvisibility assessment method of [19] vsc 1113936ωivi(i s r)where the weight ωi measures the importance of the qualityvisibility provided by company i to consumers We supposeωs ωr (12) indicating equal importance e demandsensitive to quality visibility is reasonable mostly in foodsupply chains where consumers are willing to pay a sig-nificant premium [8]

312 Cost Function with Quality Visibility e visibilityeffort cost of the upstream or downstream company isc(vi) βiv

2i a most widely used effort cost function

[33 38 40] where βi gt 0e square reflects the diseconomy of

visibility systems due to the increased information capacityefficacy requirement and management complexity brought bya higher visibility level [42] e diseconomy occurs in everycompany no matter upstream and downstream characterizingthe food supply chain In contrast except for the focal com-pany quality visibility cost of the partner company is generallyfixed or linear in other types of supply chains For example aquality inspection instruction is usually enough for mobilephone components and the mobile phone retailer rarely needsto invest in quality visibility

e related notations and variables are defined as fol-lows i sc s r are the subscripts that represent the wholesupply chain the supplier and the retailer respectively j

C D R E B are the subscripts that represent scenarios ofcentralized decision-making decentralized decision-mak-ing a revenue-sharing contract a price discount contractwith effort alignment and a price discount contract withcost-sharing respectively

Table 2 Literature related to supply chain coordination contracts

Literature Demand (or other) depends on Main decision variable Contract types (coordination or not)Cachon andLariviere [33] (Inverse demand) quantity Price order quantity Revenue-sharing (Y) buyback (Y) quantity

flexibility (Y) sales rebate (Y) etc

Xiao et al [34] Price product quality servicequality Price service quality Revenue-sharing (Y)

Kong et al [35] (Inverse demand) quantity Price order quantity leakagedecision Revenue-sharing (Y)

Bernstein andFedergruen [36] Price Price order quantity Price discount (Y)

Cai et al [37] Price Price Price discount (Y)Supply chain with costly effortCachon andLariviere [33]

(Inverse demand) quantity retailereffort Retail effort order quantity Revenue-sharing (N) quantity discount

with revenue-sharing (Y)Bhaskaran andKrishnan [38]

(Quality depends on) innovationeffort of focal and partner firms

Innovation level of focal firm andpartner firm

Revenue-sharing (N) investment sharing(N) innovation sharing (N)

Krishnan et al [39] Promotional effort Price order quantity retailerpromotional effort

Buyback (N) buyback with threemechanisms (Y)

Lambertini [40] Price quality Price RampD effort of the upstreamand downstream

Two-part tariff (N) control-linear two-parttariff (Y) state-linear two-part tariff (Y)

Cai et al [9] Price freshness Price order quantity distributorrsquosfresh-keeping effort

Price discount sharing with compensation(Y)

Gu et al [41] Customer returns Price order quantity fresh-keeping effort

Buyback (Y) revenue-sharing (N)revenue- and cost-sharing (Y)

is paper Price SC quality visibility Price quality visibility (effort) ofthe upstream and downstream

Revenue-sharing (N) price discount witheffort alignment (Y) with cost-sharing (Y)

Supplier determineswholesale price and

quality visibility level

Retailer determinesquality visibility level

and retail price

Retailerorders

Supplierproduces

Retailersells

Demandand revenue

realize

Supply chainquality visibility

observed

Figure 1 Timeline of events under consideration

6 Mathematical Problems in Engineering

w is the wholesale price of a food unitp is the retail price of a food unitvi is the food quality visibility provided by the supplychain or company i

d is the market demandθ is the largest potential demandλ is the price sensitivity coefficient of demandα is the quality visibility sensitivity coefficient ofdemandβi is company irsquos cost coefficient of the quality visibilityeffort

In this supply chain setting the supplierrsquos profit is asfollows

πs w θ minus λp + αvsc( 1113857 minus βsv2s (1)

e retailerrsquos profit is given by

πr (p minus w) θ minus λp + αvsc( 1113857 minus βrv2r (2)

and the profit of the whole supply chain is given by

πsc πs + πr p θ minus λp + αvsc( 1113857 minus βsv2s + βrv

2r1113872 1113873 (3)

e channel costs of the supplier and the retailer areomitted however by replacing w and p with w minus cs andp minus cr respectively we have the intact costs where cs is thesupplierrsquos production cost per unit and cr is the retailerrsquosretail cost per unit

32 Centralized Supply Chain e supplier and the retailerare integrated when making decisions in the centralizedsupply chain Although their own visibility systems are alsoexpected to be integrated into one the system integrationcosts and benefits are quite slight compared to the visibilityinput cost namely the effort cost is is partly because theamounts and types of quality metadata collected from theupstream and the downstream are rarely the same and thusthe two parts of the integrated visibility system are regardedas still working separately e profit function of the cen-tralized supply chain is obtained from equation (3)

πscC pC vsC vrC1113872 1113873 pC θ minus λpC +α vsC + vrC1113872 1113873

2⎡⎣ ⎤⎦

minus βsv2sC minus βrv

2rC

(4)

e profit function (4) always has second continuouspartial derivatives In order to avoid not making sense thefunction is assumed to have a maximum value in its defi-nition domain θλgtpC gt 0 and viC gt 0 erefore its Hesse

matrix H

minus 2λ α2 α2α2 minus 2βs 0α2 0 minus 2βr

⎡⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎦ is set to be negative definite

Let Δ1 16λβsβr minus α2βs minus α2βr and then we have Δ1

minus 2|H|gt 0 and 16λβi minus α2 gt 16λβi minus α2 minus α2(βiβj)gt0(i j isin s r and ine j)

Proposition 1 Given the assumption 8λβsβr minus α2βs minus

α2βr gt 0 in the centralized supply chain the optimal retailprice is plowastC (8βsβrθΔ1) and the quality visibility levelsoffered by the supply chain are vlowastsC (2αβrθΔ1)vlowastrC (2αβsθΔ1) and vlowastscC (αθ(βs + βr)Δ1) the supplychain realizes the maximum profit πlowastscC (4βsβrθ

2Δ1)

Proof Solve three first-order conditions of equation (4)jointly as follows

zπscCzpC

minus 2λpC + θ +12α vsC + vrC1113872 1113873 0

zπscCzvsC

minus 2βsvsC +12αpC 0

zπscCzvrC

minus 2βrvrC +12αpC 0

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(5)

e optimal retail price plowastC (8βsβrθΔ1) the optimalquality visibility level of the upstream vlowastsC (2αβrθΔ1) andthe optimal quality visibility level of the downstream vlowastrC

(2αβsθΔ1) can be easily derived en substituting theminto equation (4) and vsc 1113936ωivi simultaneously we havethe optimal supply chain profit vlowastscC (αθ(βs + βr)Δ1) andmaximal supply chain quality visibility πlowastscC (4βsβrθ

2Δ1)in the centralized supply chain

e assumption 8λβsβr minus α2βs minus α2βr gt 0 ensures thatthe optimal price exists in the domain byθ minus λplowastC ((8λβsβr minus α2βs minus α2βr)θΔ1)gt 0 and it is morestrict than the negative definite assumption of Hessematrix

Corollary 1 (zKzλ)lt 0 (zKzα)gt 0 (zKzβs)lt 0 and(zKzβr)lt 0 where K isin plowastC vlowastsC vlowastrC vlowastscC πlowastscC1113966 1113967

From Corollary 1 we can find that the more sensitiveconsumers are to quality visibility the greater the incentivesthat supply chain companies have to improve their qualityvisibility related to the foods in each stage so that the supplychain can charge a higher retail price and gain a biggersupply chain profit Conversely more price-sensitive con-sumers and a greater marginal cost of the visibility systemprevent the previous process

33Decentralized SupplyChain In a decentralized decision-making supply chain the supplier firstly determines its ownquality visibility level and supplies the retailer at a wholesaleprice according to the pure wholesale price contract eretailer then decides its own quality visibility level afterreceiving the delivery and sells foods at a retail price

e profit function of the retailer is given by

πrD pD vrD1113872 1113873 pD minus wD( 1113857 θ minus λpD +α vsD + vrD1113872 1113873

2⎡⎣ ⎤⎦ minus βrv

2rD

(6)

and the profit function of the supplier is as follows

Mathematical Problems in Engineering 7

πsD wD vsD pD vrD1113872 1113873 wD θ minus λpD +α vsD + vrD1113872 1113873

2⎡⎣ ⎤⎦ minus βsv

2sD

(7)

Let Δ2 32λβsβr minus 2α2βs minus α2βr rough the backwardinduction of a Stackelberg game it is easy to find that theHessian matrixes of equations (6) and (7) are negativedefinite with 16λβr minus α2 gt 0 and Δ2 2Δ1 + α2βr gt 0 whichreveals that there exists a maximum solution set of thedecentralized supply chain

Proposition 2 In the decentralized supply chain the optimalwholesale price of the supplier is wlowastD (βsθ(16λβr minus α2)λΔ2) the optimal quality visibility is vlowastsD (2αβrθΔ2) andthe optimal profit is πlowastsD (4βsβrθ

2Δ2) Ee optimal retailprice of the retailer is plowastD (βsθ(24λβr minus α2)λΔ2) the op-timal quality visibility is vlowastrD (2αβsθΔ2) and the optimalprofit is πlowastrD (4β2sβrθ

2(16λβr minus α2)Δ22) Furthermore the

supply chain realizes the optimal quality visibilityvlowastscD (αθ(βs + βr)Δ2) and the optimal profit πlowastscD

(4βsβrθ2(48λβsβr minus 3α2βs minus α2βr)Δ

22)

Proof Given wD and vs the retailerrsquos optimal retail priceand quality visibility are acquired by the first-order con-ditions of equation (6) as follows

plowastD wD vsD1113872 1113873

8βrθ + 8λβrwD + 4αβrvsD minus α2wD

16λβr minus α2

vlowastrD wD vsD1113872 1113873

2αθ + α2vsD minus 2αλwD

16λβr minus α2

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(8)

We substitute them into equation (7)

πsD wD vsD1113872 1113873 4βrλwD αvsD + 2θ minus 2λwD1113872 1113873

16λβr minus α2minus βsv

2sD

(9)

and similarly obtain the supplierrsquos optimal wholesale pricewlowastD and quality visibility vlowastsD by solving the first-orderconditions of equation (9) en it is easy to get plowastD and vlowastrD

by a substitution into equation (8) and thus the optimalperformance variables by a few further substitutions

Corollary 2

(i) πlowastscC minus πlowastscD (4β3sβrθ2(16λβr minus α2)2Δ1Δ2

2)gt 0(ii) πlowastsD minus πlowastrD (4βsβrθ

2Δ1Δ22)gt 0

(iii) vlowastscC minus vlowastscD (αβsθ(16λβr minus α2)(βs + βr)Δ1Δ2)gt 0(iv) plowastC minus plowastD minus ((βsθ(16λβr minus α2)(8λβsβr minus α2βs minus

α2βr))λΔ1Δ2)lt 0

Under the optimal equilibriums by comparing theoverall supply chain profits in the two decision-making

contexts Corollary 2 (i) indicates that the overall profit ofthe decentralized supply chain is strictly less than those ofthe centralized supply chain Since the supply chainrsquos rev-enue completely comes from the retailer to coordinate thesupply chain the optimal solution plowastC vlowastrC1113966 1113967 of integrateddecisions should be optimal for the retailer and it mustsatisfy

zπrD plowastC vlowastrC1113872 1113873

zpD

0

zπrD plowastC vlowastrC1113872 1113873

zvrD

0

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(10)

en we have wD 0 and vsD vlowastsC which mean thatthe supplier receives nothing from charging a productioncost but bears its own quality visibility cost erefore thesimple wholesale price contract cannot coordinate thesupply chain which is consistent with many previous re-searches From Corollary 2 (ii) the supplierrsquos profit is largerthan the retailerrsquos which verifies the supplierrsquos great first-move advantage in the Stackelberg game

In addition Corollary 2 (iii) and (iv) show that theoverall quality visibility level in the decentralized supplychain is lower than that in the centralized one but theformer retail price is higher than the latter It implies that thecentralized supply chain realizes not only greater profit andhigher food quality visibility but also greater consumersurplus which leads to more social welfare thus realizing awin-win between the supply chain and consumers

Corollary 3 (zKzλ)lt 0 (zKzα)gt 0 (zKzβs)lt 0 and(zKzβr)lt 0 where K isin wlowastD plowastD vlowastiD πlowastiD1113966 1113967(i s r sc)

e inspirations from Corollary 3 are similar to thosefrom Corollary 1 ie consumersrsquo sensitivity to qualityvisibility positively influences the prices and performances ofthe decentralized supply chain as opposed to the pricesensitivity and visibility cost coefficients Nevertheless itseems that the extent of the influences they have is lesssignificant than that in the centralized supply chain due tothe double marginalization which will be recognized moreintuitively in the subsequent practical case is findingindicates that a centralized or coordinated food supply chainis more efficient than a decentralized one in performanceimprovement erefore it is necessary to explore a coor-dination contract if there is no chance to integrate this foodsupply chain to a centralized one

4 Supply Chain Coordination

41 Revenue-Sharing Contract e revenue-sharing con-tract is one of the most used coordination contracts Supposethat the supplier and the retailer agree on the following ex-ante revenue-sharing contract the supplier charges a lowerwholesale price wR and receives 1 minus φ(0ltφlt 1) percent of

8 Mathematical Problems in Engineering

the retailerrsquos revenue Assuming φ 1 the contract becomesa pure wholesale price contract and ifwR 0 it is equivalentto a price discount contract with w (1 minus φ)p ereforefor a crisp wholesale price contract and a price discountcontract there is always an equivalent revenue-sharingcontract

e retailerrsquos profit function is given by

πrR pR vrR1113872 1113873 φpR minus wR( 1113857 θ minus λpR +α vsR + vrR1113872 1113873

2⎡⎣ ⎤⎦ minus βrv

2rR

(11)

Similarly by solving the first-order conditions

zπrR plowastC vlowastrC1113872 1113873

zpR

0

zπrR plowastC vlowastrC1113872 1113873

zvrR

0

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(12)

we have wR (φ minus 1)plowastC lt 0 and vsR vlowastsC is means thatif the supply chain is coordinated the supplier needs tosubsidize the retailer (1 minus φ)plowastC for each unit of foodhowever the revenue that the supplier receives from theretailer is equal to the total subsidy Just like in thewholesale price contract the supplier in the revenue-sharing contract does not realize any revenue but experi-ences the losses due to his own quality visibility cost erevenue-sharing contract as Cachon and Lariviere [33]assert cannot coordinate the supply chain with costly effortdecisions

42 Effort Alignment Policy e contracts with a singleparameter could correct the distortion in the pricing deci-sions of the upstream and downstream supply chain butthey do not address the dual-effort and pricing decisionsTwo or more parameters need to be included to align therelevant decision variables making the profit function of thelast-move decision-maker an affine transformation of theprofit function of the whole supply chain In this paper theprofit function of the retailer who plays as the last-moverdepends on the effort decisions that is the quality visibilitydecisions of both the supplier and the retailer Given thateffort can be observed it is feasible to align the supplierrsquoseffort with the retailerrsquos similar to the wholesale pricealigned with the retail price in a pure price discount contract

Theorem 1 Ee following price discount contract with effortalignment (E) can coordinate the supply chain the suppliercharges a wholesale price wE (βr(βs + βr))pE and offersquality visibility vsE (βrβs)vrE Een the retailerrsquos profitfunction is πrE φπscC and the supplierrsquos profit function isπsE (1 minus φ)πscC wlowastE (1 minus φ)plowastC vlowastsC plowastC vlowastrC1113966 1113967 is theoptimal solution set of the supply chain whereφ (βs(βs + βr))

Proof Substitute wE (βr(βs + βr))pE and vsE (βrβs)

vrE into the retailerrsquos profit function (2)

πrE pE vrE1113872 1113873 pE minus (1 minus φ)pE1113858 1113859 θ minus λpE +α vsE + vrE1113872 1113873

2⎡⎣ ⎤⎦

minus βrv2rE middot

φ βs + βr( 1113857

βs

φpE θ minus λpE +α vsE + vrE1113872 1113873

2⎡⎣ ⎤⎦

minus φ βrv2rE + βsv

2sE1113872 1113873

(13)

ie πrE(pE vrE) φπscC(pE vsE vrE) and then plowastE plowastCvlowastsE vlowastsC vlowastrE vlowastrC and wlowastE (1 minus φ)plowastC e supplierrsquosprofit function is πsE πscC minus πrE (1 minus φ)πscC

eorem 1 shows that the price discount contract al-locates the supply chain profit to the supplier and theretailer at proportions of 1 minus φ and φ respectively andcoordinates the supply chain e proportion φ is a fixedvalue dependent on the quality visibility cost coefficients ofboth sides Since the quality visibility cost function isnonlinear φ has a unique value in order to ensure alinearly affine transform of the profit functions in a three-parameter contract (w vsφ) According to the contractthe supplier loses his decision autonomy on quality visi-bility which is anchored to that of the retailer via a fixedrate (βrβs) e bigger the rate is the greater the gapbetween the supplier and retailer regarding price qualityvisibility and profit Although the contract does not allowthem to freely negotiate on the profit allocation rate it ischeaper and less tedious under specified conditions due toa reduction of one contract parameter in thedetermination

Proposition 3 Ee incentive compatibility conditions of thecontract (E) are 16λβ2r minus 16λβsβr + α2βs ge 0 for the supplierand (3βs minus βr)Δ

22 + (βs + βr)α4β

2r ge 0 for the retailer when

there is an alternative opportunity profit by a pure wholesaleprice contract

Proof In order to avoid any deviated actions it must satisfyπlowastsE (1 minus φ)πlowastscC ge πlowastsD for the supplier andπlowastrE φπlowastscC ge πlowastrD for the retailer Simplifying them theconditions are given by

φ isin φminφmax1113858 1113859 (14)

where φmax (βs(16λβr minus α2)Δ2) and φmin (βs(16λβr minus

α2)Δ1Δ22)We substitute φ (βs(βs + βr)) into equation (14) and

simplify it to 16λβ2r minus 16λβsβr + α2βs ge 0 for the supplier and(3βs minus βr)Δ22 + (βs + βr)α4β

2r ge 0 for the retailer

e two inequations in Proposition 3 guarantee that theeffort alignment policy is Pareto superior to the decen-tralized decision-making and thus it can strictly coordinatethe supply chain coordination

Mathematical Problems in Engineering 9

43 Effort Cost-Sharing Policy e price discount contractwith an effort alignment policy may not always match thenegotiation power and profit appeal of the two supply chainplayers because it is unable to arbitrarily allocate supplychain profit and whether its rigid incentive compatibilityconditions could be realized with extreme parameters isdoubtful In order to relax these restrictions and thus en-hance companiesrsquo motivations for quality visibility effortcost-sharing is introduced into the price discount contractwhere the supplier and retailer proportionately share thetotal costs of quality visibility

Theorem 2 A price discount contract with cost-sharing (B)

can coordinate the supply chain the retailer pays the suppliera wholesale price wB (1 minus φ)pB and shares the total qualityvisibility cost of the supply chain at a proportion φ (thesupplier shares 1 minus φ and 0ltφlt 1) Een the retailerrsquos profitfunction is πrB φπscC and the supplierrsquos profit function isπsB (1 minus φ)πscC Furthermore wlowastB (1 minus φ)plowastC vlowastsC1113966

plowastC vlowastrC1113967 is the optimal decision set of the supply chain

Proof With cost-sharing the retailerrsquos profit function is

πrB pB vrB1113872 1113873 pB minus wB( 1113857 θ minus λpB + αvscB1113872 1113873 minus φ βrv2rB + βsv

2sB1113872 1113873

(15)

We substitute wB (1 minus φ)pB into it to get πrB(pBvrB)

φπscC(pBvsBvrB) and πsB (1 minus φ)πscC

Compared with contract (E) the feasible range of φunder contract (B) covers the whole interval (0 1) and it isdetermined by the bargaining power of the supplier and theretailere stronger the retailerrsquos power is the greater the φWhen φ equals 0 or 1 the supply chain turns into a cen-tralized one Similarly the incentive compatibility condi-tions (14) must be satisfied when a wholesale price contract isan option In addition the information of both contracts (B)

and (E) need to include the retail price and the retailerrsquosquality visibility level while contract (B) needs to includethe supplierrsquos quality visibility level as well e difference inthe required information sets dominates the applicability ofthe two contracts and the higher information cost ofcontract (B) contributes to the arbitrarily profit allocation tosome extent

5 Practical Case

51 Data Collection We collect data from a practical freshchicken supply chain where a fresh retailer orders to itspartner farm base Fresh chicken is not the dominant meat inthe local market and its demand is elastic e retailersubmits the order plan to the farm base regularly Afterreceiving the plan the farm base slaughters all the plannedchickens and cools them to 0 to 4 degree centigrade inpackages for chilled freshness e fresh retailer is in chargeof the delivery using its own whole-process cold chainsystem from the farm base to all its fresh supermarkets

Consumers can scan the QR traceable code on the package toobtain the quality visibility from the chicken feeding to theshelf reported by the farm base and the fresh supermarketand the completeness and accuracy of the available qualityinformation depend on the visibility systems of the twocompanies Figure 2 shows the quality visibility displayed ona type of packaging for fresh chicken

First we operationalize the supply chain quality visibilityassessment model suggested by Caridi et al [19] We ignorethe mandatory information such as ingredients productdate shelf life and quality certification as shown in Figure 2and focus on the changing quality information linked to QRcode and sale scene instead ie the four information typeslisted at the end of Section 21 except the fifth one Infor-mation quality is rated and quality visibility is calculated in(0 5) e 5 of quality visibility represents that consumerscould get all the quality-related knowledge if they want andthis knowledge has an almost perfect quality e 0 indicatesconsumers hardly get any additional information exceptwhat is on the package

Second the value of each parameter is derived based onthe sales statistics of the fresh retailer during a quarter in2019 When the price remains the same for a few days andthere is a change in the information system we obtain thesensitivity coefficient of the demand to quality visibility andthe potential market demand using linear fitting similarlythe sensitivity coefficient of demand to price is obtainedwhen the information system is constant and the pricefluctuates Two sensitivity coefficients of cost to qualityvisibility are derived by quadratic fitting Historical recordsof several other quarters are used as a reference forcorrection

For simplicity we use the integers close to these pa-rameters for case analysis and the sensitivity analysis inSection 53 proves that a slight parameter deviation does notaffect the validity of the results Finally we have the potentialmarket demand θ 5000 in the quarter the sensitivitycoefficient of demand to price λ 100 the sensitivity co-efficient of demand to quality visibility α 700 the sup-plierrsquos quality visibility cost coefficient βs 1900 and theretailerrsquos quality visibility cost coefficient βr 2500

52 Contract Discussion e optimal decisions and per-formances of the supply chain in different scenarios arepresented in Table 3 In this case it is obvious that the pricediscount contract with effort alignment (E) or cost-sharing(B) coordinates the supply chain to an integrated one Incontrast the total quality visibility and profit of the supplychain in the decentralized supply chain (D) are far lowerthan those in the other scenarios because of severe doublemarginalization It is presumed a higher revenue per unitwith an increased retail price and a lower visibility cost witha decreased visibility effort in (D) however they inhibitconsumersrsquo demand which dominates both companiesrsquoprofit functions erefore there are strong practical in-terests for both the farm base and fresh retailer driving them

10 Mathematical Problems in Engineering

to seek supply chain integration or coordinated decision-making

e outcomes under contract (E) are as good as acentralized supply chain but the contract distributes supplychain profit at a fixed proportion because it requires acorrelation of the visibility efforts between the supplier andthe retailer similar to the pricing It applies to two com-panies of similar size with stable partnership since it doesnot require integrating the visibility systems of the twocompanies leaving them largely independent insteadHowever contract (B) applies to a closer partnership be-cause it requires upstream and downstream firms to inte-grate visibility systems and share effort costs In this sensethe two contracts are in the middle of the vertical integrationspectrum where the decentralized and centralized scenariosare at opposite ends

Further consider that when the profit allocation rate φ isslightly lower than the lower threshold 025 (or slightlyhigher than the upper threshold 055) the fresh retailer (orthe farm base) obtains a slightly smaller profit under con-tract (B) than that under contract (D) It seems that there isno reason for the fresh retailer (or the farm base) to deviatefrom contract (D) in terms of profit but his and hispartnerrsquos quality visibility levels would be significantly im-proved if they used contract (B) Furthermore the reducedretail price and higher supply chain visibility offered by

contract (B) lead to increased food sales and consumerwelfare as well as predictable improvements in businessmanagement and goodwill which to some extent spur thefresh retailer and the farm base to change their minds Weconclude that there is a strong stability with contract (B)ere are some existing practices in which retailers or brandowners ally with suppliers to jointly bear the costs of visi-bility systems As mentioned earlier Walmart is believed toaccept a large part of the RampD costs of the Food TrustPlatform in cooperation with IBM while the leafy-greenssuppliers just pay a service fee of 100sim10000 dollars monthlyaccording to their scales

53 Sensitivity Analysis Figures 3ndash6 show the influence ofprice sensitivity quality visibility sensitivity and visibilitycost coefficients on supply chain performances and contractparameters e shadow in each figure represents the Paretoimprovement space in the decentralized supply chain

It is easy to find that increased quality visibility sensi-tivity leads to a higher price (in Figure 4(a)) higher qualityvisibility (in Figure 4(b)) and greater profit (in Figure 4(c))regardless of the supply chain or the companies in it whilethe other three parameters have the opposite effect (inFigures 3 5 and 6)erefore when the negotiating cost of acoordination contract is too high or the supply chain has

Trademark

Category

Quarantinepassedmark QR code

EAN-13 codeProduction dateand check digit

Contents and ingredientsdiced chicken leg

Storage condition0~4degC

Shelf life7 days

Qualityhighlights

Figure 2 Quality visibility about the fresh chicken on shelf

Table 3 Optimal solution sets in different scenarios

j vlowasts vlowastr vlowastsc wlowast plowast πlowasts πlowastr φ πlowastscC 321 244 283 mdash 3490 mdash mdash mdash 8725202D 144 110 127 2753 4321 3921407 2158991 036 6080398E 321 244 283 1983 3490 4957501 3767701 043 8725202B 321 244 283 2626sim1569 3490 6566211sim3921407 2158991sim4803795 025sim055 8725202

Mathematical Problems in Engineering 11

been coordinated for more profits and quality visibilitythe companies may consider (i) promoting food posi-tioning and acquiring more price-insensitive consumerssuch as by launching ldquoorganic chickenrdquo or minipackagingfor one meal by the farm base and locating in luxurycommunities or office buildings for the fresh retailer (ii)advocating for the traceable and trackable whole-chainquality and safety from farm to table in order to attractconsumers focused on quality visibility and (iii) pur-chasing or renting a more popular cost-effective visibilitysystem and improving the interfaces and compatibility ofvisibility systems

As shown in Figures 4(a)ndash4(c) when consumers paymore attention to quality visibility the companyrsquos visibilityinvestment increases demand which compensates for thedemand reduction caused by price inflation In this respecthigher quality visibility sensitivity rapidly increases theoptimal retail price in the supply chain that is consumersrsquowillingness to pay for a high-quality visibility food In thiscase for a unit increase in quality visibility consumers arewilling to pay an extra 7 CNY (αλ) as the food premium forhigh-quality visibility

e increased quality visibility sensitivity also leads toa broader range of the profit allocation rate (increased

90 100 110 12080λ

20

30

40

50

pCwD

pDwE

(a)

90 100 110 12080λ

1

2

3

4

5

vscCvsCvrC

vscDvsDvrD

(b)

90 100 110 12080λ

120000

100000

80000

60000

40000

20000

πCπsD πscD

πrD

(c)

90 100 110 12080λ

025

030

035

040

045

050

055

φEφminφmax

(d)

Figure 3 e impacts of price sensitivity (a) Prices (b) Quality visibility (c) Profits (d) Allocation rates

12 Mathematical Problems in Engineering

φmax and decreased φmin) from Figure 4(d) while theother three parameters still have the opposite effect andnarrow the range erefore it is easier to realize supplychain coordination with a high visibility sensitivity lowprice sensibility or low-quality visibility cost coefficient

In addition a significant impact of the visibility costcoefficient on the contract (E) is observed in Figures 5(d)and 6(d) e fresh retailer (or the farm base) seizes a largershare of the supply chain profit with its own lower cost

coefficient or a higher cost coefficient of the other partyMoreover a large part of the φE curve is below 05 (byβs βr) which suggests that it is prone to contract (E) whenthe visibility cost coefficient of the fresh retailer is far beyondthat of the farm base according to incentive compatibilityconditions in Section 42 Indeed more and more retailerssource directly from farms and transport using self-builtlogistics to mitigate supply risk and quality risk whichmakes the retailerrsquos visibility cost coefficient often greater

20

30

40

50

600 650 700 750 800 850550α

pCwD

pDwE

(a)

1

2

3

4

5

600 650 700 750 800 850550α

vscCvsCvrC

vscDvsDvrD

(b)

20000

40000

60000

80000

100000

600 650 700 750 800 850550α

πCπsD πscD

πrD

(c)

025

030

035

040

045

050

055

600 650 700 750 800 850550α

φEφminφmax

(d)

Figure 4 e impacts of quality visibility sensitivity (a) Prices (b) Quality visibility (c) Profits (d) Allocation rates

Mathematical Problems in Engineering 13

than the supplierrsquos and thus it is more likely to coordinatethe supply chain with contract (E)

It is also meaningful to examine the sensitivity of eachconstraint condition to each parameter e assumption inProposition 1 is the condition to ensure a profitable supplychain coordination denoting as Cdt1 while the incentivecompatibility conditions in Proposition 3 guarantees thecompaniesrsquo participation denoting as Cdt2 for the supplierand Cdt3 for the retailer respectively We can get the in-terval of each parameter with other parameters fixed (thestrictest condition where the number is derived is in theparentheses) λgt5674(Cdt1) (Cdt1)92932gtαgt0 (Cdt2)

284900gtβsgt81126(Cdt1) (Cdt3)567735gtβrgt90388(Cdt1) e result shows that as long as Cdt1 is met what

stops the company is its own cost coefficient of qualityvisibility erefore it could be the most important thing toreduce the unit cost of visibility efforts and a number ofcompanies good at information systems are working on thatFor example Frigga launches a low-cost real-time and anultra-low-cost USB temperature recorder for cold chainlogistics and both of them are disposable and can be used formore than 90 days (see its website httpswwwfriggatechcom)

Finally from the perspective of the overall supplychain or the regulators it is good for improving qualityvisibility to promote IT innovation upgrade industriesand consumption and create a conducive environmentfor sign a contract

20

30

40

50

1700 1900 2100 23001500βs

pCwD

pDwE

(a)

1

2

3

4

5

1700 1900 2100 23001500βs

vscCvsCvrC

vscDvsDvrD

(b)

1700 1900 2100 23001500βs

20000

40000

60000

80000

100000

πCπsD πscD

πrD

(c)

1700 1900 2100 23001500βs

03

04

05

06

φEφminφmax

(d)

Figure 5 e impacts of the supplierrsquos visibility cost coefficient (a) Prices (b) Quality visibility (c) Profits (d) Allocation rates

14 Mathematical Problems in Engineering

311 Demand Function with Quality VisibilityConsumers are assumed sensitive to food price and supplychain quality visibility d(p vsc) θ minus λp + αvsc where θ isthe largest potential demand λ and α are sensitivity coef-ficients λ αgt 0 and θgt λpgt 0 Refer to the supply chainvisibility assessment method of [19] vsc 1113936ωivi(i s r)where the weight ωi measures the importance of the qualityvisibility provided by company i to consumers We supposeωs ωr (12) indicating equal importance e demandsensitive to quality visibility is reasonable mostly in foodsupply chains where consumers are willing to pay a sig-nificant premium [8]

312 Cost Function with Quality Visibility e visibilityeffort cost of the upstream or downstream company isc(vi) βiv

2i a most widely used effort cost function

[33 38 40] where βi gt 0e square reflects the diseconomy of

visibility systems due to the increased information capacityefficacy requirement and management complexity brought bya higher visibility level [42] e diseconomy occurs in everycompany no matter upstream and downstream characterizingthe food supply chain In contrast except for the focal com-pany quality visibility cost of the partner company is generallyfixed or linear in other types of supply chains For example aquality inspection instruction is usually enough for mobilephone components and the mobile phone retailer rarely needsto invest in quality visibility

e related notations and variables are defined as fol-lows i sc s r are the subscripts that represent the wholesupply chain the supplier and the retailer respectively j

C D R E B are the subscripts that represent scenarios ofcentralized decision-making decentralized decision-mak-ing a revenue-sharing contract a price discount contractwith effort alignment and a price discount contract withcost-sharing respectively

Table 2 Literature related to supply chain coordination contracts

Literature Demand (or other) depends on Main decision variable Contract types (coordination or not)Cachon andLariviere [33] (Inverse demand) quantity Price order quantity Revenue-sharing (Y) buyback (Y) quantity

flexibility (Y) sales rebate (Y) etc

Xiao et al [34] Price product quality servicequality Price service quality Revenue-sharing (Y)

Kong et al [35] (Inverse demand) quantity Price order quantity leakagedecision Revenue-sharing (Y)

Bernstein andFedergruen [36] Price Price order quantity Price discount (Y)

Cai et al [37] Price Price Price discount (Y)Supply chain with costly effortCachon andLariviere [33]

(Inverse demand) quantity retailereffort Retail effort order quantity Revenue-sharing (N) quantity discount

with revenue-sharing (Y)Bhaskaran andKrishnan [38]

(Quality depends on) innovationeffort of focal and partner firms

Innovation level of focal firm andpartner firm

Revenue-sharing (N) investment sharing(N) innovation sharing (N)

Krishnan et al [39] Promotional effort Price order quantity retailerpromotional effort

Buyback (N) buyback with threemechanisms (Y)

Lambertini [40] Price quality Price RampD effort of the upstreamand downstream

Two-part tariff (N) control-linear two-parttariff (Y) state-linear two-part tariff (Y)

Cai et al [9] Price freshness Price order quantity distributorrsquosfresh-keeping effort

Price discount sharing with compensation(Y)

Gu et al [41] Customer returns Price order quantity fresh-keeping effort

Buyback (Y) revenue-sharing (N)revenue- and cost-sharing (Y)

is paper Price SC quality visibility Price quality visibility (effort) ofthe upstream and downstream

Revenue-sharing (N) price discount witheffort alignment (Y) with cost-sharing (Y)

Supplier determineswholesale price and

quality visibility level

Retailer determinesquality visibility level

and retail price

Retailerorders

Supplierproduces

Retailersells

Demandand revenue

realize

Supply chainquality visibility

observed

Figure 1 Timeline of events under consideration

6 Mathematical Problems in Engineering

w is the wholesale price of a food unitp is the retail price of a food unitvi is the food quality visibility provided by the supplychain or company i

d is the market demandθ is the largest potential demandλ is the price sensitivity coefficient of demandα is the quality visibility sensitivity coefficient ofdemandβi is company irsquos cost coefficient of the quality visibilityeffort

In this supply chain setting the supplierrsquos profit is asfollows

πs w θ minus λp + αvsc( 1113857 minus βsv2s (1)

e retailerrsquos profit is given by

πr (p minus w) θ minus λp + αvsc( 1113857 minus βrv2r (2)

and the profit of the whole supply chain is given by

πsc πs + πr p θ minus λp + αvsc( 1113857 minus βsv2s + βrv

2r1113872 1113873 (3)

e channel costs of the supplier and the retailer areomitted however by replacing w and p with w minus cs andp minus cr respectively we have the intact costs where cs is thesupplierrsquos production cost per unit and cr is the retailerrsquosretail cost per unit

32 Centralized Supply Chain e supplier and the retailerare integrated when making decisions in the centralizedsupply chain Although their own visibility systems are alsoexpected to be integrated into one the system integrationcosts and benefits are quite slight compared to the visibilityinput cost namely the effort cost is is partly because theamounts and types of quality metadata collected from theupstream and the downstream are rarely the same and thusthe two parts of the integrated visibility system are regardedas still working separately e profit function of the cen-tralized supply chain is obtained from equation (3)

πscC pC vsC vrC1113872 1113873 pC θ minus λpC +α vsC + vrC1113872 1113873

2⎡⎣ ⎤⎦

minus βsv2sC minus βrv

2rC

(4)

e profit function (4) always has second continuouspartial derivatives In order to avoid not making sense thefunction is assumed to have a maximum value in its defi-nition domain θλgtpC gt 0 and viC gt 0 erefore its Hesse

matrix H

minus 2λ α2 α2α2 minus 2βs 0α2 0 minus 2βr

⎡⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎦ is set to be negative definite

Let Δ1 16λβsβr minus α2βs minus α2βr and then we have Δ1

minus 2|H|gt 0 and 16λβi minus α2 gt 16λβi minus α2 minus α2(βiβj)gt0(i j isin s r and ine j)

Proposition 1 Given the assumption 8λβsβr minus α2βs minus

α2βr gt 0 in the centralized supply chain the optimal retailprice is plowastC (8βsβrθΔ1) and the quality visibility levelsoffered by the supply chain are vlowastsC (2αβrθΔ1)vlowastrC (2αβsθΔ1) and vlowastscC (αθ(βs + βr)Δ1) the supplychain realizes the maximum profit πlowastscC (4βsβrθ

2Δ1)

Proof Solve three first-order conditions of equation (4)jointly as follows

zπscCzpC

minus 2λpC + θ +12α vsC + vrC1113872 1113873 0

zπscCzvsC

minus 2βsvsC +12αpC 0

zπscCzvrC

minus 2βrvrC +12αpC 0

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(5)

e optimal retail price plowastC (8βsβrθΔ1) the optimalquality visibility level of the upstream vlowastsC (2αβrθΔ1) andthe optimal quality visibility level of the downstream vlowastrC

(2αβsθΔ1) can be easily derived en substituting theminto equation (4) and vsc 1113936ωivi simultaneously we havethe optimal supply chain profit vlowastscC (αθ(βs + βr)Δ1) andmaximal supply chain quality visibility πlowastscC (4βsβrθ

2Δ1)in the centralized supply chain

e assumption 8λβsβr minus α2βs minus α2βr gt 0 ensures thatthe optimal price exists in the domain byθ minus λplowastC ((8λβsβr minus α2βs minus α2βr)θΔ1)gt 0 and it is morestrict than the negative definite assumption of Hessematrix

Corollary 1 (zKzλ)lt 0 (zKzα)gt 0 (zKzβs)lt 0 and(zKzβr)lt 0 where K isin plowastC vlowastsC vlowastrC vlowastscC πlowastscC1113966 1113967

From Corollary 1 we can find that the more sensitiveconsumers are to quality visibility the greater the incentivesthat supply chain companies have to improve their qualityvisibility related to the foods in each stage so that the supplychain can charge a higher retail price and gain a biggersupply chain profit Conversely more price-sensitive con-sumers and a greater marginal cost of the visibility systemprevent the previous process

33Decentralized SupplyChain In a decentralized decision-making supply chain the supplier firstly determines its ownquality visibility level and supplies the retailer at a wholesaleprice according to the pure wholesale price contract eretailer then decides its own quality visibility level afterreceiving the delivery and sells foods at a retail price

e profit function of the retailer is given by

πrD pD vrD1113872 1113873 pD minus wD( 1113857 θ minus λpD +α vsD + vrD1113872 1113873

2⎡⎣ ⎤⎦ minus βrv

2rD

(6)

and the profit function of the supplier is as follows

Mathematical Problems in Engineering 7

πsD wD vsD pD vrD1113872 1113873 wD θ minus λpD +α vsD + vrD1113872 1113873

2⎡⎣ ⎤⎦ minus βsv

2sD

(7)

Let Δ2 32λβsβr minus 2α2βs minus α2βr rough the backwardinduction of a Stackelberg game it is easy to find that theHessian matrixes of equations (6) and (7) are negativedefinite with 16λβr minus α2 gt 0 and Δ2 2Δ1 + α2βr gt 0 whichreveals that there exists a maximum solution set of thedecentralized supply chain

Proposition 2 In the decentralized supply chain the optimalwholesale price of the supplier is wlowastD (βsθ(16λβr minus α2)λΔ2) the optimal quality visibility is vlowastsD (2αβrθΔ2) andthe optimal profit is πlowastsD (4βsβrθ

2Δ2) Ee optimal retailprice of the retailer is plowastD (βsθ(24λβr minus α2)λΔ2) the op-timal quality visibility is vlowastrD (2αβsθΔ2) and the optimalprofit is πlowastrD (4β2sβrθ

2(16λβr minus α2)Δ22) Furthermore the

supply chain realizes the optimal quality visibilityvlowastscD (αθ(βs + βr)Δ2) and the optimal profit πlowastscD

(4βsβrθ2(48λβsβr minus 3α2βs minus α2βr)Δ

22)

Proof Given wD and vs the retailerrsquos optimal retail priceand quality visibility are acquired by the first-order con-ditions of equation (6) as follows

plowastD wD vsD1113872 1113873

8βrθ + 8λβrwD + 4αβrvsD minus α2wD

16λβr minus α2

vlowastrD wD vsD1113872 1113873

2αθ + α2vsD minus 2αλwD

16λβr minus α2

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(8)

We substitute them into equation (7)

πsD wD vsD1113872 1113873 4βrλwD αvsD + 2θ minus 2λwD1113872 1113873

16λβr minus α2minus βsv

2sD

(9)

and similarly obtain the supplierrsquos optimal wholesale pricewlowastD and quality visibility vlowastsD by solving the first-orderconditions of equation (9) en it is easy to get plowastD and vlowastrD

by a substitution into equation (8) and thus the optimalperformance variables by a few further substitutions

Corollary 2

(i) πlowastscC minus πlowastscD (4β3sβrθ2(16λβr minus α2)2Δ1Δ2

2)gt 0(ii) πlowastsD minus πlowastrD (4βsβrθ

2Δ1Δ22)gt 0

(iii) vlowastscC minus vlowastscD (αβsθ(16λβr minus α2)(βs + βr)Δ1Δ2)gt 0(iv) plowastC minus plowastD minus ((βsθ(16λβr minus α2)(8λβsβr minus α2βs minus

α2βr))λΔ1Δ2)lt 0

Under the optimal equilibriums by comparing theoverall supply chain profits in the two decision-making

contexts Corollary 2 (i) indicates that the overall profit ofthe decentralized supply chain is strictly less than those ofthe centralized supply chain Since the supply chainrsquos rev-enue completely comes from the retailer to coordinate thesupply chain the optimal solution plowastC vlowastrC1113966 1113967 of integrateddecisions should be optimal for the retailer and it mustsatisfy

zπrD plowastC vlowastrC1113872 1113873

zpD

0

zπrD plowastC vlowastrC1113872 1113873

zvrD

0

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(10)

en we have wD 0 and vsD vlowastsC which mean thatthe supplier receives nothing from charging a productioncost but bears its own quality visibility cost erefore thesimple wholesale price contract cannot coordinate thesupply chain which is consistent with many previous re-searches From Corollary 2 (ii) the supplierrsquos profit is largerthan the retailerrsquos which verifies the supplierrsquos great first-move advantage in the Stackelberg game

In addition Corollary 2 (iii) and (iv) show that theoverall quality visibility level in the decentralized supplychain is lower than that in the centralized one but theformer retail price is higher than the latter It implies that thecentralized supply chain realizes not only greater profit andhigher food quality visibility but also greater consumersurplus which leads to more social welfare thus realizing awin-win between the supply chain and consumers

Corollary 3 (zKzλ)lt 0 (zKzα)gt 0 (zKzβs)lt 0 and(zKzβr)lt 0 where K isin wlowastD plowastD vlowastiD πlowastiD1113966 1113967(i s r sc)

e inspirations from Corollary 3 are similar to thosefrom Corollary 1 ie consumersrsquo sensitivity to qualityvisibility positively influences the prices and performances ofthe decentralized supply chain as opposed to the pricesensitivity and visibility cost coefficients Nevertheless itseems that the extent of the influences they have is lesssignificant than that in the centralized supply chain due tothe double marginalization which will be recognized moreintuitively in the subsequent practical case is findingindicates that a centralized or coordinated food supply chainis more efficient than a decentralized one in performanceimprovement erefore it is necessary to explore a coor-dination contract if there is no chance to integrate this foodsupply chain to a centralized one

4 Supply Chain Coordination

41 Revenue-Sharing Contract e revenue-sharing con-tract is one of the most used coordination contracts Supposethat the supplier and the retailer agree on the following ex-ante revenue-sharing contract the supplier charges a lowerwholesale price wR and receives 1 minus φ(0ltφlt 1) percent of

8 Mathematical Problems in Engineering

the retailerrsquos revenue Assuming φ 1 the contract becomesa pure wholesale price contract and ifwR 0 it is equivalentto a price discount contract with w (1 minus φ)p ereforefor a crisp wholesale price contract and a price discountcontract there is always an equivalent revenue-sharingcontract

e retailerrsquos profit function is given by

πrR pR vrR1113872 1113873 φpR minus wR( 1113857 θ minus λpR +α vsR + vrR1113872 1113873

2⎡⎣ ⎤⎦ minus βrv

2rR

(11)

Similarly by solving the first-order conditions

zπrR plowastC vlowastrC1113872 1113873

zpR

0

zπrR plowastC vlowastrC1113872 1113873

zvrR

0

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(12)

we have wR (φ minus 1)plowastC lt 0 and vsR vlowastsC is means thatif the supply chain is coordinated the supplier needs tosubsidize the retailer (1 minus φ)plowastC for each unit of foodhowever the revenue that the supplier receives from theretailer is equal to the total subsidy Just like in thewholesale price contract the supplier in the revenue-sharing contract does not realize any revenue but experi-ences the losses due to his own quality visibility cost erevenue-sharing contract as Cachon and Lariviere [33]assert cannot coordinate the supply chain with costly effortdecisions

42 Effort Alignment Policy e contracts with a singleparameter could correct the distortion in the pricing deci-sions of the upstream and downstream supply chain butthey do not address the dual-effort and pricing decisionsTwo or more parameters need to be included to align therelevant decision variables making the profit function of thelast-move decision-maker an affine transformation of theprofit function of the whole supply chain In this paper theprofit function of the retailer who plays as the last-moverdepends on the effort decisions that is the quality visibilitydecisions of both the supplier and the retailer Given thateffort can be observed it is feasible to align the supplierrsquoseffort with the retailerrsquos similar to the wholesale pricealigned with the retail price in a pure price discount contract

Theorem 1 Ee following price discount contract with effortalignment (E) can coordinate the supply chain the suppliercharges a wholesale price wE (βr(βs + βr))pE and offersquality visibility vsE (βrβs)vrE Een the retailerrsquos profitfunction is πrE φπscC and the supplierrsquos profit function isπsE (1 minus φ)πscC wlowastE (1 minus φ)plowastC vlowastsC plowastC vlowastrC1113966 1113967 is theoptimal solution set of the supply chain whereφ (βs(βs + βr))

Proof Substitute wE (βr(βs + βr))pE and vsE (βrβs)

vrE into the retailerrsquos profit function (2)

πrE pE vrE1113872 1113873 pE minus (1 minus φ)pE1113858 1113859 θ minus λpE +α vsE + vrE1113872 1113873

2⎡⎣ ⎤⎦

minus βrv2rE middot

φ βs + βr( 1113857

βs

φpE θ minus λpE +α vsE + vrE1113872 1113873

2⎡⎣ ⎤⎦

minus φ βrv2rE + βsv

2sE1113872 1113873

(13)

ie πrE(pE vrE) φπscC(pE vsE vrE) and then plowastE plowastCvlowastsE vlowastsC vlowastrE vlowastrC and wlowastE (1 minus φ)plowastC e supplierrsquosprofit function is πsE πscC minus πrE (1 minus φ)πscC

eorem 1 shows that the price discount contract al-locates the supply chain profit to the supplier and theretailer at proportions of 1 minus φ and φ respectively andcoordinates the supply chain e proportion φ is a fixedvalue dependent on the quality visibility cost coefficients ofboth sides Since the quality visibility cost function isnonlinear φ has a unique value in order to ensure alinearly affine transform of the profit functions in a three-parameter contract (w vsφ) According to the contractthe supplier loses his decision autonomy on quality visi-bility which is anchored to that of the retailer via a fixedrate (βrβs) e bigger the rate is the greater the gapbetween the supplier and retailer regarding price qualityvisibility and profit Although the contract does not allowthem to freely negotiate on the profit allocation rate it ischeaper and less tedious under specified conditions due toa reduction of one contract parameter in thedetermination

Proposition 3 Ee incentive compatibility conditions of thecontract (E) are 16λβ2r minus 16λβsβr + α2βs ge 0 for the supplierand (3βs minus βr)Δ

22 + (βs + βr)α4β

2r ge 0 for the retailer when

there is an alternative opportunity profit by a pure wholesaleprice contract

Proof In order to avoid any deviated actions it must satisfyπlowastsE (1 minus φ)πlowastscC ge πlowastsD for the supplier andπlowastrE φπlowastscC ge πlowastrD for the retailer Simplifying them theconditions are given by

φ isin φminφmax1113858 1113859 (14)

where φmax (βs(16λβr minus α2)Δ2) and φmin (βs(16λβr minus

α2)Δ1Δ22)We substitute φ (βs(βs + βr)) into equation (14) and

simplify it to 16λβ2r minus 16λβsβr + α2βs ge 0 for the supplier and(3βs minus βr)Δ22 + (βs + βr)α4β

2r ge 0 for the retailer

e two inequations in Proposition 3 guarantee that theeffort alignment policy is Pareto superior to the decen-tralized decision-making and thus it can strictly coordinatethe supply chain coordination

Mathematical Problems in Engineering 9

43 Effort Cost-Sharing Policy e price discount contractwith an effort alignment policy may not always match thenegotiation power and profit appeal of the two supply chainplayers because it is unable to arbitrarily allocate supplychain profit and whether its rigid incentive compatibilityconditions could be realized with extreme parameters isdoubtful In order to relax these restrictions and thus en-hance companiesrsquo motivations for quality visibility effortcost-sharing is introduced into the price discount contractwhere the supplier and retailer proportionately share thetotal costs of quality visibility

Theorem 2 A price discount contract with cost-sharing (B)

can coordinate the supply chain the retailer pays the suppliera wholesale price wB (1 minus φ)pB and shares the total qualityvisibility cost of the supply chain at a proportion φ (thesupplier shares 1 minus φ and 0ltφlt 1) Een the retailerrsquos profitfunction is πrB φπscC and the supplierrsquos profit function isπsB (1 minus φ)πscC Furthermore wlowastB (1 minus φ)plowastC vlowastsC1113966

plowastC vlowastrC1113967 is the optimal decision set of the supply chain

Proof With cost-sharing the retailerrsquos profit function is

πrB pB vrB1113872 1113873 pB minus wB( 1113857 θ minus λpB + αvscB1113872 1113873 minus φ βrv2rB + βsv

2sB1113872 1113873

(15)

We substitute wB (1 minus φ)pB into it to get πrB(pBvrB)

φπscC(pBvsBvrB) and πsB (1 minus φ)πscC

Compared with contract (E) the feasible range of φunder contract (B) covers the whole interval (0 1) and it isdetermined by the bargaining power of the supplier and theretailere stronger the retailerrsquos power is the greater the φWhen φ equals 0 or 1 the supply chain turns into a cen-tralized one Similarly the incentive compatibility condi-tions (14) must be satisfied when a wholesale price contract isan option In addition the information of both contracts (B)

and (E) need to include the retail price and the retailerrsquosquality visibility level while contract (B) needs to includethe supplierrsquos quality visibility level as well e difference inthe required information sets dominates the applicability ofthe two contracts and the higher information cost ofcontract (B) contributes to the arbitrarily profit allocation tosome extent

5 Practical Case

51 Data Collection We collect data from a practical freshchicken supply chain where a fresh retailer orders to itspartner farm base Fresh chicken is not the dominant meat inthe local market and its demand is elastic e retailersubmits the order plan to the farm base regularly Afterreceiving the plan the farm base slaughters all the plannedchickens and cools them to 0 to 4 degree centigrade inpackages for chilled freshness e fresh retailer is in chargeof the delivery using its own whole-process cold chainsystem from the farm base to all its fresh supermarkets

Consumers can scan the QR traceable code on the package toobtain the quality visibility from the chicken feeding to theshelf reported by the farm base and the fresh supermarketand the completeness and accuracy of the available qualityinformation depend on the visibility systems of the twocompanies Figure 2 shows the quality visibility displayed ona type of packaging for fresh chicken

First we operationalize the supply chain quality visibilityassessment model suggested by Caridi et al [19] We ignorethe mandatory information such as ingredients productdate shelf life and quality certification as shown in Figure 2and focus on the changing quality information linked to QRcode and sale scene instead ie the four information typeslisted at the end of Section 21 except the fifth one Infor-mation quality is rated and quality visibility is calculated in(0 5) e 5 of quality visibility represents that consumerscould get all the quality-related knowledge if they want andthis knowledge has an almost perfect quality e 0 indicatesconsumers hardly get any additional information exceptwhat is on the package

Second the value of each parameter is derived based onthe sales statistics of the fresh retailer during a quarter in2019 When the price remains the same for a few days andthere is a change in the information system we obtain thesensitivity coefficient of the demand to quality visibility andthe potential market demand using linear fitting similarlythe sensitivity coefficient of demand to price is obtainedwhen the information system is constant and the pricefluctuates Two sensitivity coefficients of cost to qualityvisibility are derived by quadratic fitting Historical recordsof several other quarters are used as a reference forcorrection

For simplicity we use the integers close to these pa-rameters for case analysis and the sensitivity analysis inSection 53 proves that a slight parameter deviation does notaffect the validity of the results Finally we have the potentialmarket demand θ 5000 in the quarter the sensitivitycoefficient of demand to price λ 100 the sensitivity co-efficient of demand to quality visibility α 700 the sup-plierrsquos quality visibility cost coefficient βs 1900 and theretailerrsquos quality visibility cost coefficient βr 2500

52 Contract Discussion e optimal decisions and per-formances of the supply chain in different scenarios arepresented in Table 3 In this case it is obvious that the pricediscount contract with effort alignment (E) or cost-sharing(B) coordinates the supply chain to an integrated one Incontrast the total quality visibility and profit of the supplychain in the decentralized supply chain (D) are far lowerthan those in the other scenarios because of severe doublemarginalization It is presumed a higher revenue per unitwith an increased retail price and a lower visibility cost witha decreased visibility effort in (D) however they inhibitconsumersrsquo demand which dominates both companiesrsquoprofit functions erefore there are strong practical in-terests for both the farm base and fresh retailer driving them

10 Mathematical Problems in Engineering

to seek supply chain integration or coordinated decision-making

e outcomes under contract (E) are as good as acentralized supply chain but the contract distributes supplychain profit at a fixed proportion because it requires acorrelation of the visibility efforts between the supplier andthe retailer similar to the pricing It applies to two com-panies of similar size with stable partnership since it doesnot require integrating the visibility systems of the twocompanies leaving them largely independent insteadHowever contract (B) applies to a closer partnership be-cause it requires upstream and downstream firms to inte-grate visibility systems and share effort costs In this sensethe two contracts are in the middle of the vertical integrationspectrum where the decentralized and centralized scenariosare at opposite ends

Further consider that when the profit allocation rate φ isslightly lower than the lower threshold 025 (or slightlyhigher than the upper threshold 055) the fresh retailer (orthe farm base) obtains a slightly smaller profit under con-tract (B) than that under contract (D) It seems that there isno reason for the fresh retailer (or the farm base) to deviatefrom contract (D) in terms of profit but his and hispartnerrsquos quality visibility levels would be significantly im-proved if they used contract (B) Furthermore the reducedretail price and higher supply chain visibility offered by

contract (B) lead to increased food sales and consumerwelfare as well as predictable improvements in businessmanagement and goodwill which to some extent spur thefresh retailer and the farm base to change their minds Weconclude that there is a strong stability with contract (B)ere are some existing practices in which retailers or brandowners ally with suppliers to jointly bear the costs of visi-bility systems As mentioned earlier Walmart is believed toaccept a large part of the RampD costs of the Food TrustPlatform in cooperation with IBM while the leafy-greenssuppliers just pay a service fee of 100sim10000 dollars monthlyaccording to their scales

53 Sensitivity Analysis Figures 3ndash6 show the influence ofprice sensitivity quality visibility sensitivity and visibilitycost coefficients on supply chain performances and contractparameters e shadow in each figure represents the Paretoimprovement space in the decentralized supply chain

It is easy to find that increased quality visibility sensi-tivity leads to a higher price (in Figure 4(a)) higher qualityvisibility (in Figure 4(b)) and greater profit (in Figure 4(c))regardless of the supply chain or the companies in it whilethe other three parameters have the opposite effect (inFigures 3 5 and 6)erefore when the negotiating cost of acoordination contract is too high or the supply chain has

Trademark

Category

Quarantinepassedmark QR code

EAN-13 codeProduction dateand check digit

Contents and ingredientsdiced chicken leg

Storage condition0~4degC

Shelf life7 days

Qualityhighlights

Figure 2 Quality visibility about the fresh chicken on shelf

Table 3 Optimal solution sets in different scenarios

j vlowasts vlowastr vlowastsc wlowast plowast πlowasts πlowastr φ πlowastscC 321 244 283 mdash 3490 mdash mdash mdash 8725202D 144 110 127 2753 4321 3921407 2158991 036 6080398E 321 244 283 1983 3490 4957501 3767701 043 8725202B 321 244 283 2626sim1569 3490 6566211sim3921407 2158991sim4803795 025sim055 8725202

Mathematical Problems in Engineering 11

been coordinated for more profits and quality visibilitythe companies may consider (i) promoting food posi-tioning and acquiring more price-insensitive consumerssuch as by launching ldquoorganic chickenrdquo or minipackagingfor one meal by the farm base and locating in luxurycommunities or office buildings for the fresh retailer (ii)advocating for the traceable and trackable whole-chainquality and safety from farm to table in order to attractconsumers focused on quality visibility and (iii) pur-chasing or renting a more popular cost-effective visibilitysystem and improving the interfaces and compatibility ofvisibility systems

As shown in Figures 4(a)ndash4(c) when consumers paymore attention to quality visibility the companyrsquos visibilityinvestment increases demand which compensates for thedemand reduction caused by price inflation In this respecthigher quality visibility sensitivity rapidly increases theoptimal retail price in the supply chain that is consumersrsquowillingness to pay for a high-quality visibility food In thiscase for a unit increase in quality visibility consumers arewilling to pay an extra 7 CNY (αλ) as the food premium forhigh-quality visibility

e increased quality visibility sensitivity also leads toa broader range of the profit allocation rate (increased

90 100 110 12080λ

20

30

40

50

pCwD

pDwE

(a)

90 100 110 12080λ

1

2

3

4

5

vscCvsCvrC

vscDvsDvrD

(b)

90 100 110 12080λ

120000

100000

80000

60000

40000

20000

πCπsD πscD

πrD

(c)

90 100 110 12080λ

025

030

035

040

045

050

055

φEφminφmax

(d)

Figure 3 e impacts of price sensitivity (a) Prices (b) Quality visibility (c) Profits (d) Allocation rates

12 Mathematical Problems in Engineering

φmax and decreased φmin) from Figure 4(d) while theother three parameters still have the opposite effect andnarrow the range erefore it is easier to realize supplychain coordination with a high visibility sensitivity lowprice sensibility or low-quality visibility cost coefficient

In addition a significant impact of the visibility costcoefficient on the contract (E) is observed in Figures 5(d)and 6(d) e fresh retailer (or the farm base) seizes a largershare of the supply chain profit with its own lower cost

coefficient or a higher cost coefficient of the other partyMoreover a large part of the φE curve is below 05 (byβs βr) which suggests that it is prone to contract (E) whenthe visibility cost coefficient of the fresh retailer is far beyondthat of the farm base according to incentive compatibilityconditions in Section 42 Indeed more and more retailerssource directly from farms and transport using self-builtlogistics to mitigate supply risk and quality risk whichmakes the retailerrsquos visibility cost coefficient often greater

20

30

40

50

600 650 700 750 800 850550α

pCwD

pDwE

(a)

1

2

3

4

5

600 650 700 750 800 850550α

vscCvsCvrC

vscDvsDvrD

(b)

20000

40000

60000

80000

100000

600 650 700 750 800 850550α

πCπsD πscD

πrD

(c)

025

030

035

040

045

050

055

600 650 700 750 800 850550α

φEφminφmax

(d)

Figure 4 e impacts of quality visibility sensitivity (a) Prices (b) Quality visibility (c) Profits (d) Allocation rates

Mathematical Problems in Engineering 13

than the supplierrsquos and thus it is more likely to coordinatethe supply chain with contract (E)

It is also meaningful to examine the sensitivity of eachconstraint condition to each parameter e assumption inProposition 1 is the condition to ensure a profitable supplychain coordination denoting as Cdt1 while the incentivecompatibility conditions in Proposition 3 guarantees thecompaniesrsquo participation denoting as Cdt2 for the supplierand Cdt3 for the retailer respectively We can get the in-terval of each parameter with other parameters fixed (thestrictest condition where the number is derived is in theparentheses) λgt5674(Cdt1) (Cdt1)92932gtαgt0 (Cdt2)

284900gtβsgt81126(Cdt1) (Cdt3)567735gtβrgt90388(Cdt1) e result shows that as long as Cdt1 is met what

stops the company is its own cost coefficient of qualityvisibility erefore it could be the most important thing toreduce the unit cost of visibility efforts and a number ofcompanies good at information systems are working on thatFor example Frigga launches a low-cost real-time and anultra-low-cost USB temperature recorder for cold chainlogistics and both of them are disposable and can be used formore than 90 days (see its website httpswwwfriggatechcom)

Finally from the perspective of the overall supplychain or the regulators it is good for improving qualityvisibility to promote IT innovation upgrade industriesand consumption and create a conducive environmentfor sign a contract

20

30

40

50

1700 1900 2100 23001500βs

pCwD

pDwE

(a)

1

2

3

4

5

1700 1900 2100 23001500βs

vscCvsCvrC

vscDvsDvrD

(b)

1700 1900 2100 23001500βs

20000

40000

60000

80000

100000

πCπsD πscD

πrD

(c)

1700 1900 2100 23001500βs

03

04

05

06

φEφminφmax

(d)

Figure 5 e impacts of the supplierrsquos visibility cost coefficient (a) Prices (b) Quality visibility (c) Profits (d) Allocation rates

14 Mathematical Problems in Engineering

w is the wholesale price of a food unitp is the retail price of a food unitvi is the food quality visibility provided by the supplychain or company i

d is the market demandθ is the largest potential demandλ is the price sensitivity coefficient of demandα is the quality visibility sensitivity coefficient ofdemandβi is company irsquos cost coefficient of the quality visibilityeffort

In this supply chain setting the supplierrsquos profit is asfollows

πs w θ minus λp + αvsc( 1113857 minus βsv2s (1)

e retailerrsquos profit is given by

πr (p minus w) θ minus λp + αvsc( 1113857 minus βrv2r (2)

and the profit of the whole supply chain is given by

πsc πs + πr p θ minus λp + αvsc( 1113857 minus βsv2s + βrv

2r1113872 1113873 (3)

e channel costs of the supplier and the retailer areomitted however by replacing w and p with w minus cs andp minus cr respectively we have the intact costs where cs is thesupplierrsquos production cost per unit and cr is the retailerrsquosretail cost per unit

32 Centralized Supply Chain e supplier and the retailerare integrated when making decisions in the centralizedsupply chain Although their own visibility systems are alsoexpected to be integrated into one the system integrationcosts and benefits are quite slight compared to the visibilityinput cost namely the effort cost is is partly because theamounts and types of quality metadata collected from theupstream and the downstream are rarely the same and thusthe two parts of the integrated visibility system are regardedas still working separately e profit function of the cen-tralized supply chain is obtained from equation (3)

πscC pC vsC vrC1113872 1113873 pC θ minus λpC +α vsC + vrC1113872 1113873

2⎡⎣ ⎤⎦

minus βsv2sC minus βrv

2rC

(4)

e profit function (4) always has second continuouspartial derivatives In order to avoid not making sense thefunction is assumed to have a maximum value in its defi-nition domain θλgtpC gt 0 and viC gt 0 erefore its Hesse

matrix H

minus 2λ α2 α2α2 minus 2βs 0α2 0 minus 2βr

⎡⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎦ is set to be negative definite

Let Δ1 16λβsβr minus α2βs minus α2βr and then we have Δ1

minus 2|H|gt 0 and 16λβi minus α2 gt 16λβi minus α2 minus α2(βiβj)gt0(i j isin s r and ine j)

Proposition 1 Given the assumption 8λβsβr minus α2βs minus

α2βr gt 0 in the centralized supply chain the optimal retailprice is plowastC (8βsβrθΔ1) and the quality visibility levelsoffered by the supply chain are vlowastsC (2αβrθΔ1)vlowastrC (2αβsθΔ1) and vlowastscC (αθ(βs + βr)Δ1) the supplychain realizes the maximum profit πlowastscC (4βsβrθ

2Δ1)

Proof Solve three first-order conditions of equation (4)jointly as follows

zπscCzpC

minus 2λpC + θ +12α vsC + vrC1113872 1113873 0

zπscCzvsC

minus 2βsvsC +12αpC 0

zπscCzvrC

minus 2βrvrC +12αpC 0

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(5)

e optimal retail price plowastC (8βsβrθΔ1) the optimalquality visibility level of the upstream vlowastsC (2αβrθΔ1) andthe optimal quality visibility level of the downstream vlowastrC

(2αβsθΔ1) can be easily derived en substituting theminto equation (4) and vsc 1113936ωivi simultaneously we havethe optimal supply chain profit vlowastscC (αθ(βs + βr)Δ1) andmaximal supply chain quality visibility πlowastscC (4βsβrθ

2Δ1)in the centralized supply chain

e assumption 8λβsβr minus α2βs minus α2βr gt 0 ensures thatthe optimal price exists in the domain byθ minus λplowastC ((8λβsβr minus α2βs minus α2βr)θΔ1)gt 0 and it is morestrict than the negative definite assumption of Hessematrix

Corollary 1 (zKzλ)lt 0 (zKzα)gt 0 (zKzβs)lt 0 and(zKzβr)lt 0 where K isin plowastC vlowastsC vlowastrC vlowastscC πlowastscC1113966 1113967

From Corollary 1 we can find that the more sensitiveconsumers are to quality visibility the greater the incentivesthat supply chain companies have to improve their qualityvisibility related to the foods in each stage so that the supplychain can charge a higher retail price and gain a biggersupply chain profit Conversely more price-sensitive con-sumers and a greater marginal cost of the visibility systemprevent the previous process

33Decentralized SupplyChain In a decentralized decision-making supply chain the supplier firstly determines its ownquality visibility level and supplies the retailer at a wholesaleprice according to the pure wholesale price contract eretailer then decides its own quality visibility level afterreceiving the delivery and sells foods at a retail price

e profit function of the retailer is given by

πrD pD vrD1113872 1113873 pD minus wD( 1113857 θ minus λpD +α vsD + vrD1113872 1113873

2⎡⎣ ⎤⎦ minus βrv

2rD

(6)

and the profit function of the supplier is as follows

Mathematical Problems in Engineering 7

πsD wD vsD pD vrD1113872 1113873 wD θ minus λpD +α vsD + vrD1113872 1113873

2⎡⎣ ⎤⎦ minus βsv

2sD

(7)

Let Δ2 32λβsβr minus 2α2βs minus α2βr rough the backwardinduction of a Stackelberg game it is easy to find that theHessian matrixes of equations (6) and (7) are negativedefinite with 16λβr minus α2 gt 0 and Δ2 2Δ1 + α2βr gt 0 whichreveals that there exists a maximum solution set of thedecentralized supply chain

Proposition 2 In the decentralized supply chain the optimalwholesale price of the supplier is wlowastD (βsθ(16λβr minus α2)λΔ2) the optimal quality visibility is vlowastsD (2αβrθΔ2) andthe optimal profit is πlowastsD (4βsβrθ

2Δ2) Ee optimal retailprice of the retailer is plowastD (βsθ(24λβr minus α2)λΔ2) the op-timal quality visibility is vlowastrD (2αβsθΔ2) and the optimalprofit is πlowastrD (4β2sβrθ

2(16λβr minus α2)Δ22) Furthermore the

supply chain realizes the optimal quality visibilityvlowastscD (αθ(βs + βr)Δ2) and the optimal profit πlowastscD

(4βsβrθ2(48λβsβr minus 3α2βs minus α2βr)Δ

22)

Proof Given wD and vs the retailerrsquos optimal retail priceand quality visibility are acquired by the first-order con-ditions of equation (6) as follows

plowastD wD vsD1113872 1113873

8βrθ + 8λβrwD + 4αβrvsD minus α2wD

16λβr minus α2

vlowastrD wD vsD1113872 1113873

2αθ + α2vsD minus 2αλwD

16λβr minus α2

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(8)

We substitute them into equation (7)

πsD wD vsD1113872 1113873 4βrλwD αvsD + 2θ minus 2λwD1113872 1113873

16λβr minus α2minus βsv

2sD

(9)

and similarly obtain the supplierrsquos optimal wholesale pricewlowastD and quality visibility vlowastsD by solving the first-orderconditions of equation (9) en it is easy to get plowastD and vlowastrD

by a substitution into equation (8) and thus the optimalperformance variables by a few further substitutions

Corollary 2

(i) πlowastscC minus πlowastscD (4β3sβrθ2(16λβr minus α2)2Δ1Δ2

2)gt 0(ii) πlowastsD minus πlowastrD (4βsβrθ

2Δ1Δ22)gt 0

(iii) vlowastscC minus vlowastscD (αβsθ(16λβr minus α2)(βs + βr)Δ1Δ2)gt 0(iv) plowastC minus plowastD minus ((βsθ(16λβr minus α2)(8λβsβr minus α2βs minus

α2βr))λΔ1Δ2)lt 0

Under the optimal equilibriums by comparing theoverall supply chain profits in the two decision-making

contexts Corollary 2 (i) indicates that the overall profit ofthe decentralized supply chain is strictly less than those ofthe centralized supply chain Since the supply chainrsquos rev-enue completely comes from the retailer to coordinate thesupply chain the optimal solution plowastC vlowastrC1113966 1113967 of integrateddecisions should be optimal for the retailer and it mustsatisfy

zπrD plowastC vlowastrC1113872 1113873

zpD

0

zπrD plowastC vlowastrC1113872 1113873

zvrD

0

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(10)

en we have wD 0 and vsD vlowastsC which mean thatthe supplier receives nothing from charging a productioncost but bears its own quality visibility cost erefore thesimple wholesale price contract cannot coordinate thesupply chain which is consistent with many previous re-searches From Corollary 2 (ii) the supplierrsquos profit is largerthan the retailerrsquos which verifies the supplierrsquos great first-move advantage in the Stackelberg game

In addition Corollary 2 (iii) and (iv) show that theoverall quality visibility level in the decentralized supplychain is lower than that in the centralized one but theformer retail price is higher than the latter It implies that thecentralized supply chain realizes not only greater profit andhigher food quality visibility but also greater consumersurplus which leads to more social welfare thus realizing awin-win between the supply chain and consumers

Corollary 3 (zKzλ)lt 0 (zKzα)gt 0 (zKzβs)lt 0 and(zKzβr)lt 0 where K isin wlowastD plowastD vlowastiD πlowastiD1113966 1113967(i s r sc)

e inspirations from Corollary 3 are similar to thosefrom Corollary 1 ie consumersrsquo sensitivity to qualityvisibility positively influences the prices and performances ofthe decentralized supply chain as opposed to the pricesensitivity and visibility cost coefficients Nevertheless itseems that the extent of the influences they have is lesssignificant than that in the centralized supply chain due tothe double marginalization which will be recognized moreintuitively in the subsequent practical case is findingindicates that a centralized or coordinated food supply chainis more efficient than a decentralized one in performanceimprovement erefore it is necessary to explore a coor-dination contract if there is no chance to integrate this foodsupply chain to a centralized one

4 Supply Chain Coordination

41 Revenue-Sharing Contract e revenue-sharing con-tract is one of the most used coordination contracts Supposethat the supplier and the retailer agree on the following ex-ante revenue-sharing contract the supplier charges a lowerwholesale price wR and receives 1 minus φ(0ltφlt 1) percent of

8 Mathematical Problems in Engineering

the retailerrsquos revenue Assuming φ 1 the contract becomesa pure wholesale price contract and ifwR 0 it is equivalentto a price discount contract with w (1 minus φ)p ereforefor a crisp wholesale price contract and a price discountcontract there is always an equivalent revenue-sharingcontract

e retailerrsquos profit function is given by

πrR pR vrR1113872 1113873 φpR minus wR( 1113857 θ minus λpR +α vsR + vrR1113872 1113873

2⎡⎣ ⎤⎦ minus βrv

2rR

(11)

Similarly by solving the first-order conditions

zπrR plowastC vlowastrC1113872 1113873

zpR

0

zπrR plowastC vlowastrC1113872 1113873

zvrR

0

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(12)

we have wR (φ minus 1)plowastC lt 0 and vsR vlowastsC is means thatif the supply chain is coordinated the supplier needs tosubsidize the retailer (1 minus φ)plowastC for each unit of foodhowever the revenue that the supplier receives from theretailer is equal to the total subsidy Just like in thewholesale price contract the supplier in the revenue-sharing contract does not realize any revenue but experi-ences the losses due to his own quality visibility cost erevenue-sharing contract as Cachon and Lariviere [33]assert cannot coordinate the supply chain with costly effortdecisions

42 Effort Alignment Policy e contracts with a singleparameter could correct the distortion in the pricing deci-sions of the upstream and downstream supply chain butthey do not address the dual-effort and pricing decisionsTwo or more parameters need to be included to align therelevant decision variables making the profit function of thelast-move decision-maker an affine transformation of theprofit function of the whole supply chain In this paper theprofit function of the retailer who plays as the last-moverdepends on the effort decisions that is the quality visibilitydecisions of both the supplier and the retailer Given thateffort can be observed it is feasible to align the supplierrsquoseffort with the retailerrsquos similar to the wholesale pricealigned with the retail price in a pure price discount contract

Theorem 1 Ee following price discount contract with effortalignment (E) can coordinate the supply chain the suppliercharges a wholesale price wE (βr(βs + βr))pE and offersquality visibility vsE (βrβs)vrE Een the retailerrsquos profitfunction is πrE φπscC and the supplierrsquos profit function isπsE (1 minus φ)πscC wlowastE (1 minus φ)plowastC vlowastsC plowastC vlowastrC1113966 1113967 is theoptimal solution set of the supply chain whereφ (βs(βs + βr))

Proof Substitute wE (βr(βs + βr))pE and vsE (βrβs)

vrE into the retailerrsquos profit function (2)

πrE pE vrE1113872 1113873 pE minus (1 minus φ)pE1113858 1113859 θ minus λpE +α vsE + vrE1113872 1113873

2⎡⎣ ⎤⎦

minus βrv2rE middot

φ βs + βr( 1113857

βs

φpE θ minus λpE +α vsE + vrE1113872 1113873

2⎡⎣ ⎤⎦

minus φ βrv2rE + βsv

2sE1113872 1113873

(13)

ie πrE(pE vrE) φπscC(pE vsE vrE) and then plowastE plowastCvlowastsE vlowastsC vlowastrE vlowastrC and wlowastE (1 minus φ)plowastC e supplierrsquosprofit function is πsE πscC minus πrE (1 minus φ)πscC

eorem 1 shows that the price discount contract al-locates the supply chain profit to the supplier and theretailer at proportions of 1 minus φ and φ respectively andcoordinates the supply chain e proportion φ is a fixedvalue dependent on the quality visibility cost coefficients ofboth sides Since the quality visibility cost function isnonlinear φ has a unique value in order to ensure alinearly affine transform of the profit functions in a three-parameter contract (w vsφ) According to the contractthe supplier loses his decision autonomy on quality visi-bility which is anchored to that of the retailer via a fixedrate (βrβs) e bigger the rate is the greater the gapbetween the supplier and retailer regarding price qualityvisibility and profit Although the contract does not allowthem to freely negotiate on the profit allocation rate it ischeaper and less tedious under specified conditions due toa reduction of one contract parameter in thedetermination

Proposition 3 Ee incentive compatibility conditions of thecontract (E) are 16λβ2r minus 16λβsβr + α2βs ge 0 for the supplierand (3βs minus βr)Δ

22 + (βs + βr)α4β

2r ge 0 for the retailer when

there is an alternative opportunity profit by a pure wholesaleprice contract

Proof In order to avoid any deviated actions it must satisfyπlowastsE (1 minus φ)πlowastscC ge πlowastsD for the supplier andπlowastrE φπlowastscC ge πlowastrD for the retailer Simplifying them theconditions are given by

φ isin φminφmax1113858 1113859 (14)

where φmax (βs(16λβr minus α2)Δ2) and φmin (βs(16λβr minus

α2)Δ1Δ22)We substitute φ (βs(βs + βr)) into equation (14) and

simplify it to 16λβ2r minus 16λβsβr + α2βs ge 0 for the supplier and(3βs minus βr)Δ22 + (βs + βr)α4β

2r ge 0 for the retailer

e two inequations in Proposition 3 guarantee that theeffort alignment policy is Pareto superior to the decen-tralized decision-making and thus it can strictly coordinatethe supply chain coordination

Mathematical Problems in Engineering 9

43 Effort Cost-Sharing Policy e price discount contractwith an effort alignment policy may not always match thenegotiation power and profit appeal of the two supply chainplayers because it is unable to arbitrarily allocate supplychain profit and whether its rigid incentive compatibilityconditions could be realized with extreme parameters isdoubtful In order to relax these restrictions and thus en-hance companiesrsquo motivations for quality visibility effortcost-sharing is introduced into the price discount contractwhere the supplier and retailer proportionately share thetotal costs of quality visibility

Theorem 2 A price discount contract with cost-sharing (B)

can coordinate the supply chain the retailer pays the suppliera wholesale price wB (1 minus φ)pB and shares the total qualityvisibility cost of the supply chain at a proportion φ (thesupplier shares 1 minus φ and 0ltφlt 1) Een the retailerrsquos profitfunction is πrB φπscC and the supplierrsquos profit function isπsB (1 minus φ)πscC Furthermore wlowastB (1 minus φ)plowastC vlowastsC1113966

plowastC vlowastrC1113967 is the optimal decision set of the supply chain

Proof With cost-sharing the retailerrsquos profit function is

πrB pB vrB1113872 1113873 pB minus wB( 1113857 θ minus λpB + αvscB1113872 1113873 minus φ βrv2rB + βsv

2sB1113872 1113873

(15)

We substitute wB (1 minus φ)pB into it to get πrB(pBvrB)

φπscC(pBvsBvrB) and πsB (1 minus φ)πscC

Compared with contract (E) the feasible range of φunder contract (B) covers the whole interval (0 1) and it isdetermined by the bargaining power of the supplier and theretailere stronger the retailerrsquos power is the greater the φWhen φ equals 0 or 1 the supply chain turns into a cen-tralized one Similarly the incentive compatibility condi-tions (14) must be satisfied when a wholesale price contract isan option In addition the information of both contracts (B)

and (E) need to include the retail price and the retailerrsquosquality visibility level while contract (B) needs to includethe supplierrsquos quality visibility level as well e difference inthe required information sets dominates the applicability ofthe two contracts and the higher information cost ofcontract (B) contributes to the arbitrarily profit allocation tosome extent

5 Practical Case

51 Data Collection We collect data from a practical freshchicken supply chain where a fresh retailer orders to itspartner farm base Fresh chicken is not the dominant meat inthe local market and its demand is elastic e retailersubmits the order plan to the farm base regularly Afterreceiving the plan the farm base slaughters all the plannedchickens and cools them to 0 to 4 degree centigrade inpackages for chilled freshness e fresh retailer is in chargeof the delivery using its own whole-process cold chainsystem from the farm base to all its fresh supermarkets

Consumers can scan the QR traceable code on the package toobtain the quality visibility from the chicken feeding to theshelf reported by the farm base and the fresh supermarketand the completeness and accuracy of the available qualityinformation depend on the visibility systems of the twocompanies Figure 2 shows the quality visibility displayed ona type of packaging for fresh chicken

First we operationalize the supply chain quality visibilityassessment model suggested by Caridi et al [19] We ignorethe mandatory information such as ingredients productdate shelf life and quality certification as shown in Figure 2and focus on the changing quality information linked to QRcode and sale scene instead ie the four information typeslisted at the end of Section 21 except the fifth one Infor-mation quality is rated and quality visibility is calculated in(0 5) e 5 of quality visibility represents that consumerscould get all the quality-related knowledge if they want andthis knowledge has an almost perfect quality e 0 indicatesconsumers hardly get any additional information exceptwhat is on the package

Second the value of each parameter is derived based onthe sales statistics of the fresh retailer during a quarter in2019 When the price remains the same for a few days andthere is a change in the information system we obtain thesensitivity coefficient of the demand to quality visibility andthe potential market demand using linear fitting similarlythe sensitivity coefficient of demand to price is obtainedwhen the information system is constant and the pricefluctuates Two sensitivity coefficients of cost to qualityvisibility are derived by quadratic fitting Historical recordsof several other quarters are used as a reference forcorrection

For simplicity we use the integers close to these pa-rameters for case analysis and the sensitivity analysis inSection 53 proves that a slight parameter deviation does notaffect the validity of the results Finally we have the potentialmarket demand θ 5000 in the quarter the sensitivitycoefficient of demand to price λ 100 the sensitivity co-efficient of demand to quality visibility α 700 the sup-plierrsquos quality visibility cost coefficient βs 1900 and theretailerrsquos quality visibility cost coefficient βr 2500

52 Contract Discussion e optimal decisions and per-formances of the supply chain in different scenarios arepresented in Table 3 In this case it is obvious that the pricediscount contract with effort alignment (E) or cost-sharing(B) coordinates the supply chain to an integrated one Incontrast the total quality visibility and profit of the supplychain in the decentralized supply chain (D) are far lowerthan those in the other scenarios because of severe doublemarginalization It is presumed a higher revenue per unitwith an increased retail price and a lower visibility cost witha decreased visibility effort in (D) however they inhibitconsumersrsquo demand which dominates both companiesrsquoprofit functions erefore there are strong practical in-terests for both the farm base and fresh retailer driving them

10 Mathematical Problems in Engineering

to seek supply chain integration or coordinated decision-making

e outcomes under contract (E) are as good as acentralized supply chain but the contract distributes supplychain profit at a fixed proportion because it requires acorrelation of the visibility efforts between the supplier andthe retailer similar to the pricing It applies to two com-panies of similar size with stable partnership since it doesnot require integrating the visibility systems of the twocompanies leaving them largely independent insteadHowever contract (B) applies to a closer partnership be-cause it requires upstream and downstream firms to inte-grate visibility systems and share effort costs In this sensethe two contracts are in the middle of the vertical integrationspectrum where the decentralized and centralized scenariosare at opposite ends

Further consider that when the profit allocation rate φ isslightly lower than the lower threshold 025 (or slightlyhigher than the upper threshold 055) the fresh retailer (orthe farm base) obtains a slightly smaller profit under con-tract (B) than that under contract (D) It seems that there isno reason for the fresh retailer (or the farm base) to deviatefrom contract (D) in terms of profit but his and hispartnerrsquos quality visibility levels would be significantly im-proved if they used contract (B) Furthermore the reducedretail price and higher supply chain visibility offered by

contract (B) lead to increased food sales and consumerwelfare as well as predictable improvements in businessmanagement and goodwill which to some extent spur thefresh retailer and the farm base to change their minds Weconclude that there is a strong stability with contract (B)ere are some existing practices in which retailers or brandowners ally with suppliers to jointly bear the costs of visi-bility systems As mentioned earlier Walmart is believed toaccept a large part of the RampD costs of the Food TrustPlatform in cooperation with IBM while the leafy-greenssuppliers just pay a service fee of 100sim10000 dollars monthlyaccording to their scales

53 Sensitivity Analysis Figures 3ndash6 show the influence ofprice sensitivity quality visibility sensitivity and visibilitycost coefficients on supply chain performances and contractparameters e shadow in each figure represents the Paretoimprovement space in the decentralized supply chain

It is easy to find that increased quality visibility sensi-tivity leads to a higher price (in Figure 4(a)) higher qualityvisibility (in Figure 4(b)) and greater profit (in Figure 4(c))regardless of the supply chain or the companies in it whilethe other three parameters have the opposite effect (inFigures 3 5 and 6)erefore when the negotiating cost of acoordination contract is too high or the supply chain has

Trademark

Category

Quarantinepassedmark QR code

EAN-13 codeProduction dateand check digit

Contents and ingredientsdiced chicken leg

Storage condition0~4degC

Shelf life7 days

Qualityhighlights

Figure 2 Quality visibility about the fresh chicken on shelf

Table 3 Optimal solution sets in different scenarios

j vlowasts vlowastr vlowastsc wlowast plowast πlowasts πlowastr φ πlowastscC 321 244 283 mdash 3490 mdash mdash mdash 8725202D 144 110 127 2753 4321 3921407 2158991 036 6080398E 321 244 283 1983 3490 4957501 3767701 043 8725202B 321 244 283 2626sim1569 3490 6566211sim3921407 2158991sim4803795 025sim055 8725202

Mathematical Problems in Engineering 11

been coordinated for more profits and quality visibilitythe companies may consider (i) promoting food posi-tioning and acquiring more price-insensitive consumerssuch as by launching ldquoorganic chickenrdquo or minipackagingfor one meal by the farm base and locating in luxurycommunities or office buildings for the fresh retailer (ii)advocating for the traceable and trackable whole-chainquality and safety from farm to table in order to attractconsumers focused on quality visibility and (iii) pur-chasing or renting a more popular cost-effective visibilitysystem and improving the interfaces and compatibility ofvisibility systems

As shown in Figures 4(a)ndash4(c) when consumers paymore attention to quality visibility the companyrsquos visibilityinvestment increases demand which compensates for thedemand reduction caused by price inflation In this respecthigher quality visibility sensitivity rapidly increases theoptimal retail price in the supply chain that is consumersrsquowillingness to pay for a high-quality visibility food In thiscase for a unit increase in quality visibility consumers arewilling to pay an extra 7 CNY (αλ) as the food premium forhigh-quality visibility

e increased quality visibility sensitivity also leads toa broader range of the profit allocation rate (increased

90 100 110 12080λ

20

30

40

50

pCwD

pDwE

(a)

90 100 110 12080λ

1

2

3

4

5

vscCvsCvrC

vscDvsDvrD

(b)

90 100 110 12080λ

120000

100000

80000

60000

40000

20000

πCπsD πscD

πrD

(c)

90 100 110 12080λ

025

030

035

040

045

050

055

φEφminφmax

(d)

Figure 3 e impacts of price sensitivity (a) Prices (b) Quality visibility (c) Profits (d) Allocation rates

12 Mathematical Problems in Engineering

φmax and decreased φmin) from Figure 4(d) while theother three parameters still have the opposite effect andnarrow the range erefore it is easier to realize supplychain coordination with a high visibility sensitivity lowprice sensibility or low-quality visibility cost coefficient

In addition a significant impact of the visibility costcoefficient on the contract (E) is observed in Figures 5(d)and 6(d) e fresh retailer (or the farm base) seizes a largershare of the supply chain profit with its own lower cost

coefficient or a higher cost coefficient of the other partyMoreover a large part of the φE curve is below 05 (byβs βr) which suggests that it is prone to contract (E) whenthe visibility cost coefficient of the fresh retailer is far beyondthat of the farm base according to incentive compatibilityconditions in Section 42 Indeed more and more retailerssource directly from farms and transport using self-builtlogistics to mitigate supply risk and quality risk whichmakes the retailerrsquos visibility cost coefficient often greater

20

30

40

50

600 650 700 750 800 850550α

pCwD

pDwE

(a)

1

2

3

4

5

600 650 700 750 800 850550α

vscCvsCvrC

vscDvsDvrD

(b)

20000

40000

60000

80000

100000

600 650 700 750 800 850550α

πCπsD πscD

πrD

(c)

025

030

035

040

045

050

055

600 650 700 750 800 850550α

φEφminφmax

(d)

Figure 4 e impacts of quality visibility sensitivity (a) Prices (b) Quality visibility (c) Profits (d) Allocation rates

Mathematical Problems in Engineering 13

than the supplierrsquos and thus it is more likely to coordinatethe supply chain with contract (E)

It is also meaningful to examine the sensitivity of eachconstraint condition to each parameter e assumption inProposition 1 is the condition to ensure a profitable supplychain coordination denoting as Cdt1 while the incentivecompatibility conditions in Proposition 3 guarantees thecompaniesrsquo participation denoting as Cdt2 for the supplierand Cdt3 for the retailer respectively We can get the in-terval of each parameter with other parameters fixed (thestrictest condition where the number is derived is in theparentheses) λgt5674(Cdt1) (Cdt1)92932gtαgt0 (Cdt2)

284900gtβsgt81126(Cdt1) (Cdt3)567735gtβrgt90388(Cdt1) e result shows that as long as Cdt1 is met what

stops the company is its own cost coefficient of qualityvisibility erefore it could be the most important thing toreduce the unit cost of visibility efforts and a number ofcompanies good at information systems are working on thatFor example Frigga launches a low-cost real-time and anultra-low-cost USB temperature recorder for cold chainlogistics and both of them are disposable and can be used formore than 90 days (see its website httpswwwfriggatechcom)

Finally from the perspective of the overall supplychain or the regulators it is good for improving qualityvisibility to promote IT innovation upgrade industriesand consumption and create a conducive environmentfor sign a contract

20

30

40

50

1700 1900 2100 23001500βs

pCwD

pDwE

(a)

1

2

3

4

5

1700 1900 2100 23001500βs

vscCvsCvrC

vscDvsDvrD

(b)

1700 1900 2100 23001500βs

20000

40000

60000

80000

100000

πCπsD πscD

πrD

(c)

1700 1900 2100 23001500βs

03

04

05

06

φEφminφmax

(d)

Figure 5 e impacts of the supplierrsquos visibility cost coefficient (a) Prices (b) Quality visibility (c) Profits (d) Allocation rates

14 Mathematical Problems in Engineering

πsD wD vsD pD vrD1113872 1113873 wD θ minus λpD +α vsD + vrD1113872 1113873

2⎡⎣ ⎤⎦ minus βsv

2sD

(7)

Let Δ2 32λβsβr minus 2α2βs minus α2βr rough the backwardinduction of a Stackelberg game it is easy to find that theHessian matrixes of equations (6) and (7) are negativedefinite with 16λβr minus α2 gt 0 and Δ2 2Δ1 + α2βr gt 0 whichreveals that there exists a maximum solution set of thedecentralized supply chain

Proposition 2 In the decentralized supply chain the optimalwholesale price of the supplier is wlowastD (βsθ(16λβr minus α2)λΔ2) the optimal quality visibility is vlowastsD (2αβrθΔ2) andthe optimal profit is πlowastsD (4βsβrθ

2Δ2) Ee optimal retailprice of the retailer is plowastD (βsθ(24λβr minus α2)λΔ2) the op-timal quality visibility is vlowastrD (2αβsθΔ2) and the optimalprofit is πlowastrD (4β2sβrθ

2(16λβr minus α2)Δ22) Furthermore the

supply chain realizes the optimal quality visibilityvlowastscD (αθ(βs + βr)Δ2) and the optimal profit πlowastscD

(4βsβrθ2(48λβsβr minus 3α2βs minus α2βr)Δ

22)

Proof Given wD and vs the retailerrsquos optimal retail priceand quality visibility are acquired by the first-order con-ditions of equation (6) as follows

plowastD wD vsD1113872 1113873

8βrθ + 8λβrwD + 4αβrvsD minus α2wD

16λβr minus α2

vlowastrD wD vsD1113872 1113873

2αθ + α2vsD minus 2αλwD

16λβr minus α2

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(8)

We substitute them into equation (7)

πsD wD vsD1113872 1113873 4βrλwD αvsD + 2θ minus 2λwD1113872 1113873

16λβr minus α2minus βsv

2sD

(9)

and similarly obtain the supplierrsquos optimal wholesale pricewlowastD and quality visibility vlowastsD by solving the first-orderconditions of equation (9) en it is easy to get plowastD and vlowastrD

by a substitution into equation (8) and thus the optimalperformance variables by a few further substitutions

Corollary 2

(i) πlowastscC minus πlowastscD (4β3sβrθ2(16λβr minus α2)2Δ1Δ2

2)gt 0(ii) πlowastsD minus πlowastrD (4βsβrθ

2Δ1Δ22)gt 0

(iii) vlowastscC minus vlowastscD (αβsθ(16λβr minus α2)(βs + βr)Δ1Δ2)gt 0(iv) plowastC minus plowastD minus ((βsθ(16λβr minus α2)(8λβsβr minus α2βs minus

α2βr))λΔ1Δ2)lt 0

Under the optimal equilibriums by comparing theoverall supply chain profits in the two decision-making

contexts Corollary 2 (i) indicates that the overall profit ofthe decentralized supply chain is strictly less than those ofthe centralized supply chain Since the supply chainrsquos rev-enue completely comes from the retailer to coordinate thesupply chain the optimal solution plowastC vlowastrC1113966 1113967 of integrateddecisions should be optimal for the retailer and it mustsatisfy

zπrD plowastC vlowastrC1113872 1113873

zpD

0

zπrD plowastC vlowastrC1113872 1113873

zvrD

0

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(10)

en we have wD 0 and vsD vlowastsC which mean thatthe supplier receives nothing from charging a productioncost but bears its own quality visibility cost erefore thesimple wholesale price contract cannot coordinate thesupply chain which is consistent with many previous re-searches From Corollary 2 (ii) the supplierrsquos profit is largerthan the retailerrsquos which verifies the supplierrsquos great first-move advantage in the Stackelberg game

In addition Corollary 2 (iii) and (iv) show that theoverall quality visibility level in the decentralized supplychain is lower than that in the centralized one but theformer retail price is higher than the latter It implies that thecentralized supply chain realizes not only greater profit andhigher food quality visibility but also greater consumersurplus which leads to more social welfare thus realizing awin-win between the supply chain and consumers

Corollary 3 (zKzλ)lt 0 (zKzα)gt 0 (zKzβs)lt 0 and(zKzβr)lt 0 where K isin wlowastD plowastD vlowastiD πlowastiD1113966 1113967(i s r sc)

e inspirations from Corollary 3 are similar to thosefrom Corollary 1 ie consumersrsquo sensitivity to qualityvisibility positively influences the prices and performances ofthe decentralized supply chain as opposed to the pricesensitivity and visibility cost coefficients Nevertheless itseems that the extent of the influences they have is lesssignificant than that in the centralized supply chain due tothe double marginalization which will be recognized moreintuitively in the subsequent practical case is findingindicates that a centralized or coordinated food supply chainis more efficient than a decentralized one in performanceimprovement erefore it is necessary to explore a coor-dination contract if there is no chance to integrate this foodsupply chain to a centralized one

4 Supply Chain Coordination

41 Revenue-Sharing Contract e revenue-sharing con-tract is one of the most used coordination contracts Supposethat the supplier and the retailer agree on the following ex-ante revenue-sharing contract the supplier charges a lowerwholesale price wR and receives 1 minus φ(0ltφlt 1) percent of

8 Mathematical Problems in Engineering

the retailerrsquos revenue Assuming φ 1 the contract becomesa pure wholesale price contract and ifwR 0 it is equivalentto a price discount contract with w (1 minus φ)p ereforefor a crisp wholesale price contract and a price discountcontract there is always an equivalent revenue-sharingcontract

e retailerrsquos profit function is given by

πrR pR vrR1113872 1113873 φpR minus wR( 1113857 θ minus λpR +α vsR + vrR1113872 1113873

2⎡⎣ ⎤⎦ minus βrv

2rR

(11)

Similarly by solving the first-order conditions

zπrR plowastC vlowastrC1113872 1113873

zpR

0

zπrR plowastC vlowastrC1113872 1113873

zvrR

0

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(12)

we have wR (φ minus 1)plowastC lt 0 and vsR vlowastsC is means thatif the supply chain is coordinated the supplier needs tosubsidize the retailer (1 minus φ)plowastC for each unit of foodhowever the revenue that the supplier receives from theretailer is equal to the total subsidy Just like in thewholesale price contract the supplier in the revenue-sharing contract does not realize any revenue but experi-ences the losses due to his own quality visibility cost erevenue-sharing contract as Cachon and Lariviere [33]assert cannot coordinate the supply chain with costly effortdecisions

42 Effort Alignment Policy e contracts with a singleparameter could correct the distortion in the pricing deci-sions of the upstream and downstream supply chain butthey do not address the dual-effort and pricing decisionsTwo or more parameters need to be included to align therelevant decision variables making the profit function of thelast-move decision-maker an affine transformation of theprofit function of the whole supply chain In this paper theprofit function of the retailer who plays as the last-moverdepends on the effort decisions that is the quality visibilitydecisions of both the supplier and the retailer Given thateffort can be observed it is feasible to align the supplierrsquoseffort with the retailerrsquos similar to the wholesale pricealigned with the retail price in a pure price discount contract

Theorem 1 Ee following price discount contract with effortalignment (E) can coordinate the supply chain the suppliercharges a wholesale price wE (βr(βs + βr))pE and offersquality visibility vsE (βrβs)vrE Een the retailerrsquos profitfunction is πrE φπscC and the supplierrsquos profit function isπsE (1 minus φ)πscC wlowastE (1 minus φ)plowastC vlowastsC plowastC vlowastrC1113966 1113967 is theoptimal solution set of the supply chain whereφ (βs(βs + βr))

Proof Substitute wE (βr(βs + βr))pE and vsE (βrβs)

vrE into the retailerrsquos profit function (2)

πrE pE vrE1113872 1113873 pE minus (1 minus φ)pE1113858 1113859 θ minus λpE +α vsE + vrE1113872 1113873

2⎡⎣ ⎤⎦

minus βrv2rE middot

φ βs + βr( 1113857

βs

φpE θ minus λpE +α vsE + vrE1113872 1113873

2⎡⎣ ⎤⎦

minus φ βrv2rE + βsv

2sE1113872 1113873

(13)

ie πrE(pE vrE) φπscC(pE vsE vrE) and then plowastE plowastCvlowastsE vlowastsC vlowastrE vlowastrC and wlowastE (1 minus φ)plowastC e supplierrsquosprofit function is πsE πscC minus πrE (1 minus φ)πscC

eorem 1 shows that the price discount contract al-locates the supply chain profit to the supplier and theretailer at proportions of 1 minus φ and φ respectively andcoordinates the supply chain e proportion φ is a fixedvalue dependent on the quality visibility cost coefficients ofboth sides Since the quality visibility cost function isnonlinear φ has a unique value in order to ensure alinearly affine transform of the profit functions in a three-parameter contract (w vsφ) According to the contractthe supplier loses his decision autonomy on quality visi-bility which is anchored to that of the retailer via a fixedrate (βrβs) e bigger the rate is the greater the gapbetween the supplier and retailer regarding price qualityvisibility and profit Although the contract does not allowthem to freely negotiate on the profit allocation rate it ischeaper and less tedious under specified conditions due toa reduction of one contract parameter in thedetermination

Proposition 3 Ee incentive compatibility conditions of thecontract (E) are 16λβ2r minus 16λβsβr + α2βs ge 0 for the supplierand (3βs minus βr)Δ

22 + (βs + βr)α4β

2r ge 0 for the retailer when

there is an alternative opportunity profit by a pure wholesaleprice contract

Proof In order to avoid any deviated actions it must satisfyπlowastsE (1 minus φ)πlowastscC ge πlowastsD for the supplier andπlowastrE φπlowastscC ge πlowastrD for the retailer Simplifying them theconditions are given by

φ isin φminφmax1113858 1113859 (14)

where φmax (βs(16λβr minus α2)Δ2) and φmin (βs(16λβr minus

α2)Δ1Δ22)We substitute φ (βs(βs + βr)) into equation (14) and

simplify it to 16λβ2r minus 16λβsβr + α2βs ge 0 for the supplier and(3βs minus βr)Δ22 + (βs + βr)α4β

2r ge 0 for the retailer

e two inequations in Proposition 3 guarantee that theeffort alignment policy is Pareto superior to the decen-tralized decision-making and thus it can strictly coordinatethe supply chain coordination

Mathematical Problems in Engineering 9

43 Effort Cost-Sharing Policy e price discount contractwith an effort alignment policy may not always match thenegotiation power and profit appeal of the two supply chainplayers because it is unable to arbitrarily allocate supplychain profit and whether its rigid incentive compatibilityconditions could be realized with extreme parameters isdoubtful In order to relax these restrictions and thus en-hance companiesrsquo motivations for quality visibility effortcost-sharing is introduced into the price discount contractwhere the supplier and retailer proportionately share thetotal costs of quality visibility

Theorem 2 A price discount contract with cost-sharing (B)

can coordinate the supply chain the retailer pays the suppliera wholesale price wB (1 minus φ)pB and shares the total qualityvisibility cost of the supply chain at a proportion φ (thesupplier shares 1 minus φ and 0ltφlt 1) Een the retailerrsquos profitfunction is πrB φπscC and the supplierrsquos profit function isπsB (1 minus φ)πscC Furthermore wlowastB (1 minus φ)plowastC vlowastsC1113966

plowastC vlowastrC1113967 is the optimal decision set of the supply chain

Proof With cost-sharing the retailerrsquos profit function is

πrB pB vrB1113872 1113873 pB minus wB( 1113857 θ minus λpB + αvscB1113872 1113873 minus φ βrv2rB + βsv

2sB1113872 1113873

(15)

We substitute wB (1 minus φ)pB into it to get πrB(pBvrB)

φπscC(pBvsBvrB) and πsB (1 minus φ)πscC

Compared with contract (E) the feasible range of φunder contract (B) covers the whole interval (0 1) and it isdetermined by the bargaining power of the supplier and theretailere stronger the retailerrsquos power is the greater the φWhen φ equals 0 or 1 the supply chain turns into a cen-tralized one Similarly the incentive compatibility condi-tions (14) must be satisfied when a wholesale price contract isan option In addition the information of both contracts (B)

and (E) need to include the retail price and the retailerrsquosquality visibility level while contract (B) needs to includethe supplierrsquos quality visibility level as well e difference inthe required information sets dominates the applicability ofthe two contracts and the higher information cost ofcontract (B) contributes to the arbitrarily profit allocation tosome extent

5 Practical Case

51 Data Collection We collect data from a practical freshchicken supply chain where a fresh retailer orders to itspartner farm base Fresh chicken is not the dominant meat inthe local market and its demand is elastic e retailersubmits the order plan to the farm base regularly Afterreceiving the plan the farm base slaughters all the plannedchickens and cools them to 0 to 4 degree centigrade inpackages for chilled freshness e fresh retailer is in chargeof the delivery using its own whole-process cold chainsystem from the farm base to all its fresh supermarkets

Consumers can scan the QR traceable code on the package toobtain the quality visibility from the chicken feeding to theshelf reported by the farm base and the fresh supermarketand the completeness and accuracy of the available qualityinformation depend on the visibility systems of the twocompanies Figure 2 shows the quality visibility displayed ona type of packaging for fresh chicken

First we operationalize the supply chain quality visibilityassessment model suggested by Caridi et al [19] We ignorethe mandatory information such as ingredients productdate shelf life and quality certification as shown in Figure 2and focus on the changing quality information linked to QRcode and sale scene instead ie the four information typeslisted at the end of Section 21 except the fifth one Infor-mation quality is rated and quality visibility is calculated in(0 5) e 5 of quality visibility represents that consumerscould get all the quality-related knowledge if they want andthis knowledge has an almost perfect quality e 0 indicatesconsumers hardly get any additional information exceptwhat is on the package

Second the value of each parameter is derived based onthe sales statistics of the fresh retailer during a quarter in2019 When the price remains the same for a few days andthere is a change in the information system we obtain thesensitivity coefficient of the demand to quality visibility andthe potential market demand using linear fitting similarlythe sensitivity coefficient of demand to price is obtainedwhen the information system is constant and the pricefluctuates Two sensitivity coefficients of cost to qualityvisibility are derived by quadratic fitting Historical recordsof several other quarters are used as a reference forcorrection

For simplicity we use the integers close to these pa-rameters for case analysis and the sensitivity analysis inSection 53 proves that a slight parameter deviation does notaffect the validity of the results Finally we have the potentialmarket demand θ 5000 in the quarter the sensitivitycoefficient of demand to price λ 100 the sensitivity co-efficient of demand to quality visibility α 700 the sup-plierrsquos quality visibility cost coefficient βs 1900 and theretailerrsquos quality visibility cost coefficient βr 2500

52 Contract Discussion e optimal decisions and per-formances of the supply chain in different scenarios arepresented in Table 3 In this case it is obvious that the pricediscount contract with effort alignment (E) or cost-sharing(B) coordinates the supply chain to an integrated one Incontrast the total quality visibility and profit of the supplychain in the decentralized supply chain (D) are far lowerthan those in the other scenarios because of severe doublemarginalization It is presumed a higher revenue per unitwith an increased retail price and a lower visibility cost witha decreased visibility effort in (D) however they inhibitconsumersrsquo demand which dominates both companiesrsquoprofit functions erefore there are strong practical in-terests for both the farm base and fresh retailer driving them

10 Mathematical Problems in Engineering

to seek supply chain integration or coordinated decision-making

e outcomes under contract (E) are as good as acentralized supply chain but the contract distributes supplychain profit at a fixed proportion because it requires acorrelation of the visibility efforts between the supplier andthe retailer similar to the pricing It applies to two com-panies of similar size with stable partnership since it doesnot require integrating the visibility systems of the twocompanies leaving them largely independent insteadHowever contract (B) applies to a closer partnership be-cause it requires upstream and downstream firms to inte-grate visibility systems and share effort costs In this sensethe two contracts are in the middle of the vertical integrationspectrum where the decentralized and centralized scenariosare at opposite ends

Further consider that when the profit allocation rate φ isslightly lower than the lower threshold 025 (or slightlyhigher than the upper threshold 055) the fresh retailer (orthe farm base) obtains a slightly smaller profit under con-tract (B) than that under contract (D) It seems that there isno reason for the fresh retailer (or the farm base) to deviatefrom contract (D) in terms of profit but his and hispartnerrsquos quality visibility levels would be significantly im-proved if they used contract (B) Furthermore the reducedretail price and higher supply chain visibility offered by

contract (B) lead to increased food sales and consumerwelfare as well as predictable improvements in businessmanagement and goodwill which to some extent spur thefresh retailer and the farm base to change their minds Weconclude that there is a strong stability with contract (B)ere are some existing practices in which retailers or brandowners ally with suppliers to jointly bear the costs of visi-bility systems As mentioned earlier Walmart is believed toaccept a large part of the RampD costs of the Food TrustPlatform in cooperation with IBM while the leafy-greenssuppliers just pay a service fee of 100sim10000 dollars monthlyaccording to their scales

53 Sensitivity Analysis Figures 3ndash6 show the influence ofprice sensitivity quality visibility sensitivity and visibilitycost coefficients on supply chain performances and contractparameters e shadow in each figure represents the Paretoimprovement space in the decentralized supply chain

It is easy to find that increased quality visibility sensi-tivity leads to a higher price (in Figure 4(a)) higher qualityvisibility (in Figure 4(b)) and greater profit (in Figure 4(c))regardless of the supply chain or the companies in it whilethe other three parameters have the opposite effect (inFigures 3 5 and 6)erefore when the negotiating cost of acoordination contract is too high or the supply chain has

Trademark

Category

Quarantinepassedmark QR code

EAN-13 codeProduction dateand check digit

Contents and ingredientsdiced chicken leg

Storage condition0~4degC

Shelf life7 days

Qualityhighlights

Figure 2 Quality visibility about the fresh chicken on shelf

Table 3 Optimal solution sets in different scenarios

j vlowasts vlowastr vlowastsc wlowast plowast πlowasts πlowastr φ πlowastscC 321 244 283 mdash 3490 mdash mdash mdash 8725202D 144 110 127 2753 4321 3921407 2158991 036 6080398E 321 244 283 1983 3490 4957501 3767701 043 8725202B 321 244 283 2626sim1569 3490 6566211sim3921407 2158991sim4803795 025sim055 8725202

Mathematical Problems in Engineering 11

been coordinated for more profits and quality visibilitythe companies may consider (i) promoting food posi-tioning and acquiring more price-insensitive consumerssuch as by launching ldquoorganic chickenrdquo or minipackagingfor one meal by the farm base and locating in luxurycommunities or office buildings for the fresh retailer (ii)advocating for the traceable and trackable whole-chainquality and safety from farm to table in order to attractconsumers focused on quality visibility and (iii) pur-chasing or renting a more popular cost-effective visibilitysystem and improving the interfaces and compatibility ofvisibility systems

As shown in Figures 4(a)ndash4(c) when consumers paymore attention to quality visibility the companyrsquos visibilityinvestment increases demand which compensates for thedemand reduction caused by price inflation In this respecthigher quality visibility sensitivity rapidly increases theoptimal retail price in the supply chain that is consumersrsquowillingness to pay for a high-quality visibility food In thiscase for a unit increase in quality visibility consumers arewilling to pay an extra 7 CNY (αλ) as the food premium forhigh-quality visibility

e increased quality visibility sensitivity also leads toa broader range of the profit allocation rate (increased

90 100 110 12080λ

20

30

40

50

pCwD

pDwE

(a)

90 100 110 12080λ

1

2

3

4

5

vscCvsCvrC

vscDvsDvrD

(b)

90 100 110 12080λ

120000

100000

80000

60000

40000

20000

πCπsD πscD

πrD

(c)

90 100 110 12080λ

025

030

035

040

045

050

055

φEφminφmax

(d)

Figure 3 e impacts of price sensitivity (a) Prices (b) Quality visibility (c) Profits (d) Allocation rates

12 Mathematical Problems in Engineering

φmax and decreased φmin) from Figure 4(d) while theother three parameters still have the opposite effect andnarrow the range erefore it is easier to realize supplychain coordination with a high visibility sensitivity lowprice sensibility or low-quality visibility cost coefficient

In addition a significant impact of the visibility costcoefficient on the contract (E) is observed in Figures 5(d)and 6(d) e fresh retailer (or the farm base) seizes a largershare of the supply chain profit with its own lower cost

coefficient or a higher cost coefficient of the other partyMoreover a large part of the φE curve is below 05 (byβs βr) which suggests that it is prone to contract (E) whenthe visibility cost coefficient of the fresh retailer is far beyondthat of the farm base according to incentive compatibilityconditions in Section 42 Indeed more and more retailerssource directly from farms and transport using self-builtlogistics to mitigate supply risk and quality risk whichmakes the retailerrsquos visibility cost coefficient often greater

20

30

40

50

600 650 700 750 800 850550α

pCwD

pDwE

(a)

1

2

3

4

5

600 650 700 750 800 850550α

vscCvsCvrC

vscDvsDvrD

(b)

20000

40000

60000

80000

100000

600 650 700 750 800 850550α

πCπsD πscD

πrD

(c)

025

030

035

040

045

050

055

600 650 700 750 800 850550α

φEφminφmax

(d)

Figure 4 e impacts of quality visibility sensitivity (a) Prices (b) Quality visibility (c) Profits (d) Allocation rates

Mathematical Problems in Engineering 13

than the supplierrsquos and thus it is more likely to coordinatethe supply chain with contract (E)

It is also meaningful to examine the sensitivity of eachconstraint condition to each parameter e assumption inProposition 1 is the condition to ensure a profitable supplychain coordination denoting as Cdt1 while the incentivecompatibility conditions in Proposition 3 guarantees thecompaniesrsquo participation denoting as Cdt2 for the supplierand Cdt3 for the retailer respectively We can get the in-terval of each parameter with other parameters fixed (thestrictest condition where the number is derived is in theparentheses) λgt5674(Cdt1) (Cdt1)92932gtαgt0 (Cdt2)

284900gtβsgt81126(Cdt1) (Cdt3)567735gtβrgt90388(Cdt1) e result shows that as long as Cdt1 is met what

stops the company is its own cost coefficient of qualityvisibility erefore it could be the most important thing toreduce the unit cost of visibility efforts and a number ofcompanies good at information systems are working on thatFor example Frigga launches a low-cost real-time and anultra-low-cost USB temperature recorder for cold chainlogistics and both of them are disposable and can be used formore than 90 days (see its website httpswwwfriggatechcom)

Finally from the perspective of the overall supplychain or the regulators it is good for improving qualityvisibility to promote IT innovation upgrade industriesand consumption and create a conducive environmentfor sign a contract

20

30

40

50

1700 1900 2100 23001500βs

pCwD

pDwE

(a)

1

2

3

4

5

1700 1900 2100 23001500βs

vscCvsCvrC

vscDvsDvrD

(b)

1700 1900 2100 23001500βs

20000

40000

60000

80000

100000

πCπsD πscD

πrD

(c)

1700 1900 2100 23001500βs

03

04

05

06

φEφminφmax

(d)

Figure 5 e impacts of the supplierrsquos visibility cost coefficient (a) Prices (b) Quality visibility (c) Profits (d) Allocation rates

14 Mathematical Problems in Engineering

the retailerrsquos revenue Assuming φ 1 the contract becomesa pure wholesale price contract and ifwR 0 it is equivalentto a price discount contract with w (1 minus φ)p ereforefor a crisp wholesale price contract and a price discountcontract there is always an equivalent revenue-sharingcontract

e retailerrsquos profit function is given by

πrR pR vrR1113872 1113873 φpR minus wR( 1113857 θ minus λpR +α vsR + vrR1113872 1113873

2⎡⎣ ⎤⎦ minus βrv

2rR

(11)

Similarly by solving the first-order conditions

zπrR plowastC vlowastrC1113872 1113873

zpR

0

zπrR plowastC vlowastrC1113872 1113873

zvrR

0

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(12)

we have wR (φ minus 1)plowastC lt 0 and vsR vlowastsC is means thatif the supply chain is coordinated the supplier needs tosubsidize the retailer (1 minus φ)plowastC for each unit of foodhowever the revenue that the supplier receives from theretailer is equal to the total subsidy Just like in thewholesale price contract the supplier in the revenue-sharing contract does not realize any revenue but experi-ences the losses due to his own quality visibility cost erevenue-sharing contract as Cachon and Lariviere [33]assert cannot coordinate the supply chain with costly effortdecisions

42 Effort Alignment Policy e contracts with a singleparameter could correct the distortion in the pricing deci-sions of the upstream and downstream supply chain butthey do not address the dual-effort and pricing decisionsTwo or more parameters need to be included to align therelevant decision variables making the profit function of thelast-move decision-maker an affine transformation of theprofit function of the whole supply chain In this paper theprofit function of the retailer who plays as the last-moverdepends on the effort decisions that is the quality visibilitydecisions of both the supplier and the retailer Given thateffort can be observed it is feasible to align the supplierrsquoseffort with the retailerrsquos similar to the wholesale pricealigned with the retail price in a pure price discount contract

Theorem 1 Ee following price discount contract with effortalignment (E) can coordinate the supply chain the suppliercharges a wholesale price wE (βr(βs + βr))pE and offersquality visibility vsE (βrβs)vrE Een the retailerrsquos profitfunction is πrE φπscC and the supplierrsquos profit function isπsE (1 minus φ)πscC wlowastE (1 minus φ)plowastC vlowastsC plowastC vlowastrC1113966 1113967 is theoptimal solution set of the supply chain whereφ (βs(βs + βr))

Proof Substitute wE (βr(βs + βr))pE and vsE (βrβs)

vrE into the retailerrsquos profit function (2)

πrE pE vrE1113872 1113873 pE minus (1 minus φ)pE1113858 1113859 θ minus λpE +α vsE + vrE1113872 1113873

2⎡⎣ ⎤⎦

minus βrv2rE middot

φ βs + βr( 1113857

βs

φpE θ minus λpE +α vsE + vrE1113872 1113873

2⎡⎣ ⎤⎦

minus φ βrv2rE + βsv

2sE1113872 1113873

(13)

ie πrE(pE vrE) φπscC(pE vsE vrE) and then plowastE plowastCvlowastsE vlowastsC vlowastrE vlowastrC and wlowastE (1 minus φ)plowastC e supplierrsquosprofit function is πsE πscC minus πrE (1 minus φ)πscC

eorem 1 shows that the price discount contract al-locates the supply chain profit to the supplier and theretailer at proportions of 1 minus φ and φ respectively andcoordinates the supply chain e proportion φ is a fixedvalue dependent on the quality visibility cost coefficients ofboth sides Since the quality visibility cost function isnonlinear φ has a unique value in order to ensure alinearly affine transform of the profit functions in a three-parameter contract (w vsφ) According to the contractthe supplier loses his decision autonomy on quality visi-bility which is anchored to that of the retailer via a fixedrate (βrβs) e bigger the rate is the greater the gapbetween the supplier and retailer regarding price qualityvisibility and profit Although the contract does not allowthem to freely negotiate on the profit allocation rate it ischeaper and less tedious under specified conditions due toa reduction of one contract parameter in thedetermination

Proposition 3 Ee incentive compatibility conditions of thecontract (E) are 16λβ2r minus 16λβsβr + α2βs ge 0 for the supplierand (3βs minus βr)Δ

22 + (βs + βr)α4β

2r ge 0 for the retailer when

there is an alternative opportunity profit by a pure wholesaleprice contract

Proof In order to avoid any deviated actions it must satisfyπlowastsE (1 minus φ)πlowastscC ge πlowastsD for the supplier andπlowastrE φπlowastscC ge πlowastrD for the retailer Simplifying them theconditions are given by

φ isin φminφmax1113858 1113859 (14)

where φmax (βs(16λβr minus α2)Δ2) and φmin (βs(16λβr minus

α2)Δ1Δ22)We substitute φ (βs(βs + βr)) into equation (14) and

simplify it to 16λβ2r minus 16λβsβr + α2βs ge 0 for the supplier and(3βs minus βr)Δ22 + (βs + βr)α4β

2r ge 0 for the retailer

e two inequations in Proposition 3 guarantee that theeffort alignment policy is Pareto superior to the decen-tralized decision-making and thus it can strictly coordinatethe supply chain coordination

Mathematical Problems in Engineering 9

43 Effort Cost-Sharing Policy e price discount contractwith an effort alignment policy may not always match thenegotiation power and profit appeal of the two supply chainplayers because it is unable to arbitrarily allocate supplychain profit and whether its rigid incentive compatibilityconditions could be realized with extreme parameters isdoubtful In order to relax these restrictions and thus en-hance companiesrsquo motivations for quality visibility effortcost-sharing is introduced into the price discount contractwhere the supplier and retailer proportionately share thetotal costs of quality visibility

Theorem 2 A price discount contract with cost-sharing (B)

can coordinate the supply chain the retailer pays the suppliera wholesale price wB (1 minus φ)pB and shares the total qualityvisibility cost of the supply chain at a proportion φ (thesupplier shares 1 minus φ and 0ltφlt 1) Een the retailerrsquos profitfunction is πrB φπscC and the supplierrsquos profit function isπsB (1 minus φ)πscC Furthermore wlowastB (1 minus φ)plowastC vlowastsC1113966

plowastC vlowastrC1113967 is the optimal decision set of the supply chain

Proof With cost-sharing the retailerrsquos profit function is

πrB pB vrB1113872 1113873 pB minus wB( 1113857 θ minus λpB + αvscB1113872 1113873 minus φ βrv2rB + βsv

2sB1113872 1113873

(15)

We substitute wB (1 minus φ)pB into it to get πrB(pBvrB)

φπscC(pBvsBvrB) and πsB (1 minus φ)πscC

Compared with contract (E) the feasible range of φunder contract (B) covers the whole interval (0 1) and it isdetermined by the bargaining power of the supplier and theretailere stronger the retailerrsquos power is the greater the φWhen φ equals 0 or 1 the supply chain turns into a cen-tralized one Similarly the incentive compatibility condi-tions (14) must be satisfied when a wholesale price contract isan option In addition the information of both contracts (B)

and (E) need to include the retail price and the retailerrsquosquality visibility level while contract (B) needs to includethe supplierrsquos quality visibility level as well e difference inthe required information sets dominates the applicability ofthe two contracts and the higher information cost ofcontract (B) contributes to the arbitrarily profit allocation tosome extent

5 Practical Case

51 Data Collection We collect data from a practical freshchicken supply chain where a fresh retailer orders to itspartner farm base Fresh chicken is not the dominant meat inthe local market and its demand is elastic e retailersubmits the order plan to the farm base regularly Afterreceiving the plan the farm base slaughters all the plannedchickens and cools them to 0 to 4 degree centigrade inpackages for chilled freshness e fresh retailer is in chargeof the delivery using its own whole-process cold chainsystem from the farm base to all its fresh supermarkets

Consumers can scan the QR traceable code on the package toobtain the quality visibility from the chicken feeding to theshelf reported by the farm base and the fresh supermarketand the completeness and accuracy of the available qualityinformation depend on the visibility systems of the twocompanies Figure 2 shows the quality visibility displayed ona type of packaging for fresh chicken

First we operationalize the supply chain quality visibilityassessment model suggested by Caridi et al [19] We ignorethe mandatory information such as ingredients productdate shelf life and quality certification as shown in Figure 2and focus on the changing quality information linked to QRcode and sale scene instead ie the four information typeslisted at the end of Section 21 except the fifth one Infor-mation quality is rated and quality visibility is calculated in(0 5) e 5 of quality visibility represents that consumerscould get all the quality-related knowledge if they want andthis knowledge has an almost perfect quality e 0 indicatesconsumers hardly get any additional information exceptwhat is on the package

Second the value of each parameter is derived based onthe sales statistics of the fresh retailer during a quarter in2019 When the price remains the same for a few days andthere is a change in the information system we obtain thesensitivity coefficient of the demand to quality visibility andthe potential market demand using linear fitting similarlythe sensitivity coefficient of demand to price is obtainedwhen the information system is constant and the pricefluctuates Two sensitivity coefficients of cost to qualityvisibility are derived by quadratic fitting Historical recordsof several other quarters are used as a reference forcorrection

For simplicity we use the integers close to these pa-rameters for case analysis and the sensitivity analysis inSection 53 proves that a slight parameter deviation does notaffect the validity of the results Finally we have the potentialmarket demand θ 5000 in the quarter the sensitivitycoefficient of demand to price λ 100 the sensitivity co-efficient of demand to quality visibility α 700 the sup-plierrsquos quality visibility cost coefficient βs 1900 and theretailerrsquos quality visibility cost coefficient βr 2500

52 Contract Discussion e optimal decisions and per-formances of the supply chain in different scenarios arepresented in Table 3 In this case it is obvious that the pricediscount contract with effort alignment (E) or cost-sharing(B) coordinates the supply chain to an integrated one Incontrast the total quality visibility and profit of the supplychain in the decentralized supply chain (D) are far lowerthan those in the other scenarios because of severe doublemarginalization It is presumed a higher revenue per unitwith an increased retail price and a lower visibility cost witha decreased visibility effort in (D) however they inhibitconsumersrsquo demand which dominates both companiesrsquoprofit functions erefore there are strong practical in-terests for both the farm base and fresh retailer driving them

10 Mathematical Problems in Engineering

to seek supply chain integration or coordinated decision-making

e outcomes under contract (E) are as good as acentralized supply chain but the contract distributes supplychain profit at a fixed proportion because it requires acorrelation of the visibility efforts between the supplier andthe retailer similar to the pricing It applies to two com-panies of similar size with stable partnership since it doesnot require integrating the visibility systems of the twocompanies leaving them largely independent insteadHowever contract (B) applies to a closer partnership be-cause it requires upstream and downstream firms to inte-grate visibility systems and share effort costs In this sensethe two contracts are in the middle of the vertical integrationspectrum where the decentralized and centralized scenariosare at opposite ends

Further consider that when the profit allocation rate φ isslightly lower than the lower threshold 025 (or slightlyhigher than the upper threshold 055) the fresh retailer (orthe farm base) obtains a slightly smaller profit under con-tract (B) than that under contract (D) It seems that there isno reason for the fresh retailer (or the farm base) to deviatefrom contract (D) in terms of profit but his and hispartnerrsquos quality visibility levels would be significantly im-proved if they used contract (B) Furthermore the reducedretail price and higher supply chain visibility offered by

contract (B) lead to increased food sales and consumerwelfare as well as predictable improvements in businessmanagement and goodwill which to some extent spur thefresh retailer and the farm base to change their minds Weconclude that there is a strong stability with contract (B)ere are some existing practices in which retailers or brandowners ally with suppliers to jointly bear the costs of visi-bility systems As mentioned earlier Walmart is believed toaccept a large part of the RampD costs of the Food TrustPlatform in cooperation with IBM while the leafy-greenssuppliers just pay a service fee of 100sim10000 dollars monthlyaccording to their scales

53 Sensitivity Analysis Figures 3ndash6 show the influence ofprice sensitivity quality visibility sensitivity and visibilitycost coefficients on supply chain performances and contractparameters e shadow in each figure represents the Paretoimprovement space in the decentralized supply chain

It is easy to find that increased quality visibility sensi-tivity leads to a higher price (in Figure 4(a)) higher qualityvisibility (in Figure 4(b)) and greater profit (in Figure 4(c))regardless of the supply chain or the companies in it whilethe other three parameters have the opposite effect (inFigures 3 5 and 6)erefore when the negotiating cost of acoordination contract is too high or the supply chain has

Trademark

Category

Quarantinepassedmark QR code

EAN-13 codeProduction dateand check digit

Contents and ingredientsdiced chicken leg

Storage condition0~4degC

Shelf life7 days

Qualityhighlights

Figure 2 Quality visibility about the fresh chicken on shelf

Table 3 Optimal solution sets in different scenarios

j vlowasts vlowastr vlowastsc wlowast plowast πlowasts πlowastr φ πlowastscC 321 244 283 mdash 3490 mdash mdash mdash 8725202D 144 110 127 2753 4321 3921407 2158991 036 6080398E 321 244 283 1983 3490 4957501 3767701 043 8725202B 321 244 283 2626sim1569 3490 6566211sim3921407 2158991sim4803795 025sim055 8725202

Mathematical Problems in Engineering 11

been coordinated for more profits and quality visibilitythe companies may consider (i) promoting food posi-tioning and acquiring more price-insensitive consumerssuch as by launching ldquoorganic chickenrdquo or minipackagingfor one meal by the farm base and locating in luxurycommunities or office buildings for the fresh retailer (ii)advocating for the traceable and trackable whole-chainquality and safety from farm to table in order to attractconsumers focused on quality visibility and (iii) pur-chasing or renting a more popular cost-effective visibilitysystem and improving the interfaces and compatibility ofvisibility systems

As shown in Figures 4(a)ndash4(c) when consumers paymore attention to quality visibility the companyrsquos visibilityinvestment increases demand which compensates for thedemand reduction caused by price inflation In this respecthigher quality visibility sensitivity rapidly increases theoptimal retail price in the supply chain that is consumersrsquowillingness to pay for a high-quality visibility food In thiscase for a unit increase in quality visibility consumers arewilling to pay an extra 7 CNY (αλ) as the food premium forhigh-quality visibility

e increased quality visibility sensitivity also leads toa broader range of the profit allocation rate (increased

90 100 110 12080λ

20

30

40

50

pCwD

pDwE

(a)

90 100 110 12080λ

1

2

3

4

5

vscCvsCvrC

vscDvsDvrD

(b)

90 100 110 12080λ

120000

100000

80000

60000

40000

20000

πCπsD πscD

πrD

(c)

90 100 110 12080λ

025

030

035

040

045

050

055

φEφminφmax

(d)

Figure 3 e impacts of price sensitivity (a) Prices (b) Quality visibility (c) Profits (d) Allocation rates

12 Mathematical Problems in Engineering

φmax and decreased φmin) from Figure 4(d) while theother three parameters still have the opposite effect andnarrow the range erefore it is easier to realize supplychain coordination with a high visibility sensitivity lowprice sensibility or low-quality visibility cost coefficient

In addition a significant impact of the visibility costcoefficient on the contract (E) is observed in Figures 5(d)and 6(d) e fresh retailer (or the farm base) seizes a largershare of the supply chain profit with its own lower cost

coefficient or a higher cost coefficient of the other partyMoreover a large part of the φE curve is below 05 (byβs βr) which suggests that it is prone to contract (E) whenthe visibility cost coefficient of the fresh retailer is far beyondthat of the farm base according to incentive compatibilityconditions in Section 42 Indeed more and more retailerssource directly from farms and transport using self-builtlogistics to mitigate supply risk and quality risk whichmakes the retailerrsquos visibility cost coefficient often greater

20

30

40

50

600 650 700 750 800 850550α

pCwD

pDwE

(a)

1

2

3

4

5

600 650 700 750 800 850550α

vscCvsCvrC

vscDvsDvrD

(b)

20000

40000

60000

80000

100000

600 650 700 750 800 850550α

πCπsD πscD

πrD

(c)

025

030

035

040

045

050

055

600 650 700 750 800 850550α

φEφminφmax

(d)

Figure 4 e impacts of quality visibility sensitivity (a) Prices (b) Quality visibility (c) Profits (d) Allocation rates

Mathematical Problems in Engineering 13

than the supplierrsquos and thus it is more likely to coordinatethe supply chain with contract (E)

It is also meaningful to examine the sensitivity of eachconstraint condition to each parameter e assumption inProposition 1 is the condition to ensure a profitable supplychain coordination denoting as Cdt1 while the incentivecompatibility conditions in Proposition 3 guarantees thecompaniesrsquo participation denoting as Cdt2 for the supplierand Cdt3 for the retailer respectively We can get the in-terval of each parameter with other parameters fixed (thestrictest condition where the number is derived is in theparentheses) λgt5674(Cdt1) (Cdt1)92932gtαgt0 (Cdt2)

284900gtβsgt81126(Cdt1) (Cdt3)567735gtβrgt90388(Cdt1) e result shows that as long as Cdt1 is met what

stops the company is its own cost coefficient of qualityvisibility erefore it could be the most important thing toreduce the unit cost of visibility efforts and a number ofcompanies good at information systems are working on thatFor example Frigga launches a low-cost real-time and anultra-low-cost USB temperature recorder for cold chainlogistics and both of them are disposable and can be used formore than 90 days (see its website httpswwwfriggatechcom)

Finally from the perspective of the overall supplychain or the regulators it is good for improving qualityvisibility to promote IT innovation upgrade industriesand consumption and create a conducive environmentfor sign a contract

20

30

40

50

1700 1900 2100 23001500βs

pCwD

pDwE

(a)

1

2

3

4

5

1700 1900 2100 23001500βs

vscCvsCvrC

vscDvsDvrD

(b)

1700 1900 2100 23001500βs

20000

40000

60000

80000

100000

πCπsD πscD

πrD

(c)

1700 1900 2100 23001500βs

03

04

05

06

φEφminφmax

(d)

Figure 5 e impacts of the supplierrsquos visibility cost coefficient (a) Prices (b) Quality visibility (c) Profits (d) Allocation rates

14 Mathematical Problems in Engineering

43 Effort Cost-Sharing Policy e price discount contractwith an effort alignment policy may not always match thenegotiation power and profit appeal of the two supply chainplayers because it is unable to arbitrarily allocate supplychain profit and whether its rigid incentive compatibilityconditions could be realized with extreme parameters isdoubtful In order to relax these restrictions and thus en-hance companiesrsquo motivations for quality visibility effortcost-sharing is introduced into the price discount contractwhere the supplier and retailer proportionately share thetotal costs of quality visibility

Theorem 2 A price discount contract with cost-sharing (B)

can coordinate the supply chain the retailer pays the suppliera wholesale price wB (1 minus φ)pB and shares the total qualityvisibility cost of the supply chain at a proportion φ (thesupplier shares 1 minus φ and 0ltφlt 1) Een the retailerrsquos profitfunction is πrB φπscC and the supplierrsquos profit function isπsB (1 minus φ)πscC Furthermore wlowastB (1 minus φ)plowastC vlowastsC1113966

plowastC vlowastrC1113967 is the optimal decision set of the supply chain

Proof With cost-sharing the retailerrsquos profit function is

πrB pB vrB1113872 1113873 pB minus wB( 1113857 θ minus λpB + αvscB1113872 1113873 minus φ βrv2rB + βsv

2sB1113872 1113873

(15)

We substitute wB (1 minus φ)pB into it to get πrB(pBvrB)

φπscC(pBvsBvrB) and πsB (1 minus φ)πscC

Compared with contract (E) the feasible range of φunder contract (B) covers the whole interval (0 1) and it isdetermined by the bargaining power of the supplier and theretailere stronger the retailerrsquos power is the greater the φWhen φ equals 0 or 1 the supply chain turns into a cen-tralized one Similarly the incentive compatibility condi-tions (14) must be satisfied when a wholesale price contract isan option In addition the information of both contracts (B)

and (E) need to include the retail price and the retailerrsquosquality visibility level while contract (B) needs to includethe supplierrsquos quality visibility level as well e difference inthe required information sets dominates the applicability ofthe two contracts and the higher information cost ofcontract (B) contributes to the arbitrarily profit allocation tosome extent

5 Practical Case

51 Data Collection We collect data from a practical freshchicken supply chain where a fresh retailer orders to itspartner farm base Fresh chicken is not the dominant meat inthe local market and its demand is elastic e retailersubmits the order plan to the farm base regularly Afterreceiving the plan the farm base slaughters all the plannedchickens and cools them to 0 to 4 degree centigrade inpackages for chilled freshness e fresh retailer is in chargeof the delivery using its own whole-process cold chainsystem from the farm base to all its fresh supermarkets

Consumers can scan the QR traceable code on the package toobtain the quality visibility from the chicken feeding to theshelf reported by the farm base and the fresh supermarketand the completeness and accuracy of the available qualityinformation depend on the visibility systems of the twocompanies Figure 2 shows the quality visibility displayed ona type of packaging for fresh chicken

First we operationalize the supply chain quality visibilityassessment model suggested by Caridi et al [19] We ignorethe mandatory information such as ingredients productdate shelf life and quality certification as shown in Figure 2and focus on the changing quality information linked to QRcode and sale scene instead ie the four information typeslisted at the end of Section 21 except the fifth one Infor-mation quality is rated and quality visibility is calculated in(0 5) e 5 of quality visibility represents that consumerscould get all the quality-related knowledge if they want andthis knowledge has an almost perfect quality e 0 indicatesconsumers hardly get any additional information exceptwhat is on the package

Second the value of each parameter is derived based onthe sales statistics of the fresh retailer during a quarter in2019 When the price remains the same for a few days andthere is a change in the information system we obtain thesensitivity coefficient of the demand to quality visibility andthe potential market demand using linear fitting similarlythe sensitivity coefficient of demand to price is obtainedwhen the information system is constant and the pricefluctuates Two sensitivity coefficients of cost to qualityvisibility are derived by quadratic fitting Historical recordsof several other quarters are used as a reference forcorrection

For simplicity we use the integers close to these pa-rameters for case analysis and the sensitivity analysis inSection 53 proves that a slight parameter deviation does notaffect the validity of the results Finally we have the potentialmarket demand θ 5000 in the quarter the sensitivitycoefficient of demand to price λ 100 the sensitivity co-efficient of demand to quality visibility α 700 the sup-plierrsquos quality visibility cost coefficient βs 1900 and theretailerrsquos quality visibility cost coefficient βr 2500

52 Contract Discussion e optimal decisions and per-formances of the supply chain in different scenarios arepresented in Table 3 In this case it is obvious that the pricediscount contract with effort alignment (E) or cost-sharing(B) coordinates the supply chain to an integrated one Incontrast the total quality visibility and profit of the supplychain in the decentralized supply chain (D) are far lowerthan those in the other scenarios because of severe doublemarginalization It is presumed a higher revenue per unitwith an increased retail price and a lower visibility cost witha decreased visibility effort in (D) however they inhibitconsumersrsquo demand which dominates both companiesrsquoprofit functions erefore there are strong practical in-terests for both the farm base and fresh retailer driving them

10 Mathematical Problems in Engineering

to seek supply chain integration or coordinated decision-making

e outcomes under contract (E) are as good as acentralized supply chain but the contract distributes supplychain profit at a fixed proportion because it requires acorrelation of the visibility efforts between the supplier andthe retailer similar to the pricing It applies to two com-panies of similar size with stable partnership since it doesnot require integrating the visibility systems of the twocompanies leaving them largely independent insteadHowever contract (B) applies to a closer partnership be-cause it requires upstream and downstream firms to inte-grate visibility systems and share effort costs In this sensethe two contracts are in the middle of the vertical integrationspectrum where the decentralized and centralized scenariosare at opposite ends

Further consider that when the profit allocation rate φ isslightly lower than the lower threshold 025 (or slightlyhigher than the upper threshold 055) the fresh retailer (orthe farm base) obtains a slightly smaller profit under con-tract (B) than that under contract (D) It seems that there isno reason for the fresh retailer (or the farm base) to deviatefrom contract (D) in terms of profit but his and hispartnerrsquos quality visibility levels would be significantly im-proved if they used contract (B) Furthermore the reducedretail price and higher supply chain visibility offered by

contract (B) lead to increased food sales and consumerwelfare as well as predictable improvements in businessmanagement and goodwill which to some extent spur thefresh retailer and the farm base to change their minds Weconclude that there is a strong stability with contract (B)ere are some existing practices in which retailers or brandowners ally with suppliers to jointly bear the costs of visi-bility systems As mentioned earlier Walmart is believed toaccept a large part of the RampD costs of the Food TrustPlatform in cooperation with IBM while the leafy-greenssuppliers just pay a service fee of 100sim10000 dollars monthlyaccording to their scales

53 Sensitivity Analysis Figures 3ndash6 show the influence ofprice sensitivity quality visibility sensitivity and visibilitycost coefficients on supply chain performances and contractparameters e shadow in each figure represents the Paretoimprovement space in the decentralized supply chain

It is easy to find that increased quality visibility sensi-tivity leads to a higher price (in Figure 4(a)) higher qualityvisibility (in Figure 4(b)) and greater profit (in Figure 4(c))regardless of the supply chain or the companies in it whilethe other three parameters have the opposite effect (inFigures 3 5 and 6)erefore when the negotiating cost of acoordination contract is too high or the supply chain has

Trademark

Category

Quarantinepassedmark QR code

EAN-13 codeProduction dateand check digit

Contents and ingredientsdiced chicken leg

Storage condition0~4degC

Shelf life7 days

Qualityhighlights

Figure 2 Quality visibility about the fresh chicken on shelf

Table 3 Optimal solution sets in different scenarios

j vlowasts vlowastr vlowastsc wlowast plowast πlowasts πlowastr φ πlowastscC 321 244 283 mdash 3490 mdash mdash mdash 8725202D 144 110 127 2753 4321 3921407 2158991 036 6080398E 321 244 283 1983 3490 4957501 3767701 043 8725202B 321 244 283 2626sim1569 3490 6566211sim3921407 2158991sim4803795 025sim055 8725202

Mathematical Problems in Engineering 11

been coordinated for more profits and quality visibilitythe companies may consider (i) promoting food posi-tioning and acquiring more price-insensitive consumerssuch as by launching ldquoorganic chickenrdquo or minipackagingfor one meal by the farm base and locating in luxurycommunities or office buildings for the fresh retailer (ii)advocating for the traceable and trackable whole-chainquality and safety from farm to table in order to attractconsumers focused on quality visibility and (iii) pur-chasing or renting a more popular cost-effective visibilitysystem and improving the interfaces and compatibility ofvisibility systems

As shown in Figures 4(a)ndash4(c) when consumers paymore attention to quality visibility the companyrsquos visibilityinvestment increases demand which compensates for thedemand reduction caused by price inflation In this respecthigher quality visibility sensitivity rapidly increases theoptimal retail price in the supply chain that is consumersrsquowillingness to pay for a high-quality visibility food In thiscase for a unit increase in quality visibility consumers arewilling to pay an extra 7 CNY (αλ) as the food premium forhigh-quality visibility

e increased quality visibility sensitivity also leads toa broader range of the profit allocation rate (increased

90 100 110 12080λ

20

30

40

50

pCwD

pDwE

(a)

90 100 110 12080λ

1

2

3

4

5

vscCvsCvrC

vscDvsDvrD

(b)

90 100 110 12080λ

120000

100000

80000

60000

40000

20000

πCπsD πscD

πrD

(c)

90 100 110 12080λ

025

030

035

040

045

050

055

φEφminφmax

(d)

Figure 3 e impacts of price sensitivity (a) Prices (b) Quality visibility (c) Profits (d) Allocation rates

12 Mathematical Problems in Engineering

φmax and decreased φmin) from Figure 4(d) while theother three parameters still have the opposite effect andnarrow the range erefore it is easier to realize supplychain coordination with a high visibility sensitivity lowprice sensibility or low-quality visibility cost coefficient

In addition a significant impact of the visibility costcoefficient on the contract (E) is observed in Figures 5(d)and 6(d) e fresh retailer (or the farm base) seizes a largershare of the supply chain profit with its own lower cost

coefficient or a higher cost coefficient of the other partyMoreover a large part of the φE curve is below 05 (byβs βr) which suggests that it is prone to contract (E) whenthe visibility cost coefficient of the fresh retailer is far beyondthat of the farm base according to incentive compatibilityconditions in Section 42 Indeed more and more retailerssource directly from farms and transport using self-builtlogistics to mitigate supply risk and quality risk whichmakes the retailerrsquos visibility cost coefficient often greater

20

30

40

50

600 650 700 750 800 850550α

pCwD

pDwE

(a)

1

2

3

4

5

600 650 700 750 800 850550α

vscCvsCvrC

vscDvsDvrD

(b)

20000

40000

60000

80000

100000

600 650 700 750 800 850550α

πCπsD πscD

πrD

(c)

025

030

035

040

045

050

055

600 650 700 750 800 850550α

φEφminφmax

(d)

Figure 4 e impacts of quality visibility sensitivity (a) Prices (b) Quality visibility (c) Profits (d) Allocation rates

Mathematical Problems in Engineering 13

than the supplierrsquos and thus it is more likely to coordinatethe supply chain with contract (E)

It is also meaningful to examine the sensitivity of eachconstraint condition to each parameter e assumption inProposition 1 is the condition to ensure a profitable supplychain coordination denoting as Cdt1 while the incentivecompatibility conditions in Proposition 3 guarantees thecompaniesrsquo participation denoting as Cdt2 for the supplierand Cdt3 for the retailer respectively We can get the in-terval of each parameter with other parameters fixed (thestrictest condition where the number is derived is in theparentheses) λgt5674(Cdt1) (Cdt1)92932gtαgt0 (Cdt2)

284900gtβsgt81126(Cdt1) (Cdt3)567735gtβrgt90388(Cdt1) e result shows that as long as Cdt1 is met what

stops the company is its own cost coefficient of qualityvisibility erefore it could be the most important thing toreduce the unit cost of visibility efforts and a number ofcompanies good at information systems are working on thatFor example Frigga launches a low-cost real-time and anultra-low-cost USB temperature recorder for cold chainlogistics and both of them are disposable and can be used formore than 90 days (see its website httpswwwfriggatechcom)

Finally from the perspective of the overall supplychain or the regulators it is good for improving qualityvisibility to promote IT innovation upgrade industriesand consumption and create a conducive environmentfor sign a contract

20

30

40

50

1700 1900 2100 23001500βs

pCwD

pDwE

(a)

1

2

3

4

5

1700 1900 2100 23001500βs

vscCvsCvrC

vscDvsDvrD

(b)

1700 1900 2100 23001500βs

20000

40000

60000

80000

100000

πCπsD πscD

πrD

(c)

1700 1900 2100 23001500βs

03

04

05

06

φEφminφmax

(d)

Figure 5 e impacts of the supplierrsquos visibility cost coefficient (a) Prices (b) Quality visibility (c) Profits (d) Allocation rates

14 Mathematical Problems in Engineering

to seek supply chain integration or coordinated decision-making

e outcomes under contract (E) are as good as acentralized supply chain but the contract distributes supplychain profit at a fixed proportion because it requires acorrelation of the visibility efforts between the supplier andthe retailer similar to the pricing It applies to two com-panies of similar size with stable partnership since it doesnot require integrating the visibility systems of the twocompanies leaving them largely independent insteadHowever contract (B) applies to a closer partnership be-cause it requires upstream and downstream firms to inte-grate visibility systems and share effort costs In this sensethe two contracts are in the middle of the vertical integrationspectrum where the decentralized and centralized scenariosare at opposite ends

Further consider that when the profit allocation rate φ isslightly lower than the lower threshold 025 (or slightlyhigher than the upper threshold 055) the fresh retailer (orthe farm base) obtains a slightly smaller profit under con-tract (B) than that under contract (D) It seems that there isno reason for the fresh retailer (or the farm base) to deviatefrom contract (D) in terms of profit but his and hispartnerrsquos quality visibility levels would be significantly im-proved if they used contract (B) Furthermore the reducedretail price and higher supply chain visibility offered by

contract (B) lead to increased food sales and consumerwelfare as well as predictable improvements in businessmanagement and goodwill which to some extent spur thefresh retailer and the farm base to change their minds Weconclude that there is a strong stability with contract (B)ere are some existing practices in which retailers or brandowners ally with suppliers to jointly bear the costs of visi-bility systems As mentioned earlier Walmart is believed toaccept a large part of the RampD costs of the Food TrustPlatform in cooperation with IBM while the leafy-greenssuppliers just pay a service fee of 100sim10000 dollars monthlyaccording to their scales

53 Sensitivity Analysis Figures 3ndash6 show the influence ofprice sensitivity quality visibility sensitivity and visibilitycost coefficients on supply chain performances and contractparameters e shadow in each figure represents the Paretoimprovement space in the decentralized supply chain

It is easy to find that increased quality visibility sensi-tivity leads to a higher price (in Figure 4(a)) higher qualityvisibility (in Figure 4(b)) and greater profit (in Figure 4(c))regardless of the supply chain or the companies in it whilethe other three parameters have the opposite effect (inFigures 3 5 and 6)erefore when the negotiating cost of acoordination contract is too high or the supply chain has

Trademark

Category

Quarantinepassedmark QR code

EAN-13 codeProduction dateand check digit

Contents and ingredientsdiced chicken leg

Storage condition0~4degC

Shelf life7 days

Qualityhighlights

Figure 2 Quality visibility about the fresh chicken on shelf

Table 3 Optimal solution sets in different scenarios

j vlowasts vlowastr vlowastsc wlowast plowast πlowasts πlowastr φ πlowastscC 321 244 283 mdash 3490 mdash mdash mdash 8725202D 144 110 127 2753 4321 3921407 2158991 036 6080398E 321 244 283 1983 3490 4957501 3767701 043 8725202B 321 244 283 2626sim1569 3490 6566211sim3921407 2158991sim4803795 025sim055 8725202

Mathematical Problems in Engineering 11

been coordinated for more profits and quality visibilitythe companies may consider (i) promoting food posi-tioning and acquiring more price-insensitive consumerssuch as by launching ldquoorganic chickenrdquo or minipackagingfor one meal by the farm base and locating in luxurycommunities or office buildings for the fresh retailer (ii)advocating for the traceable and trackable whole-chainquality and safety from farm to table in order to attractconsumers focused on quality visibility and (iii) pur-chasing or renting a more popular cost-effective visibilitysystem and improving the interfaces and compatibility ofvisibility systems

As shown in Figures 4(a)ndash4(c) when consumers paymore attention to quality visibility the companyrsquos visibilityinvestment increases demand which compensates for thedemand reduction caused by price inflation In this respecthigher quality visibility sensitivity rapidly increases theoptimal retail price in the supply chain that is consumersrsquowillingness to pay for a high-quality visibility food In thiscase for a unit increase in quality visibility consumers arewilling to pay an extra 7 CNY (αλ) as the food premium forhigh-quality visibility

e increased quality visibility sensitivity also leads toa broader range of the profit allocation rate (increased

90 100 110 12080λ

20

30

40

50

pCwD

pDwE

(a)

90 100 110 12080λ

1

2

3

4

5

vscCvsCvrC

vscDvsDvrD

(b)

90 100 110 12080λ

120000

100000

80000

60000

40000

20000

πCπsD πscD

πrD

(c)

90 100 110 12080λ

025

030

035

040

045

050

055

φEφminφmax

(d)

Figure 3 e impacts of price sensitivity (a) Prices (b) Quality visibility (c) Profits (d) Allocation rates

12 Mathematical Problems in Engineering

φmax and decreased φmin) from Figure 4(d) while theother three parameters still have the opposite effect andnarrow the range erefore it is easier to realize supplychain coordination with a high visibility sensitivity lowprice sensibility or low-quality visibility cost coefficient

In addition a significant impact of the visibility costcoefficient on the contract (E) is observed in Figures 5(d)and 6(d) e fresh retailer (or the farm base) seizes a largershare of the supply chain profit with its own lower cost

coefficient or a higher cost coefficient of the other partyMoreover a large part of the φE curve is below 05 (byβs βr) which suggests that it is prone to contract (E) whenthe visibility cost coefficient of the fresh retailer is far beyondthat of the farm base according to incentive compatibilityconditions in Section 42 Indeed more and more retailerssource directly from farms and transport using self-builtlogistics to mitigate supply risk and quality risk whichmakes the retailerrsquos visibility cost coefficient often greater

20

30

40

50

600 650 700 750 800 850550α

pCwD

pDwE

(a)

1

2

3

4

5

600 650 700 750 800 850550α

vscCvsCvrC

vscDvsDvrD

(b)

20000

40000

60000

80000

100000

600 650 700 750 800 850550α

πCπsD πscD

πrD

(c)

025

030

035

040

045

050

055

600 650 700 750 800 850550α

φEφminφmax

(d)

Figure 4 e impacts of quality visibility sensitivity (a) Prices (b) Quality visibility (c) Profits (d) Allocation rates

Mathematical Problems in Engineering 13

than the supplierrsquos and thus it is more likely to coordinatethe supply chain with contract (E)

It is also meaningful to examine the sensitivity of eachconstraint condition to each parameter e assumption inProposition 1 is the condition to ensure a profitable supplychain coordination denoting as Cdt1 while the incentivecompatibility conditions in Proposition 3 guarantees thecompaniesrsquo participation denoting as Cdt2 for the supplierand Cdt3 for the retailer respectively We can get the in-terval of each parameter with other parameters fixed (thestrictest condition where the number is derived is in theparentheses) λgt5674(Cdt1) (Cdt1)92932gtαgt0 (Cdt2)

284900gtβsgt81126(Cdt1) (Cdt3)567735gtβrgt90388(Cdt1) e result shows that as long as Cdt1 is met what

stops the company is its own cost coefficient of qualityvisibility erefore it could be the most important thing toreduce the unit cost of visibility efforts and a number ofcompanies good at information systems are working on thatFor example Frigga launches a low-cost real-time and anultra-low-cost USB temperature recorder for cold chainlogistics and both of them are disposable and can be used formore than 90 days (see its website httpswwwfriggatechcom)

Finally from the perspective of the overall supplychain or the regulators it is good for improving qualityvisibility to promote IT innovation upgrade industriesand consumption and create a conducive environmentfor sign a contract

20

30

40

50

1700 1900 2100 23001500βs

pCwD

pDwE

(a)

1

2

3

4

5

1700 1900 2100 23001500βs

vscCvsCvrC

vscDvsDvrD

(b)

1700 1900 2100 23001500βs

20000

40000

60000

80000

100000

πCπsD πscD

πrD

(c)

1700 1900 2100 23001500βs

03

04

05

06

φEφminφmax

(d)

Figure 5 e impacts of the supplierrsquos visibility cost coefficient (a) Prices (b) Quality visibility (c) Profits (d) Allocation rates

14 Mathematical Problems in Engineering

been coordinated for more profits and quality visibilitythe companies may consider (i) promoting food posi-tioning and acquiring more price-insensitive consumerssuch as by launching ldquoorganic chickenrdquo or minipackagingfor one meal by the farm base and locating in luxurycommunities or office buildings for the fresh retailer (ii)advocating for the traceable and trackable whole-chainquality and safety from farm to table in order to attractconsumers focused on quality visibility and (iii) pur-chasing or renting a more popular cost-effective visibilitysystem and improving the interfaces and compatibility ofvisibility systems

As shown in Figures 4(a)ndash4(c) when consumers paymore attention to quality visibility the companyrsquos visibilityinvestment increases demand which compensates for thedemand reduction caused by price inflation In this respecthigher quality visibility sensitivity rapidly increases theoptimal retail price in the supply chain that is consumersrsquowillingness to pay for a high-quality visibility food In thiscase for a unit increase in quality visibility consumers arewilling to pay an extra 7 CNY (αλ) as the food premium forhigh-quality visibility

e increased quality visibility sensitivity also leads toa broader range of the profit allocation rate (increased

90 100 110 12080λ

20

30

40

50

pCwD

pDwE

(a)

90 100 110 12080λ

1

2

3

4

5

vscCvsCvrC

vscDvsDvrD

(b)

90 100 110 12080λ

120000

100000

80000

60000

40000

20000

πCπsD πscD

πrD

(c)

90 100 110 12080λ

025

030

035

040

045

050

055

φEφminφmax

(d)

Figure 3 e impacts of price sensitivity (a) Prices (b) Quality visibility (c) Profits (d) Allocation rates

12 Mathematical Problems in Engineering

φmax and decreased φmin) from Figure 4(d) while theother three parameters still have the opposite effect andnarrow the range erefore it is easier to realize supplychain coordination with a high visibility sensitivity lowprice sensibility or low-quality visibility cost coefficient

In addition a significant impact of the visibility costcoefficient on the contract (E) is observed in Figures 5(d)and 6(d) e fresh retailer (or the farm base) seizes a largershare of the supply chain profit with its own lower cost

coefficient or a higher cost coefficient of the other partyMoreover a large part of the φE curve is below 05 (byβs βr) which suggests that it is prone to contract (E) whenthe visibility cost coefficient of the fresh retailer is far beyondthat of the farm base according to incentive compatibilityconditions in Section 42 Indeed more and more retailerssource directly from farms and transport using self-builtlogistics to mitigate supply risk and quality risk whichmakes the retailerrsquos visibility cost coefficient often greater

20

30

40

50

600 650 700 750 800 850550α

pCwD

pDwE

(a)

1

2

3

4

5

600 650 700 750 800 850550α

vscCvsCvrC

vscDvsDvrD

(b)

20000

40000

60000

80000

100000

600 650 700 750 800 850550α

πCπsD πscD

πrD

(c)

025

030

035

040

045

050

055

600 650 700 750 800 850550α

φEφminφmax

(d)

Figure 4 e impacts of quality visibility sensitivity (a) Prices (b) Quality visibility (c) Profits (d) Allocation rates

Mathematical Problems in Engineering 13

than the supplierrsquos and thus it is more likely to coordinatethe supply chain with contract (E)

It is also meaningful to examine the sensitivity of eachconstraint condition to each parameter e assumption inProposition 1 is the condition to ensure a profitable supplychain coordination denoting as Cdt1 while the incentivecompatibility conditions in Proposition 3 guarantees thecompaniesrsquo participation denoting as Cdt2 for the supplierand Cdt3 for the retailer respectively We can get the in-terval of each parameter with other parameters fixed (thestrictest condition where the number is derived is in theparentheses) λgt5674(Cdt1) (Cdt1)92932gtαgt0 (Cdt2)

284900gtβsgt81126(Cdt1) (Cdt3)567735gtβrgt90388(Cdt1) e result shows that as long as Cdt1 is met what

stops the company is its own cost coefficient of qualityvisibility erefore it could be the most important thing toreduce the unit cost of visibility efforts and a number ofcompanies good at information systems are working on thatFor example Frigga launches a low-cost real-time and anultra-low-cost USB temperature recorder for cold chainlogistics and both of them are disposable and can be used formore than 90 days (see its website httpswwwfriggatechcom)

Finally from the perspective of the overall supplychain or the regulators it is good for improving qualityvisibility to promote IT innovation upgrade industriesand consumption and create a conducive environmentfor sign a contract

20

30

40

50

1700 1900 2100 23001500βs

pCwD

pDwE

(a)

1

2

3

4

5

1700 1900 2100 23001500βs

vscCvsCvrC

vscDvsDvrD

(b)

1700 1900 2100 23001500βs

20000

40000

60000

80000

100000

πCπsD πscD

πrD

(c)

1700 1900 2100 23001500βs

03

04

05

06

φEφminφmax

(d)

Figure 5 e impacts of the supplierrsquos visibility cost coefficient (a) Prices (b) Quality visibility (c) Profits (d) Allocation rates

14 Mathematical Problems in Engineering

φmax and decreased φmin) from Figure 4(d) while theother three parameters still have the opposite effect andnarrow the range erefore it is easier to realize supplychain coordination with a high visibility sensitivity lowprice sensibility or low-quality visibility cost coefficient

In addition a significant impact of the visibility costcoefficient on the contract (E) is observed in Figures 5(d)and 6(d) e fresh retailer (or the farm base) seizes a largershare of the supply chain profit with its own lower cost

coefficient or a higher cost coefficient of the other partyMoreover a large part of the φE curve is below 05 (byβs βr) which suggests that it is prone to contract (E) whenthe visibility cost coefficient of the fresh retailer is far beyondthat of the farm base according to incentive compatibilityconditions in Section 42 Indeed more and more retailerssource directly from farms and transport using self-builtlogistics to mitigate supply risk and quality risk whichmakes the retailerrsquos visibility cost coefficient often greater

20

30

40

50

600 650 700 750 800 850550α

pCwD

pDwE

(a)

1

2

3

4

5

600 650 700 750 800 850550α

vscCvsCvrC

vscDvsDvrD

(b)

20000

40000

60000

80000

100000

600 650 700 750 800 850550α

πCπsD πscD

πrD

(c)

025

030

035

040

045

050

055

600 650 700 750 800 850550α

φEφminφmax

(d)

Figure 4 e impacts of quality visibility sensitivity (a) Prices (b) Quality visibility (c) Profits (d) Allocation rates

Mathematical Problems in Engineering 13

than the supplierrsquos and thus it is more likely to coordinatethe supply chain with contract (E)

It is also meaningful to examine the sensitivity of eachconstraint condition to each parameter e assumption inProposition 1 is the condition to ensure a profitable supplychain coordination denoting as Cdt1 while the incentivecompatibility conditions in Proposition 3 guarantees thecompaniesrsquo participation denoting as Cdt2 for the supplierand Cdt3 for the retailer respectively We can get the in-terval of each parameter with other parameters fixed (thestrictest condition where the number is derived is in theparentheses) λgt5674(Cdt1) (Cdt1)92932gtαgt0 (Cdt2)

284900gtβsgt81126(Cdt1) (Cdt3)567735gtβrgt90388(Cdt1) e result shows that as long as Cdt1 is met what

stops the company is its own cost coefficient of qualityvisibility erefore it could be the most important thing toreduce the unit cost of visibility efforts and a number ofcompanies good at information systems are working on thatFor example Frigga launches a low-cost real-time and anultra-low-cost USB temperature recorder for cold chainlogistics and both of them are disposable and can be used formore than 90 days (see its website httpswwwfriggatechcom)

Finally from the perspective of the overall supplychain or the regulators it is good for improving qualityvisibility to promote IT innovation upgrade industriesand consumption and create a conducive environmentfor sign a contract

20

30

40

50

1700 1900 2100 23001500βs

pCwD

pDwE

(a)

1

2

3

4

5

1700 1900 2100 23001500βs

vscCvsCvrC

vscDvsDvrD

(b)

1700 1900 2100 23001500βs

20000

40000

60000

80000

100000

πCπsD πscD

πrD

(c)

1700 1900 2100 23001500βs

03

04

05

06

φEφminφmax

(d)

Figure 5 e impacts of the supplierrsquos visibility cost coefficient (a) Prices (b) Quality visibility (c) Profits (d) Allocation rates

14 Mathematical Problems in Engineering

than the supplierrsquos and thus it is more likely to coordinatethe supply chain with contract (E)

It is also meaningful to examine the sensitivity of eachconstraint condition to each parameter e assumption inProposition 1 is the condition to ensure a profitable supplychain coordination denoting as Cdt1 while the incentivecompatibility conditions in Proposition 3 guarantees thecompaniesrsquo participation denoting as Cdt2 for the supplierand Cdt3 for the retailer respectively We can get the in-terval of each parameter with other parameters fixed (thestrictest condition where the number is derived is in theparentheses) λgt5674(Cdt1) (Cdt1)92932gtαgt0 (Cdt2)

284900gtβsgt81126(Cdt1) (Cdt3)567735gtβrgt90388(Cdt1) e result shows that as long as Cdt1 is met what

stops the company is its own cost coefficient of qualityvisibility erefore it could be the most important thing toreduce the unit cost of visibility efforts and a number ofcompanies good at information systems are working on thatFor example Frigga launches a low-cost real-time and anultra-low-cost USB temperature recorder for cold chainlogistics and both of them are disposable and can be used formore than 90 days (see its website httpswwwfriggatechcom)

Finally from the perspective of the overall supplychain or the regulators it is good for improving qualityvisibility to promote IT innovation upgrade industriesand consumption and create a conducive environmentfor sign a contract

20

30

40

50

1700 1900 2100 23001500βs

pCwD

pDwE

(a)

1

2

3

4

5

1700 1900 2100 23001500βs

vscCvsCvrC

vscDvsDvrD

(b)

1700 1900 2100 23001500βs

20000

40000

60000

80000

100000

πCπsD πscD

πrD

(c)

1700 1900 2100 23001500βs

03

04

05

06

φEφminφmax

(d)

Figure 5 e impacts of the supplierrsquos visibility cost coefficient (a) Prices (b) Quality visibility (c) Profits (d) Allocation rates

14 Mathematical Problems in Engineering

6 Conclusions

is paper examines a food supply chain decision-makingproblem in which both the supplier and the retailer deter-mine prices and quality visibility and both demand andcosts depend on each companyrsquos quality visibility Wepropose two price discount contracts with effort alignmentand with cost-sharing to coordinate the supply chain Afterdiscovering a Pareto improvement opportunity by com-paring the supply chain performances under the centralizedand decentralized (wholesale price contract) situations wedemonstrate that the two modified contracts other than acommon revenue-sharing contract could coordinate thesupply chain and we give their boundary conditions ex-cluding the deviated actions eir strengths and limitations

are presented as well as their feasibility and stability whichare confirmed by a practical case of a chicken supply chainSensitivity analysis is conducted to reveal the impacts of fourexogenous coefficients on the decisions and performances ofthe supply chain which provide some meaningful mana-gerial implications related to supply chain quality visibility

e results prove that the decentralized supply chain isfar inferior to the centralized supply chain in terms of bothquality visibility and profit due to the existence of doublemarginalization Both the supplier and the retailer haveenough incentives to realize supply chain coordination froman inefficient wholesale price contract However othersimple contracts are also invalid unless more than oneparameter is introduced when the profit functions of all theplayers depend on the prices and efforts of both the

20

30

40

50

2300 2500 2700 29002100βr

pCwD

pDwE

(a)

1

2

3

4

5

2300 2500 2700 29002100βr

vscCvsCvrC

vscDvsDvrD

(b)

2300 2500 2700 29002100βr

20000

40000

60000

80000

100000

120000

πCπsD πscD

πrD

(c)

2300 2500 2700 29002100βr

03

04

05

06

φEφminφmax

(d)

Figure 6 e impacts of the retailerrsquos visibility cost coefficient (a) Prices (b) Quality visibility (c) Profits (d) Allocation rates

Mathematical Problems in Engineering 15

upstream and downstream supply chains in this modelwhich is different from most of the existing studies eeffort alignment and cost-sharing policies correct the dis-tortions in the decisions on multiple layers e former issimpler at a fixed profit allocation rate whereas the latter canarbitrarily allocate supply chain profits to the supplier andretailer despite a larger information set being needed Inreality considering that the quality visibility marginal costsof fresh retailers are relatively high the incentive compat-ibility condition of the retailer seems to be more easilysatisfied when an opportunity profit exits Furthermoresince the coordination contracts improve everyonersquos qualityvisibility considerably there is still a good chance for thecompanies to pursue coordination even if eitherrsquos profit isslightly eroded which guarantees the practical applicabilityof the two contracts

Supply chain coordination not only provides opportu-nities to improve the performance of supply chain companiesbut it also increases sales and consumer welfare at a lowerretail price which implies potential benefits such as higherbrand awareness and goodwill It may be effective to improvesupply chain profit and quality visibility using improved foodpositioning publicity for quality assurance or a more cost-effective visibility system Furthermore IT innovation in-dustries and consumption upgradation and contractingconvenience also help from the holistic point of view

Our study has limitations that lead to further researchsuggestions e demand function in the model is classicallylinear which may be applicable for foods with elastic de-mand and within certain ranges of price and quality visi-bility However daily consumption products exceptnecessities generally have high elasticities and so do each ofthe competing brands in the same category of necessities Itwould be interesting to discuss different demand functionsand pricing models and examine the effects of revenue-sharing buyback quantity flexibility and quantitypricediscount contracts in the case that quality visibility effort isnot observed Another research direction in the future is tostudy the quality visibility strategies in the multisuppliermultiretailer or multistage supply chain

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

is research was funded by the National Natural ScienceFoundation of China (grant numbers 71390330 and71371151) Major Program of National Fund of Philosophyand Social Science of China (grant number 15ZDB150) andNational Key Research and Development Program of China(grant number 2019YFB1704103)

References

[1] A Marucheck N Greis C Mena and L Cai ldquoProduct safetyand security in the global supply chain issues challenges andresearch opportunitiesrdquo Journal of Operations Managementvol 29 no 7-8 pp 707ndash720 2011

[2] C Speier J M Whipple D J Closs and M D Voss ldquoGlobalsupply chain design considerations mitigating product safetyand security risksrdquo Journal of Operations Managementvol 29 no 7-8 pp 721ndash736 2011

[3] Y Sheffi ldquoPreparing for disruptions through early detectionrdquoMIT SloanManagement Review vol 57 no 1 pp 31ndash42 2015

[4] X Wang and D Li ldquoA dynamic product quality evaluationbased pricing model for perishable food supply chainsrdquoOmega vol 40 no 6 pp 906ndash917 2012

[5] M S Sodhi and C S Tang ldquoResearch opportunities in supplychain transparencyrdquo Production and Operations Manage-ment vol 28 no 12 pp 2946ndash2959 2019

[6] GEODIS Supply Chain Worldwide Survey Geodis FreightForwarding 2017

[7] N Granados and A Gupta ldquoTransparency strategy com-peting with information in a digital worldrdquo MIS Quarterlyvol 37 no 2 pp 637ndash641 2013

[8] N El Benni H Stolz R Home et al ldquoProduct attributes andconsumer attitudes affecting the preferences for infant milkformula in Chinamdasha latent class approachrdquo Food Quality andPreference vol 71 pp 25ndash33 2019

[9] X Q Cai J Chen Y B Xiao and X L Xu ldquoOptimization andcoordination of fresh product supply chains with freshness-keeping effortrdquo Production and Operations Managementvol 19 no 3 pp 261ndash278 2010

[10] S Somapa M Cools andW Dullaert ldquoCharacterizing supplychain visibilitymdasha literature reviewrdquo Ee InternationalJournal of Logistics Management vol 29 no 1 pp 308ndash3392018

[11] R C Lamming N D Caldwell D A Harrison andW Phillips ldquoTransparency in supply relationships conceptand practicerdquo Journal of Supply Chain Management vol 37no 3 pp 4ndash10 2001

[12] P A Bartlett D M Julien and T S Baines ldquoImprovingsupply chain performance through improved visibilityrdquo EeInternational Journal of Logistics Management vol 18 no 2pp 294ndash313 2007

[13] J Holmstrom K Framling and T Ala-Risku ldquoe uses oftracking in operations management synthesis of a researchprogramrdquo International Journal of Production Economicsvol 126 no 2 pp 267ndash275 2010

[14] A Musa A Gunasekaran and Y Yusuf ldquoSupply chainproduct visibility methods systems and impactsrdquo ExpertSystems with Applications vol 41 no 1 pp 176ndash194 2014

[15] T Kraft L Valdes and Y Zheng ldquoSupply chain visibility andsocial responsibility investigating consumersrsquo behaviors andmotivesrdquo Manufacturing amp Service Operations Managementvol 20 no 4 pp 617ndash636 2018

[16] M Barratt and A Oke ldquoAntecedents of supply chain visibilityin retail supply chains a resource-based theory perspectiverdquoJournal of Operations Management vol 25 no 6 pp 1217ndash1233 2007

[17] Y K Tse and K H Tan ldquoManaging product quality risk in amulti-tier global supply chainrdquo International Journal ofProduction Research vol 49 no 1 pp 139ndash158 2011

[18] N Granados A Gupta and R J Kauffman ldquoResearchcommentary-information transparency in business-to-con-sumer markets concepts framework and research agendardquo

16 Mathematical Problems in Engineering

Information Systems Research vol 21 no 2 pp 207ndash2262010

[19] M Caridi L Crippa A Perego A Sianesi and A TuminoldquoDo virtuality and complexity affect supply chain visibilityrdquoInternational Journal of Production Economics vol 127 no 2pp 372ndash383 2010

[20] M Caridi A Moretto A Perego and A Tumino ldquoebenefits of supply chain visibility a value assessment modelrdquoInternational Journal of Production Economics vol 151pp 1ndash19 2014

[21] D Delen B C Hardgrave and R Sharda ldquoRFID for bettersupply-chain management through enhanced informationvisibilityrdquo Production and Operations Management vol 16no 5 pp 613ndash624 2007

[22] B D Williams J Roh T Tokar and M Swink ldquoLeveragingsupply chain visibility for responsiveness the moderating roleof internal integrationrdquo Journal of Operations Managementvol 31 no 7-8 pp 543ndash554 2013

[23] Y K Tse and K H Tan ldquoManaging product quality risk andvisibility in multi-layer supply chainrdquo International Journal ofProduction Economics vol 139 no 1 pp 49ndash57 2012

[24] L Guo ldquoQuality disclosure formats in a distribution channelrdquoManagement Science vol 55 no 9 pp 1513ndash1526 2009

[25] M Zhao C Dong and T C E Cheng ldquoQuality disclosurestrategies for small business enterprises in a competitivemarketplacerdquo European Journal of Operational Researchvol 270 no 1 pp 218ndash229 2018

[26] J Wu X Zhai C Zhang and X Liu ldquoSharing quality in-formation in a dual-supplier network a game theoreticperspectiverdquo International Journal of Production Researchvol 49 no 1 pp 199ndash214 2011

[27] S Piramuthu P Farahani and M Grunow ldquoRFID-generatedtraceability for contaminated product recall in perishable foodsupply networksrdquo European Journal of Operational Researchvol 225 no 2 pp 253ndash262 2013

[28] B Ghosh and M R Galbreth ldquoe impact of consumer at-tentiveness and search costs on firm quality disclosure acompetitive analysisrdquo Management Science vol 59 no 11pp 2604ndash2621 2013

[29] C Riganelli and A Marchini ldquoGovernance and quality dis-closure the palm oil issuerdquo British Food Journal vol 119no 8 pp 1718ndash1731 2017

[30] R W Buell and B Kalkanci ldquoHow transparency into internaland external responsibility initiatives influences consumerchoicerdquo Management Science 2020

[31] S Baiman P E Fischer and M V Rajan ldquoInformationcontracting and quality costsrdquo Management Science vol 46no 6 pp 776ndash789 2000

[32] Y Hou F Wei S X Li Z Huang and A Ashley ldquoCoor-dination and performance analysis for a three-echelon supplychain with a revenue sharing contractrdquo International Journalof Production Research vol 55 no 1 pp 202ndash227 2017

[33] G P Cachon andM A Lariviere ldquoSupply chain coordinationwith revenue-sharing contracts strengths and limitationsrdquoManagement Science vol 51 no 1 pp 30ndash44 2005

[34] T Xiao D Yang and H Shen ldquoCoordinating a supply chainwith a quality assurance policy via a revenue-sharing con-tractrdquo International Journal of Production Research vol 49no 1 pp 99ndash120 2011

[35] G Kong S Rajagopalan and H Zhang ldquoRevenue sharing andinformation leakage in a supply chainrdquo Management Sciencevol 59 no 3 pp 556ndash572 2013

[36] F Bernstein and A Federgruen ldquoDecentralized supply chainswith competing retailers under demand uncertaintyrdquo Man-agement Science vol 51 no 1 pp 18ndash29 2005

[37] G Cai Z G Zhang and M Zhang ldquoGame theoretical per-spectives on dual-channel supply chain competition withprice discounts and pricing schemesrdquo International Journal ofProduction Economics vol 117 no 1 pp 80ndash96 2009

[38] S R Bhaskaran and V Krishnan ldquoEffort revenue and costsharing mechanisms for collaborative new product devel-opmentrdquo Management Science vol 55 no 7 pp 1152ndash11692009

[39] H Krishnan R Kapuscinski and D A Butz ldquoCoordinatingcontracts for decentralized supply chains with retailer pro-motional effortrdquo Management Science vol 50 no 1pp 48ndash63 2004

[40] L Lambertini ldquoCoordinating research and development ef-forts for quality improvement along a supply chainrdquo Euro-pean Journal of Operational Research vol 270 no 2pp 599ndash605 2018

[41] B Gu Y Fu and Y Li ldquoFresh-keeping effort and channelperformance in a fresh product supply chain with loss-averseconsumersrsquo returnsrdquo Mathematical Problems in Engineeringvol 2018 Article ID 4717094 20 pages 2018

[42] H Demirkan and H K Cheng ldquoe risk and informationsharing of application services supply chainrdquo EuropeanJournal of Operational Research vol 187 no 3 pp 765ndash7842008

Mathematical Problems in Engineering 17

upstream and downstream supply chains in this modelwhich is different from most of the existing studies eeffort alignment and cost-sharing policies correct the dis-tortions in the decisions on multiple layers e former issimpler at a fixed profit allocation rate whereas the latter canarbitrarily allocate supply chain profits to the supplier andretailer despite a larger information set being needed Inreality considering that the quality visibility marginal costsof fresh retailers are relatively high the incentive compat-ibility condition of the retailer seems to be more easilysatisfied when an opportunity profit exits Furthermoresince the coordination contracts improve everyonersquos qualityvisibility considerably there is still a good chance for thecompanies to pursue coordination even if eitherrsquos profit isslightly eroded which guarantees the practical applicabilityof the two contracts

Supply chain coordination not only provides opportu-nities to improve the performance of supply chain companiesbut it also increases sales and consumer welfare at a lowerretail price which implies potential benefits such as higherbrand awareness and goodwill It may be effective to improvesupply chain profit and quality visibility using improved foodpositioning publicity for quality assurance or a more cost-effective visibility system Furthermore IT innovation in-dustries and consumption upgradation and contractingconvenience also help from the holistic point of view

Our study has limitations that lead to further researchsuggestions e demand function in the model is classicallylinear which may be applicable for foods with elastic de-mand and within certain ranges of price and quality visi-bility However daily consumption products exceptnecessities generally have high elasticities and so do each ofthe competing brands in the same category of necessities Itwould be interesting to discuss different demand functionsand pricing models and examine the effects of revenue-sharing buyback quantity flexibility and quantitypricediscount contracts in the case that quality visibility effort isnot observed Another research direction in the future is tostudy the quality visibility strategies in the multisuppliermultiretailer or multistage supply chain

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

is research was funded by the National Natural ScienceFoundation of China (grant numbers 71390330 and71371151) Major Program of National Fund of Philosophyand Social Science of China (grant number 15ZDB150) andNational Key Research and Development Program of China(grant number 2019YFB1704103)

References

[1] A Marucheck N Greis C Mena and L Cai ldquoProduct safetyand security in the global supply chain issues challenges andresearch opportunitiesrdquo Journal of Operations Managementvol 29 no 7-8 pp 707ndash720 2011

[2] C Speier J M Whipple D J Closs and M D Voss ldquoGlobalsupply chain design considerations mitigating product safetyand security risksrdquo Journal of Operations Managementvol 29 no 7-8 pp 721ndash736 2011

[3] Y Sheffi ldquoPreparing for disruptions through early detectionrdquoMIT SloanManagement Review vol 57 no 1 pp 31ndash42 2015

[4] X Wang and D Li ldquoA dynamic product quality evaluationbased pricing model for perishable food supply chainsrdquoOmega vol 40 no 6 pp 906ndash917 2012

[5] M S Sodhi and C S Tang ldquoResearch opportunities in supplychain transparencyrdquo Production and Operations Manage-ment vol 28 no 12 pp 2946ndash2959 2019

[6] GEODIS Supply Chain Worldwide Survey Geodis FreightForwarding 2017

[7] N Granados and A Gupta ldquoTransparency strategy com-peting with information in a digital worldrdquo MIS Quarterlyvol 37 no 2 pp 637ndash641 2013

[8] N El Benni H Stolz R Home et al ldquoProduct attributes andconsumer attitudes affecting the preferences for infant milkformula in Chinamdasha latent class approachrdquo Food Quality andPreference vol 71 pp 25ndash33 2019

[9] X Q Cai J Chen Y B Xiao and X L Xu ldquoOptimization andcoordination of fresh product supply chains with freshness-keeping effortrdquo Production and Operations Managementvol 19 no 3 pp 261ndash278 2010

[10] S Somapa M Cools andW Dullaert ldquoCharacterizing supplychain visibilitymdasha literature reviewrdquo Ee InternationalJournal of Logistics Management vol 29 no 1 pp 308ndash3392018

[11] R C Lamming N D Caldwell D A Harrison andW Phillips ldquoTransparency in supply relationships conceptand practicerdquo Journal of Supply Chain Management vol 37no 3 pp 4ndash10 2001

[12] P A Bartlett D M Julien and T S Baines ldquoImprovingsupply chain performance through improved visibilityrdquo EeInternational Journal of Logistics Management vol 18 no 2pp 294ndash313 2007

[13] J Holmstrom K Framling and T Ala-Risku ldquoe uses oftracking in operations management synthesis of a researchprogramrdquo International Journal of Production Economicsvol 126 no 2 pp 267ndash275 2010

[14] A Musa A Gunasekaran and Y Yusuf ldquoSupply chainproduct visibility methods systems and impactsrdquo ExpertSystems with Applications vol 41 no 1 pp 176ndash194 2014

[15] T Kraft L Valdes and Y Zheng ldquoSupply chain visibility andsocial responsibility investigating consumersrsquo behaviors andmotivesrdquo Manufacturing amp Service Operations Managementvol 20 no 4 pp 617ndash636 2018

[16] M Barratt and A Oke ldquoAntecedents of supply chain visibilityin retail supply chains a resource-based theory perspectiverdquoJournal of Operations Management vol 25 no 6 pp 1217ndash1233 2007

[17] Y K Tse and K H Tan ldquoManaging product quality risk in amulti-tier global supply chainrdquo International Journal ofProduction Research vol 49 no 1 pp 139ndash158 2011

[18] N Granados A Gupta and R J Kauffman ldquoResearchcommentary-information transparency in business-to-con-sumer markets concepts framework and research agendardquo

16 Mathematical Problems in Engineering

Information Systems Research vol 21 no 2 pp 207ndash2262010

[19] M Caridi L Crippa A Perego A Sianesi and A TuminoldquoDo virtuality and complexity affect supply chain visibilityrdquoInternational Journal of Production Economics vol 127 no 2pp 372ndash383 2010

[20] M Caridi A Moretto A Perego and A Tumino ldquoebenefits of supply chain visibility a value assessment modelrdquoInternational Journal of Production Economics vol 151pp 1ndash19 2014

[21] D Delen B C Hardgrave and R Sharda ldquoRFID for bettersupply-chain management through enhanced informationvisibilityrdquo Production and Operations Management vol 16no 5 pp 613ndash624 2007

[22] B D Williams J Roh T Tokar and M Swink ldquoLeveragingsupply chain visibility for responsiveness the moderating roleof internal integrationrdquo Journal of Operations Managementvol 31 no 7-8 pp 543ndash554 2013

[23] Y K Tse and K H Tan ldquoManaging product quality risk andvisibility in multi-layer supply chainrdquo International Journal ofProduction Economics vol 139 no 1 pp 49ndash57 2012

[24] L Guo ldquoQuality disclosure formats in a distribution channelrdquoManagement Science vol 55 no 9 pp 1513ndash1526 2009

[25] M Zhao C Dong and T C E Cheng ldquoQuality disclosurestrategies for small business enterprises in a competitivemarketplacerdquo European Journal of Operational Researchvol 270 no 1 pp 218ndash229 2018

[26] J Wu X Zhai C Zhang and X Liu ldquoSharing quality in-formation in a dual-supplier network a game theoreticperspectiverdquo International Journal of Production Researchvol 49 no 1 pp 199ndash214 2011

[27] S Piramuthu P Farahani and M Grunow ldquoRFID-generatedtraceability for contaminated product recall in perishable foodsupply networksrdquo European Journal of Operational Researchvol 225 no 2 pp 253ndash262 2013

[28] B Ghosh and M R Galbreth ldquoe impact of consumer at-tentiveness and search costs on firm quality disclosure acompetitive analysisrdquo Management Science vol 59 no 11pp 2604ndash2621 2013

[29] C Riganelli and A Marchini ldquoGovernance and quality dis-closure the palm oil issuerdquo British Food Journal vol 119no 8 pp 1718ndash1731 2017

[30] R W Buell and B Kalkanci ldquoHow transparency into internaland external responsibility initiatives influences consumerchoicerdquo Management Science 2020

[31] S Baiman P E Fischer and M V Rajan ldquoInformationcontracting and quality costsrdquo Management Science vol 46no 6 pp 776ndash789 2000

[32] Y Hou F Wei S X Li Z Huang and A Ashley ldquoCoor-dination and performance analysis for a three-echelon supplychain with a revenue sharing contractrdquo International Journalof Production Research vol 55 no 1 pp 202ndash227 2017

[33] G P Cachon andM A Lariviere ldquoSupply chain coordinationwith revenue-sharing contracts strengths and limitationsrdquoManagement Science vol 51 no 1 pp 30ndash44 2005

[34] T Xiao D Yang and H Shen ldquoCoordinating a supply chainwith a quality assurance policy via a revenue-sharing con-tractrdquo International Journal of Production Research vol 49no 1 pp 99ndash120 2011

[35] G Kong S Rajagopalan and H Zhang ldquoRevenue sharing andinformation leakage in a supply chainrdquo Management Sciencevol 59 no 3 pp 556ndash572 2013

[36] F Bernstein and A Federgruen ldquoDecentralized supply chainswith competing retailers under demand uncertaintyrdquo Man-agement Science vol 51 no 1 pp 18ndash29 2005

[37] G Cai Z G Zhang and M Zhang ldquoGame theoretical per-spectives on dual-channel supply chain competition withprice discounts and pricing schemesrdquo International Journal ofProduction Economics vol 117 no 1 pp 80ndash96 2009

[38] S R Bhaskaran and V Krishnan ldquoEffort revenue and costsharing mechanisms for collaborative new product devel-opmentrdquo Management Science vol 55 no 7 pp 1152ndash11692009

[39] H Krishnan R Kapuscinski and D A Butz ldquoCoordinatingcontracts for decentralized supply chains with retailer pro-motional effortrdquo Management Science vol 50 no 1pp 48ndash63 2004

[40] L Lambertini ldquoCoordinating research and development ef-forts for quality improvement along a supply chainrdquo Euro-pean Journal of Operational Research vol 270 no 2pp 599ndash605 2018

[41] B Gu Y Fu and Y Li ldquoFresh-keeping effort and channelperformance in a fresh product supply chain with loss-averseconsumersrsquo returnsrdquo Mathematical Problems in Engineeringvol 2018 Article ID 4717094 20 pages 2018

[42] H Demirkan and H K Cheng ldquoe risk and informationsharing of application services supply chainrdquo EuropeanJournal of Operational Research vol 187 no 3 pp 765ndash7842008

Mathematical Problems in Engineering 17

Information Systems Research vol 21 no 2 pp 207ndash2262010

[19] M Caridi L Crippa A Perego A Sianesi and A TuminoldquoDo virtuality and complexity affect supply chain visibilityrdquoInternational Journal of Production Economics vol 127 no 2pp 372ndash383 2010

[20] M Caridi A Moretto A Perego and A Tumino ldquoebenefits of supply chain visibility a value assessment modelrdquoInternational Journal of Production Economics vol 151pp 1ndash19 2014

[21] D Delen B C Hardgrave and R Sharda ldquoRFID for bettersupply-chain management through enhanced informationvisibilityrdquo Production and Operations Management vol 16no 5 pp 613ndash624 2007

[22] B D Williams J Roh T Tokar and M Swink ldquoLeveragingsupply chain visibility for responsiveness the moderating roleof internal integrationrdquo Journal of Operations Managementvol 31 no 7-8 pp 543ndash554 2013

[23] Y K Tse and K H Tan ldquoManaging product quality risk andvisibility in multi-layer supply chainrdquo International Journal ofProduction Economics vol 139 no 1 pp 49ndash57 2012

[24] L Guo ldquoQuality disclosure formats in a distribution channelrdquoManagement Science vol 55 no 9 pp 1513ndash1526 2009

[25] M Zhao C Dong and T C E Cheng ldquoQuality disclosurestrategies for small business enterprises in a competitivemarketplacerdquo European Journal of Operational Researchvol 270 no 1 pp 218ndash229 2018

[26] J Wu X Zhai C Zhang and X Liu ldquoSharing quality in-formation in a dual-supplier network a game theoreticperspectiverdquo International Journal of Production Researchvol 49 no 1 pp 199ndash214 2011

[27] S Piramuthu P Farahani and M Grunow ldquoRFID-generatedtraceability for contaminated product recall in perishable foodsupply networksrdquo European Journal of Operational Researchvol 225 no 2 pp 253ndash262 2013

[28] B Ghosh and M R Galbreth ldquoe impact of consumer at-tentiveness and search costs on firm quality disclosure acompetitive analysisrdquo Management Science vol 59 no 11pp 2604ndash2621 2013

[29] C Riganelli and A Marchini ldquoGovernance and quality dis-closure the palm oil issuerdquo British Food Journal vol 119no 8 pp 1718ndash1731 2017

[30] R W Buell and B Kalkanci ldquoHow transparency into internaland external responsibility initiatives influences consumerchoicerdquo Management Science 2020

[31] S Baiman P E Fischer and M V Rajan ldquoInformationcontracting and quality costsrdquo Management Science vol 46no 6 pp 776ndash789 2000

[32] Y Hou F Wei S X Li Z Huang and A Ashley ldquoCoor-dination and performance analysis for a three-echelon supplychain with a revenue sharing contractrdquo International Journalof Production Research vol 55 no 1 pp 202ndash227 2017

[33] G P Cachon andM A Lariviere ldquoSupply chain coordinationwith revenue-sharing contracts strengths and limitationsrdquoManagement Science vol 51 no 1 pp 30ndash44 2005

[34] T Xiao D Yang and H Shen ldquoCoordinating a supply chainwith a quality assurance policy via a revenue-sharing con-tractrdquo International Journal of Production Research vol 49no 1 pp 99ndash120 2011

[35] G Kong S Rajagopalan and H Zhang ldquoRevenue sharing andinformation leakage in a supply chainrdquo Management Sciencevol 59 no 3 pp 556ndash572 2013

[36] F Bernstein and A Federgruen ldquoDecentralized supply chainswith competing retailers under demand uncertaintyrdquo Man-agement Science vol 51 no 1 pp 18ndash29 2005

[37] G Cai Z G Zhang and M Zhang ldquoGame theoretical per-spectives on dual-channel supply chain competition withprice discounts and pricing schemesrdquo International Journal ofProduction Economics vol 117 no 1 pp 80ndash96 2009

[38] S R Bhaskaran and V Krishnan ldquoEffort revenue and costsharing mechanisms for collaborative new product devel-opmentrdquo Management Science vol 55 no 7 pp 1152ndash11692009

[39] H Krishnan R Kapuscinski and D A Butz ldquoCoordinatingcontracts for decentralized supply chains with retailer pro-motional effortrdquo Management Science vol 50 no 1pp 48ndash63 2004

[40] L Lambertini ldquoCoordinating research and development ef-forts for quality improvement along a supply chainrdquo Euro-pean Journal of Operational Research vol 270 no 2pp 599ndash605 2018

[41] B Gu Y Fu and Y Li ldquoFresh-keeping effort and channelperformance in a fresh product supply chain with loss-averseconsumersrsquo returnsrdquo Mathematical Problems in Engineeringvol 2018 Article ID 4717094 20 pages 2018

[42] H Demirkan and H K Cheng ldquoe risk and informationsharing of application services supply chainrdquo EuropeanJournal of Operational Research vol 187 no 3 pp 765ndash7842008

Mathematical Problems in Engineering 17