Omega 38 (2010) 136 -- 144

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Omega

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Selecting sourcing partners for amake-to-order supply chain

Jinfeng Yuea,∗, Yu Xiaa, Thuhang Tranb

aDepartment of Management and Marketing, Jennings Jones College of Business, Middle Tennessee State University, MTSU Box 75, Murfreesboro, TN 37132, USAbDepartment of Management and Marketing, Middle Tennessee State University, Jennings Jones College of Business, MTSU Box 449, Murfreesboro, TN 37132, USA

A R T I C L E I N F O A B S T R A C T

Article history:Received 23 August 2008Accepted 23 July 2009This manuscript was processed by AreaEditor ChandraAvailable online 5 August 2009Keywords:Sourcing partner selectionMake-to-order supply chain managementPortfolioManufacturing

Make-to-order manufacturers face an idiosyncratic and complex situation in the sourcing selection pro-cess. Although they can source from several key suppliers, each order requires custom key parts thatcannot be stocked. Our research provides a decision model to facilitate the sourcing process for these man-ufacturers using information about their sourcing partners' cost and processing time. The manufacturercan calculate the total cost and on-time probability for all possible combinations of certified suppliers andkey part allotments to obtain a sourcing portfolio with several sourcing alternatives for a desired servicelevel. The portfolio allows the manufacturer to make trade-offs between cost and reliability to finish thejob on time. Additionally, the portfolio can be obtained for a given due date or for reduced due dates ina competitive bid situation. The portfolio approach allows the manufacturer to maintain control over thesourcing selection process by partnering with sourcing members to keep costs low without losing theneeded flexibility to meet customer demands.

© 2009 Elsevier Ltd. All rights reserved.

1. Research motivation and significance

Today's competitive market and rapidly evolving technology aredriving manufacturers to rethink their sourcing options in order tobe more flexible while still controlling costs. Multiple part suppliersand irregular delivery time requirements from customers make thesupplier selection process of a make-to-order manufacturer morecomplicated. Nonetheless, manufacturers can meet their strategicgoals more effectively and operate more efficiently by designing andmanaging their supply networks to find the best long-term sourc-ing solutions, regardless of the number of suppliers or whether thesupplies are outsourced or in-sourced. This research proposes a se-lection process to help the make-to-order manufacturer prioritizeand source from a menu of options.

As a recent analysis by the Gartner Group shows, manufactur-ers can enable capability building, global growth, increased agility,and profitability by treating suppliers as partners [1]. Through oper-ational integration with its suppliers, a manufacturer can gain sig-nificant production efficiencies as evidence of General Motors' (GM)Gravatai plant in Brazil [2]. Moreover, Procter & Gamble (P&G) hasshown how the use of a sourcing system based on expressive com-petition generated 9.6% savings on $3 billion of sourcing [3]. How-ever, both GM and P&G have smooth production processes where

∗ Corresponding author. Tel.: +16158985126; fax: +16158985308.E-mail addresses: jyue@mtsu.edu (J. Yue), axia@mtsu.edu (Y. Xia), ttran@mtsu.edu

(T. Tran).

0305-0483/$ - see front matter © 2009 Elsevier Ltd. All rights reserved.doi:10.1016/j.omega.2009.07.004

considerable research has already been thoroughly conducted. Inother manufacturing structures, just-in-time (JIT) and regular inven-tory control systems are not feasible because of special parts relatedwith each customer order. One example of this type of sourcingstructure can be found when Lucent Technology (recently acquiredby Alcatel) orders key parts from its sourcing partners to fulfill itscustomer orders of telephone switches [4]. Make-to-order manu-facturers like Lucent produce customer ordered products containingthousands of components. Customer orders may be very unstable,unpredictable, and usually require very short delivery time sincethey can be the results of winning bids. Each customer order iscustomized with specific requirements resulting in special orderingfor some key parts which cannot be pre-inventory, and the key partreceiving time and cost vary with each order. The slowest key partdetermines the make-to-order product starting processing time andthe final delivery time as well. In addition, in order to win the bid,the make-to-order manufacturer must submit a competitive deliverydate and an attractive bidding price or risk losing the contract. How-ever, an overly aggressive delivery date or/and bidding price maylead to delivery schedule slippage, loss of reputation, late penalties,and even loss of capital. In the worst case scenario, key componentshortages caused by booming demand and temporary insufficientcapacities of the key part sourcing partners become the bottlenecksfor the make-to-order manufacturer's serviceability. Therefore, themake-to-order manufacturers need some useful tools to help themto select the key part sourcing partners and determine the orderquantity for each of the partners in the fast changing environment.This research aims to introduce such a sourcing partner selection

J. Yue et al. / Omega 38 (2010) 136–144 137

tool for the make-to-order manufacturers when they face irregularcustomized orders and short delivery time. Unlike most existing lit-erature while only one factor is considered, our approach uses cost,available capacity, and stochastic processing time information of thecertified part suppliers—three most important factors in selection,and finally provides broad choices for the make-to-order manufac-turers.

The proposed sourcing partner selection process has several ad-vantages for the make-to-order manufacturers. First, the make-to-order manufacturer can cooperate with its sourcing partners andmake the selection independently, based on their capacities, cost,and processing time information, to decide on a sourcing solution tomeet its customers' needs. The manufacturer can eliminate key partbottlenecks by engaging with sourcing partners to decide quantityallocations. Given the degree of information sharing and cooperationrequired, the manufacturer can build a productive long-term rela-tionship with its partners while maintaining control over its sourc-ing process. Second, the portfolio provides the manufacturer withseveral possible non-inferior sourcing alternatives which give themanufacturer some flexibility in the sourcing decision. The portfoliomay have a sole solution and/or multiple-source solutions, and theorder may be evenly or unevenly split. Depending on the require-ment for high probability or low cost, the manufacturer can choosea sourcing solution that fits its needs. Third, this tool enables themanufacturer to determine the shortest possible due date (while stillmaintaining the desired service level) to win the bid without plac-ing additional pressure on the sourcing partners. Decreasing the duedate usually requires the manufacturer provide additional resourcesto ensure completion of the order. However, our approach workswithin the boundaries and constraints of the sourcing partners toprovide a competitive sourcing solution.

The remainder of the paper is organized as follows. Section 2provides the literature in related past studies. Section 3 introducesthemathematical functions for the supplier selection criteria. Section4 has the frontier portfolio search process. Section 5 is the numericalexamples followed by the discussion and final conclusions.

2. Literature review

Traditional Deming's quality management idea suggests a solesourcing partnership for a manufacturer for better coordination andquality control. However, in nowadays' global business environment,unpredictable risks exist in all links of the supply chain; people'sideas in sourcing have been changed accordingly. In March 2000,Ericsson had to shut down its production line and bite the $400 mil-lion loss because its sole supplier, Philips microchip plant in Albu-querque, NM was on fire; while Nokia, although relays on Philipsas its major supplier, was able to solve the chip shortage problemquickly with their multi-supplier base [5].

Most manufacturers now hold a few comparable suppliers as abase for their sourcing resource to reduce supply chain risk. However,the strategies about how many suppliers to use, and how to allocatejobs among the suppliers, single sourcing, dual sourcing, or multiplesourcing, have always been an important research issue. We herebyreview two streams that are most relevant to our research: onefocuses on reducing supply chain risk and managing disruptions;and the other studies the allocation of jobs among suppliers withconstraints in capacity, time, and budget.

Considering risks associated with a supplier network, Bergeret al. [6] present a decision-tree based model (BGZ model) to deter-mine the optimal number of suppliers for a firm. Ruiz-Torres andMahmoodi [7] extend it by considering the presence of supplierfailure risks. In another effort, Berger and Zeng [8] study the optimalsupply size under a number of scenarios with various financial lossfunctions, the operating cost functions and the probabilities of all the

suppliers being down. Yu et al. [10] evaluate the impacts of supplydisruption risks between the choice of single and dual sources. Xiaoand Qi [11] examine the effects of price competition and demanddisruption on the coordination for a dual sourcing system.

On the other stream, previous studies have focused primarilyon minimizing costs or minimizing lead-time while using the otheralong with quality, discounts, or capacity as constraints [12]. Hongand Hayya [13] use mathematical programming to determine theoptimal number of suppliers and related allocation decisions to min-imize ordering, holding, transportation, and inspection costs. Thosewho recommend dual sourcing find that it can reduce inventorycosts and provide lower overall costs if the mean lead times are sig-nificantly different [14], and minimize stock outs when lead-timeuncertainty cannot be reduced [15]. Some have examined the issueof uneven split orders with dual sourcing to determine when dualsourcing is superior to sole sourcing while considering demand con-ditions, lead-time, and various costs such as transportation, holding,shortage, and expediting costs [16–18].

The common thread running through the existing studies is thesearch for a single optimal solution given the various demand condi-tions to meet the required service level or to minimize costs. Variousmethods such as decision trees [6,19], greedy algorithm [20], anddiscrete-time Markov chain [21] are used to approach the optimal.One notable study by Linn et al. [22] integrates two key characteris-tics (i.e., price and quality) into a capability index and price compar-ison chart (CPC) mapping the choices a manufacturer has; however,the method does not incorporate split orders. Another notable studyby Murthy et al. [23] uses the Lagrangian relaxation technique tominimize sourcing and purchasing costs in a make-to-order supplychain where suppliers provide single sealed bids or open-bid dy-namic auctions. Because of the bidding process, the allocation is, infact, determined by the supplier.

This research proposes a frontier approach with stochastic jobprocessing times. In some cases, the manufacturer needs the flex-ibility of having different sourcing options to address the supplierbottleneck problems that may arise during booming demand or rawmaterial shortages. The decision model allows the manufacturer tomake sourcing cost-reliability trade-offs, depending on its prefer-ences, to meet the customer's due date.

This approach differs from many others in several ways. It is es-pecially useful in cases where the manufacturer faces a short-termproblem of market demand outpacing key parts suppliers' capacity.It may provide several sourcing choices for the manufacturer usinginformation about the sourcing partners, such as cost, capacity, andprocessing time distribution. If a due date is given, our proceduredetermines a portfolio with different sourcing partners and quan-tity allocation options so that the manufacturer can make a trade-offbetween cost and the probability of finishing the job on time. Fur-thermore, our procedure can help the manufacturer obtain a port-folio with the shortest possible due date that can satisfy the desiredservice level.

3. Mathematical functions for the major selection criteria

The model applies to the situation when a manufacturer re-ceives (or decides to bid) a customer order that is unique andcomes with several make-to-order key parts. For each key part, themanufacturer has multiple certified sourcing partners (suppliers)with similar qualities. With the required (or bidding) due date anddesired service level, the manufacturer needs to decide how toallocate the sourcing quantity to each certified supplier for eachkey part. To do so, the manufacturer needs to have each supplier'scost structure and stochastic processing time information for thatparticular part at that particular time. Although there are manyother factors that may influence the sourcing portfolio selection,

138 J. Yue et al. / Omega 38 (2010) 136–144

meeting the due date and reducing costs are the most importantcriteria. In this research, we collect information of the suppliers'processing time and cost structure, and then use the information tocalculate the probabilities to meet due dates and the related costsunder different sourcing portfolios. The details are explained in thissection.

The notations used in this study are as follows:

m number of key partski number of certified suppliers for key part iSij the jth supplier that is certified tomake part i (j=1, 2, . . . , ki)�ij mean of the unit processing time for supplier Sij�2ij variance of the unit processing time for supplier Sij

nij assigned order units of part i to supplier jNi required number of units for part iVij variable cost per unit of supplier SijFij fixed cost of supplier Sijbij binary variable to indicate if supplier Sij is selected by the

manufacturerCij cost of sourcing nij units of part i from supplier SijCi cost of sourcing part iC total sourcing cost of all key partsT part required time, all key parts are required to finish by

part required time�(x) cumulative probability for standard normal score xPij probability for supplier Sij to finish its assigned order by

time TPi probability for chosen suppliers to finish all required Ni

part i by time TP probability to finish all key parts by time TSL desired service level of finishing all key parts (i.e., the or-

der) by time T

A desired service level (SL) is a preset requirement that themanufacturer desires to reach, while the probability (P) is the ser-vice level the manufacturer reaches each time it allocates the partorders to suppliers. Ideally, P should be higher than or equal toSL(P � SL).

Our model starts with the assumption that one particular ordercontains m key parts; for each key part i (i = 1,2, . . . ,m), Ni items areneeded, and ki certified suppliers (denoted as Sij , j = 1, 2, . . . , ki) areavailable. We assume that the processing time of each item by sup-plier Sij follows an independent identical normal distribution withmean �ij and variance �2

ij. We assume this information is known tothe manufacturer when it makes the sourcing decision. The sourcingcost from supplier Sij includes both the unit variable cost, Vij , and afixed cost Fij if the supplier Sij is chosen.

The distribution of processing time has always been a questionin the real world. Many researches assume certain distributions forprocessing times, for example negative binomial distribution by Yueet al. [24]. Normal distribution is one of the widely used approaches.This research assumes the processing time follows independent nor-mal distribution to calculate the probability for a supplier to finishcertain items. While in reality, the distribution of the processing timeand the probability to finish certain items in a specific time can beestimated by experience and past data. The idea of this research canbe easily extended to any other distributions after some justificationin the calculation of the probabilities.

When estimating processing time, mean (�) and variance (�2)are the two most important variables. As we assume that theprocessing time for each item follows independent identical dis-tribution, unit processing time mean (�ij) can be estimated as thesample average of the past unit processing times; also, unit pro-cessing time variance (�2

ij) can be estimated as the sample varianceof the past unit processing times. Therefore, both the processingtime mean and variance for a supplier to finish assigned items are

proportional to the number of items assigned (�=nij�ij,�2=nij�2

ij).Note that in reality, unit processing time may not be independentlyidentical. Then the processing time mean and variance for assignedjobs shall be estimated as sample average and sample variance ofthe past processing times with similar assignments. Other tech-niques, for example, marginal unit processing time and/or covari-ance of the unit processing times can be considered. Although theestimation of the mean and variance of the processing time can bedifferent depending on the business reality, it only influences thecalculation of the probability for a supplier to finish the assignedorder by time T. The procedure of the proposed method staysthe same.

We assume that if all the key parts are finished by required timeT, then the manufacturer has no problem catching the order duedate. On the other hand, if any key part cannot be finished by thepart required time T, the order cannot be fulfilled on time.

Note that in this research, individual delivery time from a sup-plier to the manufacturer is not considered. The research focuses onthe sourcing portfolio among suppliers; therefore, processing timeis the emphasis instead. However, delivery time can be included inthis model by adjusting the part required time T to be individuallydifferent to suppliers as T minus a constant, which estimates the de-livery time from a certain supplier to the make-to-order manufac-turer. Delivery time can be considered as a constant as the result ofthe development in transportation management and the existence ofpunctual delivery service contractors such as UPS, Federal Express,and so on.

Themanufacturer needs to decide a sourcing portfolio by orderingnij units (i = 1,2, . . . ,m; j=1, 2, . . . , ki) from the supplier Sij. Since thereare Ni items of part i for the order, we have

ki∑j=1

nij = Ni. (1)

The cost from supplier Sij is

Cij(nij) = Fij × bij + Vij × nij where bij ={0 if nij = 0;

1 if nij >0.(2)

The probability to finish nij items of part i from supplier Sij withintime T is

Pij(nij) =

⎧⎪⎪⎨⎪⎪⎩

�

⎛⎝T − nij × �ij√

nij × �2ij

⎞⎠ if nij �0;

1 if nij = 0.

(3)

Theoretically, if more than one supplier is used for a key part, thelongest finishing time among the sourcing suppliers (i.e., the partbottleneck) determines the finishing time for the part. Therefore,for a given allocation of the key part i, denoted as nij (j = 1, 2, . . . , ki)called the part portfolio, the probability of finishing part i by time T iscalculated, by independent property, as the multiplication of all theprobabilities of finishing the allocated units by time T of ki certifiedsuppliers.

Pi(nij, j = 1, 2, . . . , ki) =ki∏j=1

Pij(nij). (4)

Similarly, the longest finishing time of all the parts (i.e., the orderbottleneck) determines the finishing time for the order. The proba-bility of no delays for an order is the probability of finishing all partsby a given part required time T, which equals the product of the

J. Yue et al. / Omega 38 (2010) 136–144 139

probabilities of each individual part,

P(i = 1, 2, . . . ,m;nij, j = 1, 2, . . . , ki) =m∏i=1

Pi(nij, j = 1, 2, . . . , ki). (5)

If this probability is not less than the desired service level SL, therelated portfolio, which is the allocation of all key parts to sourcingpartners, denoted as nij (i = 1,2, . . . ,m; j=1, 2, . . . , ki) called the sourc-ing portfolio, is valid for the given order. In addition, the associatedcost function for sourcing part i is obtained by the sum of the costfunctions of all ki certified suppliers for part i

Ci(nij, j = 1, 2, . . . , ki) =ki∑j=1

Cij(nij). (6)

The associated cost of sourcing all m key parts is the summation ofthe sourcing costs of all parts,

C(i = 1, 2, . . . ,m; nij, j = 1, 2, . . . , ki) =m∑i=1

Ci(nij, j = 1, 2, . . . , ki). (7)

This research aims to support the manufacturers' sourcing deci-sion by providing a group of superior choices of portfolios, calledfrontier sourcing portfolios, which considers the cost and probabilityof finishing the order on time.

4. Frontier portfolios search

This section introduces a frontier portfolio search process to helpmake-to-order manufacturers to allocate the part order to suppli-ers while spontaneously considering two factors, the probability tofinish the order by part required time (P) and the related cost forthe manufacturer (C). Constrained optimization approach is not cho-sen here mainly for two reasons. First, trade-offs exist between thetwo factors, P and C. By evolving more suppliers with additionalcosts, the manufacturer may have higher chances to finish the or-der on time, and vice versa. However, it is hard to quantify howmuch certain improvement in the probability is worth to the manu-facturer, since it is really a case-by-case scenario depending on howimportant the order is, who the bid competitors are, the specific re-quirement of the customer, and a lot of other issues that cannot bepredetermined. Second, we cannot preset the weights of the twofactors, e.g., which one is more important than the other is, and howmuch more important. This again should be a case-by-case decisionof the make-to-order manufacturer, as each order shall be handledindividually. Therefore, instead of a constrained optimization ap-proach we hereby propose a frontier approach, which provides themanufacturer a pool of options, where all options satisfy the man-ufacturer's service level requirement; however, none of them is su-perior to the others in terms of factors P and C. The manufacturerthen can make decisions among the options depending on specificcases it faces.

Our frontier approach starts with the search of part portfolio.Given a part required time T, for each of the key parts, we find apool of sourcing portfolios that satisfy the service level requirementand among them, none is inferior to the other. These sourcing port-folios form the portfolio frontier of the key part. We then check allcombinations of the key part frontier portfolios, and compare themto find the order portfolio frontier. The order portfolio frontier con-tains a pool of combinations of the key part portfolios that satisfythe service level requirement, and none is inferior to the other. Tofind the shortest due date that a manufacturer can endure, we canshorten the part required time T unit by unit, until no order frontierportfolio is available. Then the last due date with an available orderfrontier portfolio is the shortest due date that the manufacturer canhandle.

In comparing two portfolios A and B, whether they are part orsourcing portfolios, if A has lower cost and higher probability thanB, then A is superior to B, and B is inferior to A. However, a supe-rior relationship may not always exist between two portfolios. Sincea single optimal portfolio with both the highest probability and thelowest cost may not exist, we may obtain several portfolios thatform the frontier. A frontier portfolio has the following properties:any frontier portfolio is not superior to any other frontier portfo-lio, but any non-frontier portfolio is inferior to at least one frontierportfolio. In order to determine the sourcing portfolio, the algorithmstarts with the part frontier portfolios, and only the part frontierportfolios can be used in the sourcing frontier portfolio. In practice,our algorithm can be utilized to obtain the frontier portfolios for themanufacturer's sourcing decision.

4.1. Part portfolio frontier search

The procedure begins with the part portfolio frontier search fora particular key part i (i = 1,2 . . . ,m) with Ni items and ki certifiedsuppliers. To make the frontier search more efficient, the certifiedsuppliers Sij (j=1, 2, . . . , ki) for each part i are ranked in an increasingorder of their unit variable cost Vij (Vi1 �Vi2 � · · · �Vili ).

Starting with only one supplier to finish the entire part job, allpossible combinations of suppliers will be examined eventually. Tobe placed into the frontier pool, a single supplier or a combinationof suppliers must have sufficient capacity to finish the job with thedesired service level and is not inferior to any other supplier combi-nation. If the part finishing probability is less than the desired servicelevel, then the final order will not meet the desired service level.

Once a portfolio satisfies the desired service level, it is comparedwith existing portfolios in the frontier pool. This portfolio can beplaced in the frontier pool if it is not inferior to any existing frontierpool portfolios. Additionally, any existing frontier pool portfolio thatis inferior to this portfolio must be removed from the frontier pool.

4.1.1. Search Algorithm ITo ensure that the service level is met, for each combination of

suppliers, we only use the portfolio which maximizes the probabilityto finish the job. This procedure can be conducted by Search AlgorithmI introduced below.

Search Algorithm I:

Step 1. Without losing generality, order the j suppliers in in-creasing order of their unit variable cost. Denote the suppliers asS1, S2, . . . , Sj.Step 2. Initially assign q1 = Ni − j + 1 quantity to supplier S1 andq2=q3=· · ·=qj=1 quantity items to the remaining j−1 suppliers.Step 3. Calculate the probability Pi(q1, q2, . . . , qj) by Eq. (5) and letP̃ = Pi(q1, q2, . . . , qj).Step 4. Find maximum probability portfolio by moving only oneitem from one supplier to another supplier,

4.1. Let r = 1;4.2. Check if qr = 1, if yes, go to Step 4.4;4.3. Calculate the probabilities of finishing allocated units after

moving one item from supplier r to one of the remaining suppliersusing Eq. (5). Compare the highest probability with P̃, if it is morethan P̃, then replace P̃ with it;

4.4. r = r+1. Check if r = j+1, if no, go to 4.2.Step 5. If replacement in Step 4 is available, update the portfolioassociatedwith new P̃. Since further improvement is still possible,repeat Step 4. If replacement is not available, the existing portfolioprovides the highest probability for the given combination of thesuppliers. Calculate the related cost Ci(q1, q2, . . . , qj) per Eq. (6).The search is finished.

140 J. Yue et al. / Omega 38 (2010) 136–144

Start

Order j suppliers in increasing order of their unit variable costs; S1, S2, … , Sj

r = 1; “Change” = “No”

qr = qr - 1r = r + 1

Pi > P?

Let q1 = Ni– j +1,q2 = q3 = … = qj = 1

Calculate P = Pi

Try qk = qk + 1.For k = r +1 to j,

Calculate highest Pi

“Change” =“Yes”

Stop

qr =1?

P = Pi; “Change” = “Yes”Keep updated portfolio

qr = qr +1.Keep original qk(k = r +1 to j)

no

no

no

yes

yes

yes

yes

no

Calculate Ci~

~

~

r = j+1

Fig. 1. Flowchart of Search Algorithm I, highest probability part portfolio search.

We can use the same approach to find the highest probabilityportfolio for all combinations of suppliers. The details of the searchprocess are illustrated in Fig. 1.

4.1.2. Search Algorithm IIOnce the highest probability portfolio for each combination is

obtained from Search Algorithm I, we use the following Search Algo-rithm II to find the part frontier portfolios. The part frontier portfoliofor each part contains job allocations that each of them is superiorto another job allocation that does not belong to the frontier, andnone of them is superior to another job allocation that belongs tothe frontier. The details of the search process are illustrated in Fig. 2.

Search Algorithm II:

Step 1. Initially, the frontier pool is empty, � = (∅).Step 2. Let j = 0;

2.1. Let j = j+1. Consider the portfolios with j number suppliers;2.2. Determine all possible combinations of j number suppliersamong the valid suppliers;2.3. Check if a combination can be put into the pool;

2.3.1. For a combination of suppliers, find the highest probabilityportfolio (the quantity assigned to each supplier);

if j = 1, use Eq. (4) to calculate Pi(Ni) for the chosen supplier;if j > 1, use Search Algorithm I;

2.3.2. If the probability is higher than the desired service levelSL, calculate the associated cost by Eq. (6). Otherwise, go tostep 2.3.4;

2.3.3. Compare the portfolio with all portfolios in the pool �.If this portfolio is inferior to any portfolio in the pool, it shouldnot be in the pool. Otherwise place it into the pool �. If anypool portfolio is inferior to the portfolio, remove the inferior poolportfolio from the pool �;2.3.4. Confirm all combinations of j number suppliers have beenchecked. If not, for another combination, go back to 2.3.1;

2.4. Check if j=ki, if not, go back to 2.1. Otherwise, the part frontieris obtained. Stop the algorithm.

Search Algorithms I and II enable the manufacturer to find single-source or multiple-source part portfolio frontier with exact quantityallocations for all key parts.

4.2. Sourcing portfolio frontier search

Once the part portfolio frontiers are determined for all key parts,the manufacturer can use the part portfolio frontiers to find thesourcing portfolio frontier. One portfolio from each part frontier ischosen and combined to form a sourcing portfolio frontier candidate.Similar to the part portfolio frontier search, the sourcing frontiercandidate must be checked to ensure that it can meet the desiredservice level. Then, the eligible candidates are compared against oneanother to find the superior sourcing portfolios, which comprise thesourcing frontier.

4.3. Due date reduction

In the previous subsection, algorithms were presented to obtainboth the part and sourcing frontier portfolios under the assumptionof a given due date. However, a due date may not always be given,and the manufacturer may need to quote a due date for bidding.Certainly, a shorter due date has a higher chance to win the bid, butit may also mean higher cost and lower probability to finish on time.Furthermore, certain due dates may never be attainable for a desiredservice level due to the suppliers' capacity constraints. Therefore, weneed a procedure to obtain the shortest possible due date.

The due date reduction process starts with an arbitrary partrequired time with which the manufacturer is confident. The partrequired time is then decreased by one unit of time (days in our ex-ample) to find the related frontier. Once a time unit reduction gen-erates a portfolio in the frontier, the shortest possible time for thedesired service level is obtained as the latest time before deduction.

5. Numerical example and discussion

We use the following numerical example to illustrate the situ-ation a manufacturer may face. First, we assume, to fulfill the cus-tomer order, all key parts need to be finished within 14 days (T = 14),and the manufacturer has a desired service level of 95% (SL = 95.0%).Four key parts (with quantities of 60, 40, 80, and 10, respectively)are necessary for final assembly of the product. There are five, four,six, and four certified suppliers, respectively, for each key part. Theassociated cost and processing time information for all certified sup-pliers for each key part are presented in Table 1. The number of partsneeded, suppliers' mean processing time �ij, processing time vari-ance �2

ij, fixed cost Fij, and variable cost Vij are listed in columns 1–6,respectively. For this frontier search, all probabilities in our exampleare calculated to an accuracy rate of 0.1%. In practice, any improve-ment less than 0.1% is not significant.

5.1. Search for part frontier portfolio

We start our process by searching for part frontier portfolio forPart 1. The five suppliers for Part 1 have probabilities 0.386, 0.602,

J. Yue et al. / Omega 38 (2010) 136–144 141

j = 0,? empty

Is probability ≥ SL?

Calculate cost

Is portfolio inferiorto any one in Ω?

Ω = Ω + portfolio

Is any one in ?inferior to that

portfolio?

j = ki ?

no

yes

yes

yes

yes

no

no

no

no

Find all possible combinations of j suppliers

For each combination, find highest probabilitypart portfolio.

All combinations of j suppliers

considered?

Stop

yes

j = j+1

Ω = Ω – (all inferiors)

Fig. 2. Flowchart of Search Algorithm II, part frontier portfolio search.

0.952, 0.822, and 0.902 to finish the job individually by T = 14 days.Since the desired service level is 95.0%, only supplier S13 can be con-sidered for the initial frontier pool. The related portfolio is (n13 = 60,P1 = 0.952, C1 = $3110). We put it into the frontier for now.

Next, we consider sourcing from two suppliers. We use SearchAlgorithm I to find the highest probability part portfolio when sourc-ing to more than one part suppliers. For example, when sourcingto both suppliers S11 and S12, by Search Algorithm I, we first assignS11 59 items, S12 one item, the probability is 0.414. Then, one unitis moved from S11 to S12 (S11 58 items, S12 2 items); the probabil-ity increases to 0.442. This process is repeated until the probabilitycannot be increased anymore. For this example, the final portfoliofor the combination of S11 and S12 is (n11 = 29, n12 = 31, P1 = 0.997,C1 = $3236).

Since (n11 = 29, n12 = 31, P1 = 0.997, C1 = $3236) is not inferiorto the initial frontier portfolio (n13 = 60, P1 = 0.952, C1 = $3110), itis added to the frontier. When sourcing to S11 and S13, the highestprobability portfolio can be found as (n11 = 25, n13 = 35, P1 = 1.000,C1 = $3300), it is again added to the frontier. When sourcing to S11and S14, the highest probability portfolio can be found as (n11 = 28,n14 = 32, P1 = 0.998, C1 = $3424), which is inferior to (n11 = 25,n13 = 35, P1 = 1.000, C1 = $3300) and shall not be included in thefrontier pool. Similarly, the portfolio (n11 = 28, n15 = 32, P1 = 0.998,C1 =$3468) and other remaining portfolios sourced to multiple sup-pliers are inferior to the existing frontier portfolios. The frontier port-folios for Part 1 are: (n13 = 60, P1 = 0.952, C1 = $3110), (n11 = 29,n12 = 31, P1 = 0.997, C1=$3236), and (n11 = 25, n13 = 35, P1 = 1.000,C1 = $3300). Likewise, we can find part frontier portfolios for the

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Table 1Parts and the certified suppliers' parameters.

Part no. Suppliers Mean of the unit Variance of the unit Fixed cost Variable cost(units required) processing time (�ij) processing time (�2

ij) (Fij : $) (Vij : $)

1 (60) S11 0.25 0.20 420 38S12 0.22 0.16 350 44S13 0.15 0.15 350 46S14 0.18 0.20 340 50S15 0.15 0.25 320 52

2 (40) S21 0.30 0.40 100 30S22 0.50 0.60 150 34S23 0.45 0.25 120 36S24 0.35 0.30 160 38

3 (80) S31 0.10 0.05 300 30S32 0.09 0.06 250 31S33 0.11 0.04 200 34S34 0.11 0.03 180 36S35 0.10 0.06 180 38S36 0.10 0.04 170 40

4 (10) S41 2.00 0.20 1000 280S42 2.10 0.10 980 290S43 1.80 0.15 970 300S44 1.60 0.20 1020 310

Table 2Part frontier portfolios for all key parts when T = 14 days.

Part Frontier portfolios

Part 1 (n13 = 60, P1 = 0.952, C1 = $3110) (n11 = 29, n12 = 31, P1 = 0.997,C1 = $3236)

(n11 = 25, n13 = 35, P1 = 1.000,C1 = $3300)

Part 2 (n21 = 26, n22 = 14, P2 = 0.965,C2 = $1506)

(n21 = 22, n23 = 18, P2 = 0.991,C2 = $1528)

(n21 = 20, n24 = 20, P2 = 0.996,C2 = $1620)

(n21 = 17, n22 = 10, n23 = 13,P2 = 1.000, C2 = $1688)

Part 3 (n31 = 80, P3 = 0.999, C3 = $2700) (n34 = 80, P3 = 1.000, C1 = $3060)Part 4 (n41 = 5, n42 = 5, P4 = 1.000, C4 = $4830)

remaining parts 2–4; all frontier portfolios for each part are listed inTable 2.

5.2. Search for order frontier portfolio

In our example, there are three, four, two, and one frontier port-folios for each key part, respectively, giving us 24 possible combina-tions (3×4×2×1 = 24) which can be candidates for sourcing frontierportfolios. For each combination of part frontier portfolios, the prob-ability to finish the job by time T and related cost can be calculated byEqs. (5) and (7). Among the combinations, six of them have a prob-ability lower than 95.0% and will not be considered. The remaining18 can be ordered from the highest probability to the lowest. Thenthe corresponding costs can be compared to find the inferior port-folios for removal. Eight combinations of the part frontier portfoliosremain, forming the sourcing frontier portfolios linked in Fig. 3; theother unlinked dots represent qualified sourcing portfolios that arenot eligible for the frontier. The frontier contains the group of su-perior choices that the manufacturer can select, depending on itspreference for reliability and cost.

5.3. Due date reduction

Continuing with the previous example, if T is reduced to 13, 12,11, 10, and 9 days, the sourcing frontiers can be obtained as shownin Fig. 4. Once T is reduced to 8 days, no part frontier portfoliois available for Part 2; therefore, no sourcing frontier portfolio isavailable for the order. The shortest due date is derived from part

Fig. 3. Order frontiers for T = 14 and 9.

required time T = 9 (see Fig. 3 for the possible portfolios and thefrontier). The manufacturer can maintain its supply chain servicelevel while reducing the due date by 5 days. By choosing an optionfrom the sourcing frontier for a particular due date, the manufacturerknows the sourcing suppliers, the allocation of parts, and the precisepart order costs for a certain service level.

J. Yue et al. / Omega 38 (2010) 136–144 143

Fig. 4. Frontier changes from T = 14 to 9.

5.4. Discussion

5.4.1. Discussion of the procedureFor manufacturers in need of sourcing flexibility, our method pro-

vides choices to them in terms of due date, service level and cost.The manufacturer can make its sourcing decision, whether a singlesupplier or combinations of suppliers, depending on the situation.When the due date is sufficiently long, a single supplier is most likelythe best choice for each part so the manufacturer has fewer frontierportfolio options. In this instance, Deming's quality point of using asingle supplier for each part is ideal. When the due date is short-ened, a single supplier may not have sufficient capacity to finishthe entire job by itself. Consequently, several supplier combinationsare comparably capable of fulfilling the requirement for each part,and thus, the number of frontier portfolios increases so the manu-facturer has more choices. When the due date is shortened further,the number of supplier combinations that can finish the job for eachpart varies. In our example, the number of sourcing frontier optionschanged from 8 to 18, 13, 6, 9, and 5 when the part required timewas reduced from 14 to 13, 12, 11, 10, and 9 days, respectively.Most importantly, when the due date is shortened, the frontier con-tains only portfolios sourced from multiple suppliers. The numberof sourcing suppliers is decided by the due date and the suppliers'capacities.

Furthermore, when the part required time T is shortened, the partfrontier portfolios change. As a result, the sourcing frontier portfoliomay have different options. A shorter due date corresponds witha more inferior sourcing frontier, that is, higher cost and/or lowerprobability as shown in Fig. 4.

When the due date is reduced, some key parts have a higher prob-ability to finish on time with more suppliers involved, e.g., Part 3;however, some other parts may have lower probability to finish ontime due to the capacity limit, e.g., Parts 2 and 4. The part that can-not be finished with the desired service level on time becomes thebottleneck. In our example, Part 2 is the bottleneck since it cannotbe finished in 8 days with the required service level. The manufac-turer can readily use the method proposed here to determine thebottleneck in their sourcing plan. To resolve the bottleneck problemand improve its performance, the manufacturer may want to buildstrategic relationships with its bottleneck part sourcing partner, orit may find more suppliers for the bottleneck part.

5.4.2. Discussion of the computational competencyOne potential problem of the proposed method is the compu-

tational competency since searching for maximum probability partfrontier portfolio enumerates all possible combinations when multi-ple suppliers are considered in Search Algorithm I. In particular, whenj suppliers are considered to work on N items of a certain part, amaximum of 1/2(N − j)j(j − 1) runs of calculation may be needed.This number is linearly related to the number of items, however,quadratic to the number of suppliers. For example, when 1000 itemsare allocated to two suppliers, the maximum number of runs of cal-culation is 998; while when 1000 items are allocated to three sup-pliers, the maximum number of runs increases to 2991; when 1000items are allocated to 10 suppliers, the maximum number of runsjumps to 44550.

In practice, as we order the suppliers by their variable costs, ifwe do not see probability increases when moving one item to latersuppliers, we can cease the iteration of moves from this supplier.Therefore, the maximum number of runs will rarely be reached.Furthermore, when we have a large number of items, techniquessuch as, set the probability accuracy rate to 1% or 0.1%, thereforeignore minor changes in probability; or move the items as a groupof 10 or 100 instead of individually, can also decrease the numberof calculations dramatically.

The number of calculation runs also increases as the number ofkey parts increases as we repeat the same procedure to find frontierportfolio for another key part. This increase is linear and minor.

In fact, as long as the number of certified suppliers for a key partis not huge, the hardware and software of most nowadays comput-ers shall be sufficient to take the task of calculation of the proposedmethod. Fortunately, many businesses today do follow Deming's phi-losophy. They keep and control their supplier base to be restrictedand limited.

6. Conclusion

Make-to-order manufacturers face challenges in the sourcing se-lection process since customer orders are always accompanied withspecial requirements, and key parts and/or components may not bekept in inventory. Instead, the manufacturer must speciallly orderkey parts from the sourcing partners after receipt of the customerorder. Consequently, the make-to-order manufacturer has three ma-jor issues to consider: (i) meeting the due date, (ii) reducing cost,and (iii) alleviating bottlenecks. When quality is relatively consistentacross competitors, the manufacturer must compete on price (cost),due date, and a higher customer service level to win the customercontract in bidding.

In this research, we examine the problem of how the make-to-order manufacturer can select key sourcing partners (with severalcertified suppliers for each key part) and allocate quantities to eachsourcing partner. Our sourcing heuristic enablesmake-to-orderman-ufacturers with multiple key parts and several certified suppliers foreach part to improve service level as well as decrease costs and de-livery times. It can work equally well for cases when a due date isgiven or when the manufacturer must find the shortest due datefor a competitive bid. The portfolio enables the manufacturer to im-prove its flexibility and customer service. Moreover, the level of in-formation sharing required can encourage the manufacturer to builda close, cooperative, and productive long-term relationship with itssuppliers to meet the common goal of winning the customer's bid.

As the Lucent case [4] highlights, make-to-order manufactur-ers operating in a turbulent competitive environment need to bothmaintain control over and retain some degree of flexibility in itssourcing decision. It may be detrimental to the manufacturer's long-term need for production support of new products and innova-tions if we relegate the sourcing decision to outsourcing partners

144 J. Yue et al. / Omega 38 (2010) 136–144

completely. However, the manufacturer still requires sourcing alter-natives in the event of component shortages and/or booming marketdemand. Using the frontier portfolio approach, the make-to-ordermanufacturer is able to have both control and flexibility while work-ing within the parameters of its sourcing partners. Over time, thisapproach may lead sourcing partners to improve their own operat-ing performance (e.g., capacity, cost, and processing time) in orderto qualify for the manufacturer's sourcing frontier portfolio. As a re-sult, the manufacturer may have even more sourcing choices or beable to improve its portfolio.

The limitation of this research lies in several aspects. First, sincethe method enumerates all possible combinations to find the port-folio with highest possibility when multiple suppliers are consid-ered, when the number of qualified key part suppliers is large, thecomputational efficiency suffers dramatically. Second, in calculatingthe probability of finishing the assigned jobs, the processing timefor each job is assumed following independent normal distributions,whichmay not be the case in reality. Instead, themanufacturer needsto adjust the method in practice by estimating the probability fromhistorical information of the processing times. Finally, two criteria,replenishment cost and on time probability, are considered in eval-uating job assignment portfolios. While in reality, other issues, suchas product quality, delivery time, supplier capacity expansion, andeven order bidding strategy may need to be included in the decision.

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