supply chains made up with sme’s: basic requirements of ...5.1.2.1 newsboy problem ... 5.2.1...

e-MENSA – SSA Project

E-MENSA – SSA PROJECT - WGMAP

BASIC REQUIREMENTS OF A MANAGEMENT MODEL FOR SUPPLY CHAINS MADE UP WITH SME’s

List of contents

1. PURPOSE OF THE DOCUMENT............................................................................. 3

2. BASICS OF SMEC MODEL ...................................................................................... 5

3 COLLABORATIVE STRATEGIC PLANNING ......................................................... 6 3.1 Market positioning - Quality Function Deployment (QFD)......................................... 7 3.2 Supply Chain Competitive positioning - the SCOR Roadmap ...................................... 9

3.2.1 Definition of the Supply Chain processes................................................................................. 9 3.2.2 Supply chain evaluation.......................................................................................................... 12 3.2.3 Supply chain comparison with competitors.......................................................................... 15 3.2.4 Competitive relocation............................................................................................................ 15

4 CRITERIA FOR INFORMATION SHARING......................................................... 17 4.1 Types of information and their value .............................................................................. 17

4.1.1 Downstream information. ....................................................................................................... 17 4.1.2 Upstream information ............................................................................................................. 19

4.2 Incentives to information sharing in a supply chain.................................................... 20 4.3 Conclusions on information sharing................................................................................ 23

5. CRITERIA OF OPERATIONS OPTIMIZATION .................................................. 25 5.1 Notes on Inventory Management..................................................................................... 28

5.1.1 Deterministic models.............................................................................................................. 29 5.1.2 Stochastic Models................................................................................................................... 31

5.1.2.1 Newsboy Problem ............................................................................................................. 31 5.1.2.2 (s,S) policy for a single period ....................................................................................... 32 5.1.2.3 Reorder Point Policy ...................................................................................................... 32 5.1.2.4 Reorder Cycle Policy...................................................................................................... 33 5.1.2.5 The (s, S) Policy ............................................................................................................. 35 5.1.2.6 The two-bin policy .......................................................................................................... 35

5.1.3 Choice of inventory policy ...................................................................................................... 36 5.1.4 Implications for Supply Chains Made up of SME’s ............................................................ 36

5.2 Collaborating through Contracts .................................................................................. 37 5.2.1 Newsvendor model .................................................................................................................. 38 5.2.2 The wholesale price contract.................................................................................................. 40 5.2.3 The buyback contract ............................................................................................................. 42 5.2.4 The revenue-sharing contract ................................................................................................ 44

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5.2.5 The quantity-flexibility contract ........................................................................................... 45 5.2.6 The sales-rebate contract........................................................................................................ 46 5.2.7 The quantity-discount contract.............................................................................................. 48 5.2.8 Conclusions on contracts analysis.......................................................................................... 49 5.2.9 Need for further research effort on collaborating through contracts ................................ 50

5.3 Dynamic pricing ................................................................................................................ 52 6. QUALITY CONSISTENCY CRITERIA.................................................................... 56

7. OPERATION ANALYSIS CRITERIA ...................................................................... 59 7.1 Analyses of operations versus objectives........................................................................ 59 7.2 Analyses of strategic plan versus actual market conditions ......................................... 60

7.2.1 Reference market definition................................................................................................... 61 7.2.2 Selection of target group of consumers ................................................................................ 63 7.2.3 Strategy check ......................................................................................................................... 64

8. CRITERIA OF FINANCING IMPROVEMENT PROJECTS ................................ 65

9. EXECUTION CRITERIA ......................................................................................... 69

APPENDIX A................................................................................................................... 74

Coordination with contracts in supply chains with multiple retailers ........................... 74 A.1 competing retailers with fixed consumer price............................................................. 74 A.2 Competing retailers with market-clearing prices......................................................... 78



e-MENSA – SSA Project Basic requirements of a management model for Supply Chains made up with SME’s 1. PURPOSE OF THE DOCUMENT WGMAP activities of the first semester of E-Mensa project have provided the following:

• An outline of the technologies currently available to supply chains. It has been shown that there is a whole world of useful tools out there; but only those that support the execution of transactions among Supply Chain (SC) members appear fully mature (“e-execution”), whereas those which should support collaboration efforts (“e-collaboration”) are not yet fully available or are in the process of being better understood.

• A wide discussion on the problems which haunt supply chains in the agrifood business. It has been shown that most of these problems stem from difficulties in integrating the various activities of the SC members taking appropriate care of their different specific interests. It has also been shown to what extent e-platform technologies can come to help.

• A review of the most advanced models today available for managing supply chains, such as CPFR (Collaborative Planning Forecasting and Replenishment), which originates from a Harvard University project, and SCOR (Supply Chain Operation Reference model) which is proposed in a wide industrial context coordinated by the “Supply Chain Council”.

All three results show, among other things, the relevance of establishing relationships of collaboration among SC members. In fact, the advanced models reviewed refer to the collaboration as to the focal point in managing supply chains in today business arena. It is to be underlined that the collaboration, these models refer to, is that typical of a partnership, instead of the traditional supplier-client relationship, and implies a much more complex set of interactions among SC members. Despite the very high value of the above models, as well as of others less widely known such as “the Driving Forces” [Robert, Michel, Strategy Pure and Simple II, New York, Mcgraw-Hill, 1998] and the “Supply Chain Progression” [Poirier, Charles C., The Path to Supply Chain Leadership, Supply Chain Management Review, (2/3), pp. 16-26, Fall 1998], just to mention a few, they have a bounded applicability to the supply chains of the agrifood business in Europe, which are made up mostly of SME’s, whereas those models refer to supply chains either made up of, or controlled by, large enterprises. There are a number of reasons for being cautious in applying those models to supply chains made up of SME’s, due to their differentiating features with respect to SC controlled by large enterprises. The most relevant of these features are the following:




• A lower level of control, due to the lack of a dominating member, as it is usually the large enterprise in “its” supply chain. This feature makes the collaboration among SC members much more critical.

• A higher level of difficulty in establishing the collaboration among SC members. As a matter of fact, when moving from a supplier-client relationship to a partnership, the required collaboration activities become much more complex and demanding, so that to add further costs and efforts to those already born by each SC member. A dominating large enterprise can force each member to bear these costs and efforts towards a collaborative behavior that is deemed beneficial to the whole SC, whereas, in a SC made up of sole SME’s, the process of collaboration is to be framed in such a way to make it convincing that it is beneficial for any single member.

• A lower level of information sharing, again due to the lack of a dominating member which provides to set up the stream of information necessary to grant coordination (but can also hide selected information to ensure its own interest).

• The much higher difficulty in accessing financial resources to implement SC improvement projects. In SC controlled by a large enterprise, is this one that usually grants that access; in SC made up of sole SME’s, the only way to gather sufficient financial resources may just be the collective contribution of all SC members. On the other hand, the costs of improvement projects usually focus on few members, whereas the benefits are gathered by all, so that an approach of collaborative financing of those improvements assumes the status of a mutual support feature, which has been and is the success key for many associations.

In addition to the signals that have emerged from the studies already conducted within e-Mensa project, one can ask why all this interest in the theme of collaboration. The more convincing answer is that products and services have become more and more complex over the last years, partly due to the increasingly higher expectations of consumers and partly due to an increasingly pierce competition which has taken enterprises to produce products and services endowed with more and more quality features, such as, for instance, those which deal with food safety and food origin or those which provide added benefits from food packages. These higher levels of quality have required higher levels of specialization, which are critical factors for those enterprises that want to tackle all of them. For these reason, among others, most enterprises have increasingly resorted to outsourcing and have focused on few or one of the activities of the product-service life cycle. As a consequence, today products and services are typically the aggregation of the results of the activities of many different enterprises, that we call “Supply Chain”. In order for a SC to output the best product-service, it is requested that each member provide its best result and that the results from all members be aggregated in the best way; the former requirement is the traditional subject of the enterprise management



e-MENSA – SSA Project discipline, whereas the latter, i.e. the integration of the results of the activities of SC members, is exactly the main subject of supply chain management and it stands to reason that there is no integration without collaboration. Hence the attention given today to the subject of collaboration by all those which deal with supply chain improvements. The intent of this document is that of turning the information collected within e-Mensa project into a proposal for a management model for supply chains operating within the agribusiness industry, hence supply chains made up of SME’s. For the reasons already stated, the model is aimed at obtaining high levels of collaboration among the SC members. In the following, the model is referred to as SMEC (Small Medium Enterprise Chain model) 2. BASICS OF SMEC MODEL SMEC is simply based on two corner stones:

• in order for a SC to achieve high levels of collaboration there must be a communality of intents among SC members;

• there must be a whole set of operational criteria on how to collaborate for concretely meeting those intents.

Common intents must be explicitly stated with the participation of all SC members: within SMEC that occurs through the activity of “Collaborative Strategic Planning” (§3). SMEC also suggests a set of “Collaborative Operation Criteria” aimed at meeting concretely the objectives stated in the Collaborative Strategic Plan. These criteria are framed into subsets:

Information sharing criteria (§ 4) Operations optimization criteria (§ 5) Quality consistency criteria (§ 6) Operation Analysis criteria (§ 7) Criteria of financing improvement projects (§ 8) Execution criteria (Collaboration Support Tools, i.e. e-platform tools) (§ 9)

In framing SMEC model, suggestions have been taken from CPFR model (as to the overall framework) and from SCOR model (as to part of the strategic planning). It is to be understood that some of the above criteria have been the subject matter of research to varied extent; for instance operation optimization has been the focus of much research on logistics, whereas collaborative financing has less been explored. Hence this document also reports on research results already available and addresses those issues that should be subjected to further research efforts.



e-MENSA – SSA Project 3 COLLABORATIVE STRATEGIC PLANNING There are many available definitions of strategic planning and of what should and should not be considered as strategic, such as the interesting and practical one which calls strategic whatever changes the basis for competition [Stalk, George, Jr., Time – the next source of competitive advantage, Harvard Business Review, July-August 1988]. We will also adopt such a practical approach on our proposal for strategic planning within supply chains made up of SME’s. Needless to say, the activity of strategic planning is to be conducted through a coral approach by all SC members, more than any other activity, because there cannot be collaboration if there hasn’t been a clear definition, shared by all members, of where the supply chain wants to go. The strategic plan has to deal with both - market positioning and - competitive positioning. As to the former, the supply chain members have to define the following:

• what market to get into (what typology of product-service); • which consumer target group the SC wants to appeal to; • what are the core benefits those consumers expect to be delivered by products-

services of that market; • what are the features to build into the SC product-service to deliver those benefits.

As to the latter, the supply chain members have to identify:

• who are the competitors in that market; • what are the product-service attributes and the related “perceptual dimensions”

that are relevant for positioning the SC with respect to competitors; • what is the current SC position with respect to competitors; • which new position the members want their SC to move into; • what is to be done to move to the new position.

Lots of questions above! SMEC suggests to find answers to those questions through the application of two new, yet tested, methodologies:

• The Quality Function Deployment, for market positioning and • The SCOR roadmap for competitive positioning.

The following is a summary description of the two methodologies, details of which can be found in the specialized literature also accessible through internet.



e-MENSA – SSA Project 3.1 Market positioning - Quality Function Deployment (QFD) QFD is a structured approach proposed for solving problems associated with the development or the improvement of any product or service. The main features of QFD are its focus on customer requirements, the facilitation of multidisciplinary teamwork and the use of a comprehensive matrix (called the “House of Quality” matrix) to display information, perceptions and decisions. The “multidisciplinary teamwork” feature makes it particularly suitable as an approach of collaboration among members of supply chains made up of SME’s, i.e. decentralized sets of heterogeneous enterprises. Of the advantages of employing QFD within these supply chains, documented in a research program conducted in Italy by ENEA, the most interesting have been:

• Superior identification of customer profile; • Better match between customer requirements and product-service offered by the

supply chain; • Higher cohesion, among the SC members, resulting by the collaborative aspects

of the approach. Basically, QFD is a team tool that obtains customer requirements and translates these into characteristics of a product or service to ensure customer satisfaction. The most common QFD process is known as the “House of Quality” matrix, an example of which is provided by the next figure. The House of Quality matrix is created by a multidisciplinary team who translate a set of customer requirements, drawing upon market research and benchmarking data, into an appropriate number of prioritized engineering targets to be met by a selected product/service design. One of the major assets of QFD is the ability of the matrix to adapt to a wide variety of different problems or groups of users. The general format of the “House of Quality” consists of six major components that are completed during the course of a QFD project:

I. Customer Requirements - a structured list of requirements derived from the customer identification and grouped into the related “perceptual dimensions”.

II. Technical Requirements – a structured set of relevant and measurable product characteristics.

III. Planning Matrix – illustrates customer perceptions observed in market survey. Includes relative importance of customer requirements and the performance of the supply chain (as well as that of competitors) in meeting those requirements.

IV. Interrelationship matrix – explores the strength of the relationship between the customer requirements and the technical requirements.

V. Technical correlation – used to identify where technical requirements support or impede each other in the product design.

VI. Technical priorities, benchmarks and targets – used to record the priorities assigned to technical requirements by the matrix, the measures of technical performance achieved by competitive products and the degree of difficulty involved in developing each requirement.




The final output from the matrix is a set of target values for each technical requirement to be met by the selected product-service, which are linked back to the original demands of the customer. It is worth noticing that the QFD process also provides an evaluation of how one’s own product-service performs when compared with the competition. This is also a functionality that is provided by the SCOR roadmap and is not in contrast with that process but can be seen as a useful preliminary analysis; as it will be shown in a while, the SCOR roadmap, from an analytical point of view, is much more restrained into a structural approach, but suggests very practical solutions to change one’s own competitive position.



e-MENSA – SSA Project The process of building the House of Quality matrix through a coral approach has a dramatic impact on setting up relations of active partnership among the SC members. More often than not, the onset of this process reveals that the various SC members have quite different perceptions on what is the target group of costumers of the supply chain. Whereas the process serves the purpose of aligning those perceptions, the initial stage is to be watched carefully because it may be the case that what was thought to be just one target group of costumers, to an attentive analysis, turns out to be more than one group with different requirements. In any case, before initiating the process of building the House of Quality matrix, a first attempt, to state whether the supply chain is targeting more than one group of costumers, must be made and the House of Quality must be build for each of those groups. Later on, the process will point out whether the groups are really different or whether they are more numerous than those initially identified. 3.2 Supply Chain Competitive positioning - the SCOR Roadmap The SCOR process is already extensively described in the report provided by AINIA and ILIM as wgm9 of e-Mensa. In the following, some references to that document are taken just to show the use of the SCOR Roadmap within SMEC model. SCOR Roadmap can be summarized into four basic steps:

1. Definition of the supply chain processes;

2. Evaluation of how the supply chain performs those processes;

3. Comparison of the supply chain performances with those of competitors in the same market and definition of the supply chain current competitive position;

4. Definition of the new desired competitive position of the supply chain and

identification of what is to be done to move to that new position. 3.2.1 Definition of the Supply Chain processes. The first thing to do is that of drawing a map of the supply chain, identifying all the SC members an their relative sites of activities. That can be done starting from a geographic map and marking the above sites on it (for those who have taken the time to read the SCOR published documents, it won’t go unnoticed that the map, always used in the examples, is that of the whole globe and that the sites are marked as those owned by the enterprise and those that are independent, implicitly unveiling the origin of SCOR as a model for supply chains controlled by large multinational enterprises). The next step is that of stating the type of processes conducted in each of the above sites.



e-MENSA – SSA Project First we should recall that SCOR considers three levels of processes which differ from each other in terms of level of abstraction: • Level 1 (Top Level) refers to the highest level of abstraction and assumes that all

supply chain processes can be classified as one of five general subtypes: Plan, Source, Make, Deliver and Return and that complex supply chains are made up of multiple combinations of these basic processes.

• Level 2(Configuration Level) refers to a lower level of abstraction, hence a higher level of detail. In level 2 each level 1 process can be further described by Process Types (or Process Categories).

• Level 3 presents detailed Process Element Information for each Level 2 Process Category.

The very comfortable thing is that SCOR already provides a framework of general processes, categories and process elements, so that, for any specific supply chain, the above analysis can be conducted simply selecting and assembling the available basic components. The three levels of abstraction are functional to the process of evaluation of the supply chain operation as it will be clear in a while. The processes of level 1 are : • Plan, i.e. Planning and Management of Demand/Supply for the whole supply chain; • Source, i.e. Sourcing Stocked, Make-to-Order and Engineer-to-Order products; • Make, i.e. Make-to-Stock, Make-to-Order and Engineer-to-Order Production

Execution; • Deliver, i.e. Order, Warehouse, Transportation and Installation Management for

Stocked, Make-to-Order and Engineer-to-Order products; • Return, i.e. return of raw materials and/or receipt of finished goods returned by

clients. At level 2, each level 1 process can be typified as one the predefined level 2 processes that are listed for it. For instance a process defined as “Plan” at level 1 can be typified, at level 2, as either a process of planning for the whole supply chain (P1) or of planning for Source (P2), or of planning for Make (P3).. and so on. The following figure provides a sketch of how level1 processes are turned into level 2 ones.




Notice that each level 2 process is indicated with a letter and a number. At level three an analogous typifying of the level 2 processes occurs, providing more detailed information on the processes being analyzed. These definitions are just functional to the identification of our supply chain: once the SC map is drawn, each SC member site is featured in terms of level 1 processes which take place in it; then, these processes are further detailed as level 2 processes. After that, the SC map could look as the following:

where couples of letters and numbers indicate level 2 processes implemented in the associated sites.



e-MENSA – SSA Project The next step is that of drawing a diagram which functionally connects the various level 2 processes: what is achieved is called “Thread Diagram” and could look as the following:

What is nice and comfortable is that the possible functional connections are already foreseen by the SCOR Roadmap, so one has just to choose those that fit his/her supply chain of interest. The same kind of proceeding goes for the level 3 processes (again, just selecting among what the SCOR Roadmap has set out). What is all that for? Now it comes the more interesting part of the procedure: the supply chain evaluation. 3.2.2 Supply chain evaluation SCOR defines five generic performance attributes and three levels of measures that the analysts can use. These three levels of measures are directly related to the three levels of processes that define the supply chain. To get quickly a graphic explanation, consider the simple supply chain defined in terms of its level 1, level 2 and level 3 processes:




This figure suggests where we could measure a supply chain process. In the case of m0 and m1 measures, we are measuring the performance of the supply chain as a whole; the difference is that m0 refers to internal aspects of operation (Internal Facing Measures) and m1 refers to how customer expectations are met (Customer Facing Measures). But m2 measures check on the performance of one of the level 2 processes, while m3 measures check on the performance of specific level 3 sub-processes within a level 2 process. Now, for each level of measure, SCOR provide the performance attributes and the type of measures for those attributes (called “metrics”). In the following table the performance attributes and the related metrics of level 1 are indicated.

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e-MENSA – SSA Project SCOR Performance attributes and level 1 metrics To be noticed that performance attributes are regrouped into “customer facing attributes” and “internal facing attributes”. If one is willing to get more details, he/she can evaluate any single level 2 process, resorting to the same performance attributes, as for level 1, but metrics of different nature. As indicated in the example below, where the level 2 process being evaluate is a “Source Stocked Product – S1”:

Performance attributes and metrics of lev2 process S1-Source Stocked Product SCOR Roadmap provides procedures to calculate each metric based on the measures performed on one’s own supply chain of interest.



e-MENSA – SSA Project 3.2.3 Supply chain comparison with competitors Thanks to the above standardized approach to the supply chain definition and performance evaluation, once the metrics are quantified, our supply chain performances can be compared, in terms of performances, to the benchmarks of the related sector of activities, as in the following example:

In the column marked as “actual”, the performance values of our SC are reported. These values can be compared with those reported in the “industry benchmark” columns, where actually, in three different columns, we find the values which identify a distribution of performances over the same industry (that is the meaning of “parity”, reported as the value which is overcome by half of the supply chains in the industry, while “advantage” is overcome by a smaller fraction of SC, such as 25%, and “superior” is overcome by a small minority, such as 5%). 3.2.4 Competitive relocation The inspection of a table, like the one above, provides very useful hints at how to relocate a supply chain with respect to the other competitors. For instance, in the example above, order fulfillment and response time are clear lags of our supply chain and a strategic relocation might consists of improving these two performances: it will be up to the supply chain decision makers (the team of representatives of all SC members in the



e-MENSA – SSA Project SMEC model) to decide whether the supply chain is to be moved to “parity” or to “advantage” or to a position of “best in class” in the whole industry (“superior”). There are organizations, working with the Supply Chain Council, that track benchmarks and can provide generic benchmarks for SCOR measures for specific industries. If a supply chain wants specific benchmark data, it needs contract with one of the benchmarking groups. For a fee and the provision of the data related to the client supply chain, the benchmarking group will provide the latest composite data for a specific industry. One group is the “Performance Measurement Group LLC”, a group that works closely with the Supply Chain Council, but there are several other sources of benchmarks. It is worth noticing that, in addition to get data on the performance benchmarks, one can also get an evaluation, by the benchmarking group, of the improvement being pursued; such as the ones indicated in the last right column of the table above, where, for instance, the relocation of the supply chain, from current to “parity” fulfillment level, is valued in terms of 30 million dollars as annual revenues. So the decision makers can really base their decision on a cost-benefit analysis, comparing the expected costs with the expected economic benefits of the supply chain relocation. But, that is not all: for the more common improvements, among the ones that can be sought through the above standard process of evaluation, the Supply Chain Council and the benchmarking groups can suggest the reference “best practices”, i.e. the practices which have already been successfully adopted by the supply chains, that are scored as “superior”.



e-MENSA – SSA Project 4 CRITERIA FOR INFORMATION SHARING The performance of a supply chain depends critically on how its members coordinate their decisions and its hard to imagine collaboration without some form of information sharing. Despite that, information sharing doesn’t avail yet of a sound and tested methodology, but it does avail of the results of recent researches, a survey of which is provided in this section. Practically all the studies, referred to in this section, are conceptual researches, each based on a well defined business model (as to, for instance, supply chain structure, replenishment policy, business variables controlled by SC members… and the like); it stands to reason that the results of the studies are dependent upon those models and need to be well analyzed before extending those results to more general business conditions; however they provide an outline of what are the impact and the problems of information sharing among members of a supply chain. 4.1 Types of information and their value The studies that will be referenced in this section measure the value of information through the improvement in the supply chain performances afforded by information sharing. Information sharing in a supply chain is usually divided into two types:

• downstream information, i.e. information pertaining to the downstream part of the supply chain (the part closer to the end consumer);

• upstream information, which comes from the upper part of the supply chain. 4.1.1 Downstream information. In addition to the orders from the downstream levels (e.g. orders of retailers sent to an upstream supplier), the information in this category which can be relevant for sharing and has been studied in various researches is of the following types:

• the consumer demand faced by retailers; • inventory status of the downstream level; • real-time sales data at the retail level (collecting this information puts the supplier

in the position of a central planner for the supply chain). All the studies which have been reviewed report advantages on cost savings either of the supply chain or of just the supplier. This savings are of a few percents, or a few tens of percent in cases where the supplier knows the demand faced by the retailers and also the related sales data. However these quantitative indications come from simulations performed applying well defined and documented business models, but are not real world experimentations.



e-MENSA – SSA Project Another type of downstream information, perhaps the most important, which can be shared within a supply chain, is “demand forecast”, one of the key drivers for production-inventory planning decisions. On the specific value of demand forecast, there is a study, conducted in a two echelon supply chain consisting of a central depot and N retailers, that shows the value of making forecasts of the demand over future periods and of revising these forecasts as time progresses and new information becomes available: this value consists in lower system-wide costs and also lower system-wide inventory position (if backorder penalty cost is higher than holding cost) [Gulu, R. (1997). A two echelon allocation model and the value of information under correlated forecasts and demands. European Journal of Operational Research 99, 396-400]. On the same topic, another study shows that the information contained in the demand forecast can be seen as a substitute for excess production capacity (measured as the difference between average production capacity and expectation of the demand); in other words, ideally managed demand forecast takes to the elimination of excess production capacity [Toktay, B., L.Wein (2001). Analysis of a forecasting-production-inventory system with stationary demand. Management Science 47(9), 1268-1281]. As to sharing demand forecast information among members of supply chains, a study conducted on an elementary supply chain, made up just of one supplier and one retailer, but modeled as a team (both share a common objective to minimize the system-wide costs) has shown that revising forecast update, in the replenishment decisions, reduces the supply chain costs by 11% and information sharing between retailer and supplier brings in an additional reduction of 10% [Aviv, Y. (2001). The effect of collaborative forecasting on supply chain performance. Management Science 47(10), 1326-1343] An advantage, often greeted, of sharing demand forecast information is the reduction of the “bullwhip effect”. This refers to a phenomenon where the replenishment orders generated by a stage in a supply chain exhibit more volatility than the demand the stage faces. That, in turn, causes a kind of chain reaction, with increased order oscillations as we move upstream the supply chain, as in the figure below, which shows larger order oscillations from consumer (C), to retailer (R), to distributor (D) and so on.

Many economists have studied the bullwhip phenomenon, responsible for huge excess inventory costs; they are interested in it because empirical observations seem to refute



e-MENSA – SSA Project conventional wisdom that inventory smoothes production, in that it should be a buffer to smooth out the peaks and valleys of demand. On this instability, many explanations have been provided and a very wide belief is that forecast collaboration, among SC members, contributes to the elimination of the bullwhip effect; in fact, this is a corner stone of the CPFR approach. However, it is worth noticing that not all the research studies are aligned on this conclusion. 4.1.2 Upstream information In addition to the information coming from the demand side, SC members may share information coming from the supply side, which is usually referred to as “upstream information” and is related to

• cost, • lead time, • capacity.

As to sharing cost information, a study has been conducted on a simple SC, made up of one retailer which faces a random customer demand and buys a product while offering a quantity-payment schedule (i.e. a base purchase price, as function of quantity, that the retailer seeks to optimize) to a set of N potential suppliers, which openly bid up the product price, through an English auction process. Each supplier has its own production cost. The result of the study is that the optimum quantity-payment schedule corresponds to a 50-50 split of the retailer’s revenue with the supplier; the result also shows that if the retailer were informed on the production cost of the suppliers, the whole supply chain profit would be higher (through higher quantity of product purchased by the retailer and resold to final consumers) than that accrued when cost information were not shared. It’s interesting to notice that the study provides a quantification of the efficiency created by the suppliers disclosure of their production cost and concludes wondering why they should do that [Chen, F., Auctioning supply contracts. Working paper. Columbia University (2001)]. As to sharing lead time information, there is a study on a simple supply chain made up of a supplier and a retailer which faces random consumer demand and backlogs excess demand; on hand inventory incurs holding cost and customer back orders incur penalty cost. The study analysis is done, from the retailer standpoint, on how to minimize the long run holding and backorder costs. The results provide an analytical value of allowing the retailers to know the status of a replenishment order. This value increases with order volumes and numerical simulations have shown that the percentage cost savings, due to lead time information, can be as high as 40% [Chen, F., B. Yu. Quantifying the value of lead time information in a single-location inventory system. Working paper, Columbia University (2001)]. The same authors of the previous paper are also studying the value of providing a retailer with the information on the capacity of its supplier. The study refers this value to



e-MENSA – SSA Project the difference in volume between an order placed at a time when full capacity is available and an order placed at a later time when the supplier capacity may already be in part engaged by other retailers, all in conditions of uncertainty. Assuming that information sharing is advantageous, then one has to tackle the problem of how to manage the distribution of information; in other words, should all the information be managed by a central body of coordination or should part of the information be left to local management ? On that, other studies hint at the benefits of decentralization of information, keeping, on the central body, the decision on what policy to adopt (in the specific case, for replenishment) and leaving to the local bodies (organized in cost centers) the full decision on how to apply the same policy on the base of local information (in the specific case, the local demand). Local information is considered as made in part of transferable data and in part of specific knowledge, transferable only over some time (in other words, “experience”). The difference between centralized and decentralized systems captures the trade off between coordination, information sharing and local knowledge. The same studies show that this decentralization makes the supply chain more robust against mistakes made by local managers (i.e. the SC members). These conclusions hint at the opportunity to maintain some degree of freedom of the SC member enterprises, taking full chance on their knowledge of their respective markets, even when the supply chain can afford a central body, enabled to coordinate the whole supply chain. 4.2 Incentives to information sharing in a supply chain All the studies, above referred to, show clear advantages to the supply chain from information sharing. But the residual problem is on the incentives for sharing information among the independent SME’s members of a decentralized supply chain. As a matter of fact, it may not suffice that sharing information have a value and it may be required that at least part of this value accrue on all SC members. Criteria considered valid in deeming on the existence of this incentive are usually two:

• Nash equilibrium (all SC members optimize their advantages so optimizing the whole SC advantage);

• Pareto improvement (al least part of the SC members collect advantages which can then be shared with those which didn’t; so that, at the end, everyone is better off).

It is not to be forgotten that information sharing in supply chains with independent players is tricky. When a player has superior information, two things may happen. He may withhold it to gain strategic advantage, or he may revel it to gain cooperation from others. If the former, the less informed players try to provide incentive for him to revel his private information; this is called “screening”. If the latter, we have “signaling”, i.e. reveling information in a credible way.



e-MENSA – SSA Project The potential impact of screening can be shown just considering a simple model with a monopolist who offers a line of goods, differentiated along a quality dimension, to two different consumers with the possibility to deny one consumer access to the product offered to the other consumer. Whereas the monopolist selects the strategy which maximizes his profit, it can be shown that screening between the two consumers has the potential to increase the surplus of at least one of the two consumers (so providing a Pareto improvement). The potential impact of signaling can be shown considering a simple supply chain made by one manufacturer and one retailer, with the latter facing a demand, linearly decreasing with the selling price, which can assume two different states, a high state and a low one, of which only one of the SC member is fully informed. If one analyzes the two players game, which try to maximize their profits, he/she will find that without signaling the profit of one member is maximized at the expenses of the other member and the supply chain total profit is far from its maximum achievable, whereas signaling between the two members moves their profits towards the maximums of both and so is for the supply chain profit. The subject of incentives to information sharing is the most interesting in competitive environments. However the incentives to information sharing among horizontal competitors, e.g. competing retailers sharing market demand information, is anything but a clear cut, making more complex the efforts towards collaboration. A whole body of literature in economics, devoted to this subject, show that whether or not it is optimal for competitors to share information depends on many things, including:

• the type of competition (either Cournot, i.e. competition in quantities of product, or Bertrand, i.e. competition in prices);

• type of information (e.g. common demand information or private cost information);

• whether the products-services sold by the competitors are substitutes or complements.

The most significant indications provided by this literature are the followings. In case of duopoly with demand information: in Cournot competition with substitutes (or Bertrand competition with complements), no information sharing is the unique equilibrium; in Cournot competition with complements (or Bertrand competition with substitutes), complete information sharing is the unique equilibrium. The concept of unique equilibrium above refers to the solution of the game, with incomplete information, that the two members of the duopoly engage; a game which is solved using the concept of Bayesian Nash equilibrium (in practice, the profits maximization for both members) [Vives, X., Duopoly information equilibrium: Cournot and Bertrand. Journal of Economic Theory 34, 71-94 (1984)].



e-MENSA – SSA Project In case of duopoly with cost information, Cournot and Bertrand competition, with substitutes, complete (respectively, no) information sharing is a dominant strategy in Cournot (respectively, Bertrand) competition. [Gal-Or, E. (1986). Information transmission – Cournot and Bertrand equilibria. Review of Economic Studies LIII, 85-92]. To be noticed that changing the type of information, from demand to cost, reverses the incentives for information sharing. In case of oligopoly with demand information and Cournot competition with substitutes, no information sharing is the unique symmetric Nash equilibrium, which provides no incentive to information sharing [Gal-Or, E. (1985). Information sharing in oligopoly. Econometrica 53 (2), 329-343]. The most significant case, about the incentives to share information among members of a supply chain made up of SME’s, is that provided by the study of Li [Li, L. Information sharing in a supply chain with horizontal competition. Management Science 48(9), 1196-1212 (2002)]. The study considers a supply chain with one manufacturer and n retailers competing with each other, with a consumer demand which can randomly change (modeled as price = a + r - quantity, where a is a known constant and r is a random variable). The study considers that, in general, only k<n of the n retailers may decide to share their private information on demand, hence information on the factor r, with the manufacturer. The manufacture sets the whole sale price based on the information he receives from the retailers and each retailer sets the quantity he wants from the manufacturer that, then, will provide to produce the sum of the ordered quantities. The results of the study are quite intuitive and are, in summary, the following. If the information shared among the k retailers is significant, it will affect their behavior which can be observed by the n-k retailers that didn’t share information. So, in principle, a retailer has no incentive to share information and the study shows that a retailer is even better off (higher profit) switching from sharing to not sharing information. On the other hand, the manufacturer profit increases with k. Hence an advantageous solution is that in which the manufacturer pays the retailers for their private information, if, of course, the manufacturer gains from information sharing exceed the losses of the retailers. A specific result of the study is that the supply chain profits, with all retailers sharing information, is higher than those with no retailer sharing, only if the information to be shared is sufficiently informative and the retailers are enough numerous, which is a very intuitive result. Under these conditions, there exists a Pareto improvement if the manufacturer pays the retailers for sharing their information. The above result is a clear indication that, if it is true that information sharing is advantageous for the supply chain, it also true that it has to be the subject of attentive management. This judgment is strengthened by the other result, of the same study, on retailers sharing their cost information, rather than demand information. Also in this case, even though the manufacturer gets anything but benefits from the sharing, complete



e-MENSA – SSA Project information sharing, i.e. with all the retailers that decide to share their cost information with the manufacturer, is not always an equilibrium and is the unique equilibrium sometimes. But, what is most important, complete information sharing increases the supply chain’s total profit. It is clear, from all the above, that further research is necessary on information sharing within supply chains made up of SME’, a research not limited to analytical analyses but also to experimentations with real life supply chains, although this is a very challenging effort. 4.3 Conclusions on information sharing All the studies, referenced in this sections, collectively show a positive value of information sharing among members of supply chains; however, with today limited knowledge and experiences gathered with the operations of decentralized supply chains, this value is not always quantifiable so that to afford the statement of well defined procedures of information sharing; further research is necessary and a careful trial and error approach has to accompany the definition of a process of information sharing in a supply chain made up of independent SME’s in order to point out clear advantages for them all and then to provide the right incentives. Whereas vertical sharing of information of various nature always appears beneficial, horizontal sharing sometimes doesn’t; therefore, it will not come to a surprise that in a context where we can have both vertical and horizontal sharing of information, as in a supply chain with members competing horizontally, the approach to information sharing can’t be reported as a straightforward procedure and is to be designed with care. The set of studies referenced in this section provides us with an outline on potentials and problems on information sharing within a supply chain. Though valuable, but with variable measures, information sharing needs also incentives for the SC members to practice it. We have seen two criteria for identifying the existence of incentives: Nash equilibrium and Pareto improvement. These two criteria actually feature incentives with very different strength. As a matter of fact conditions of Nash equilibrium are spontaneously pursued by SC members, whereas conditions of Pareto improvement need to be quantitatively analyzed and managed. The studies show there are lots of factors that affect the strength of incentives:

• how information is going to be shared (vertically or horizontally), • the many types of information (on demand, on costs.. and the like), • the kind of competition among SC members (Cournot or Bertrand), • substitutability or complementarity of the product-service of the supply chain, • the actual value of the information to be shared.



e-MENSA – SSA Project The studies confirm that the subject of information sharing is anything but trivial; in fact, they always refer to very simplified structures of supply chains and to just a few of those factors at a time. In a real world supply chain, all those factors will play at the same time and the SC structure may be quite complex. In conclusion, the message that comes from these studies is that, in real supply chains, information sharing must be pursued, because it may have strategic implications (it may change the competitive position of the supply chain), but is not achievable with any panacea approach; the incentives will likely be associated to Pareto improvements, rather than to Nash equilibrium, and will require a careful managerial approach based on all above factors.



e-MENSA – SSA Project 5. CRITERIA OF OPERATIONS OPTIMIZATION Optimization of a supply chain refers to the process of choosing the best supply chain configuration and, within this, of choosing the best operation parameters. When the supply chain is owned by a large enterprise, this one has a whole range of alternatives in deciding which facilities to build and where, so that the choice of an optimal configuration and of an optimal operation can be done , to some extent, concurrently. In case of a supply chain made up of SME’s, configuring the supply chain is the same as selecting the members SME’s, so that, usually, there is much less latitude in defining the best configuration, which comes to be determined also by variables not fully controlled by the SME’s, which are seeking new partners. That usually results in being less able to choose concurrently configuration and operation parameters: usually, the optimization parameters will be chosen after the various SME’s have join the supply chain. In any case, when alternatives are available, such as when making decisions on whether to accept a new member, a comparison between the optimum operations of the old and of the new configuration will help. The focus of this section is then on optimizing the operation of a supply chain which has already been configured. In principle, optimizing the SC operation aims at providing the best service to customers, so that to maximize revenues, while minimizing operational costs. Usually, increasing service levels implies costs that increase, beyond some value of service level, more rapidly than sales, so that there exists a service level for which maximum revenues are expected, as shown in the figure below.



e-MENSA – SSA Project The normal approach to optimization is that of selecting first the appropriate level of service and then to find the best operation parameters to achieve this level of service. The identification of the best operation parameters is a very large topic covered by the logistics science and this section will just recall some of the issues of particular importance to supply chains made up of SME’s. In extreme summary, the operations parameters to be optimized are those of production (primary production as well as transformation, in agrifood), transportation, inventory management and marketing. A basic principle to bare always in mind is that, in a supply chain, these activities are interrelated, so that one cannot achieve the optimum SC operation parameters through optimizing these activities one by one and, less than ever, optimizing the operation of any single SC member separately. The right process is that of optimizing concurrently the whole set of activities of the SC members. That is what makes the optimization problem much more complex to be solved through analytic techniques (which, as already mentioned, are one of the core subject of logistics). In addition, for the SC made up of SME’s, what makes the optimization problem even more challenging is that a concurrent optimization implies a centralized approach to the SC management, which, we should say, “by definition”, is not a reality in these supply chains. A simple solution to this difficulty could appear that of always having a specific member devoted to managing the whole set of SC activities ( a sort of “Supply Chain Manager”); but the effectiveness of this solution is more theoretical than practical, because it implies the existence of conditions which endow this member with the appropriate strength and authority for deciding and enforcing policies that the SC activities, performed by independent members, must comply with. The above is to state explicitly that the concurrent optimization of the activities of an SC made up with SME’s is one of its most relevant problems, which deserves to be deeply investigated in a research project. Among the necessary conditions, that allow concurrent optimization, is the sharing of information (for a quick review, see sect. 4) on the costs structures of each SC member. Not only SC members may be little inclined to provide information on their cost structure, but also, when these information are provided, there is the problem of ascertaining their truthfulness (a member may have interest in appearing more or less efficient then what it really is) and of keeping these information up to date (the efficiency of an enterprise changes over time and with the surrounding conditions). As usual in the issues mentioned in this document, the problem is both of managerial and of technological nature: only through appropriate agreements of collaboration the members will provide their private information (later in sect. 5.2), but, at the same time, the members SME’s must avail of tools which can ease the exchange of information and keep these information up to date, otherwise the extra effort required could be discouraging.



e-MENSA – SSA Project As already mentioned above , the normal approach to optimization is that of selecting first the appropriate level of service and then to find the best operation parameters to achieve that level of service. Usually, finding the best operation parameters is translated into that of minimizing their costs (concurrently). The inner problem in this process is that of deciding how to share the activities among the various SC members so that to minimize total cost. This decision is not trivial for the following simple reason. Even assuming each member basically operates at its minimum (average) cost, this level of efficiency is kept only for a limited range in the amount of the activity to be performed: far from the amount where the minimum is reached, the average cost will usually increase. Hence each member will participate in the SC activities with a given (minimum) cost only within constrains of minimum and maximum amount of the activity to be performed. If it were otherwise, the problem of dividing activities among SC members would be easily solved assigning the whole activity to the member with the minimum cost with respect to the others. Just for the sake of providing a sketch of how the optimization problems are stated, let us consider a very simple supply chain with a set of Distribution Centers (V1) which send one type of product to a set of Demand Points (V2).

The optimization problems consists of determining the amounts of product that each distribution center is to send to each demand point, so that total operation cost of the supply chain is minimum. Defining the variables as in the following: dj the demand of customer j; qi the capacity of distribution center i; ui a decision variable which indicates the amount of product in the distribution center i;



e-MENSA – SSA Project sij a decision variable that indicates the amount of product to be sent from distribution center i to demand point j ; Cij(sij) the cost of transporting sij units of product from center i to point j ; Fi (ui) the cost of operating center i at level ui . The minimization problem can be stated as in the following: Minimize ( ) ( )i

Viiij

Vjij

ViuFsC ∑∑∑

∈∈∈

+121

Subject to , i

Vjij us =∑

∈ 2

1Vi∈

, djsVi

ij =∑∈ 1

2Vj∈

, ii qu ≤ 1Vi∈ , , 0≥ijs 1Vi∈ 2Vj∈ , 0≥iu 1Vi∈ Problems of this kind are usually solved with approaches of Linear Programming (LP), in particular of Mix Integer Programming (MIP) since some decision variables are either 0 or 1. Usually these problems are “NP-hard”, i.e. , informally, these problems require a special effort to be reduced to forms for which the time required to solve them, with a reference computer, is a polynomial function of the problem size and hence increases rapidly with the same problem size, i.e. with the number of SC members. The special effort usually consists in a heuristic algorithm proposed to get, in a reasonable computational time, to a solution which, if not optimal, is at least quite close to optimal. From the above, it stands to reason that these optimization problems can only be tackled with appropriate computerized Decision Support Systems. In a real world supply chain, decision is to be made on how to share, among the member SME’s, the whole set of activities, which, as already mentioned earlier, are those of production, transformation, transportation, inventory management and marketing. Beyond seeking a high level of (vertical) integration among these activities, in a supply chain, each of the same activities should be performed in the best available way, which represents the points to start from, in performing concurrent optimization. Directions on the best approaches available for each of these activities is out of the scope of this document and is the subject matter of specific working groups of e-Mensa project. However, the activity of inventory management deserves some notes here, because it is referenced in some other sections of this document. 5.1 Notes on Inventory Management First, a quick look at the reasons for holding inventories:




• improving service levels; • reducing overall logistics costs through the exploitation of economies of scale

(e.g. in transportation); • making seasonal items available throughout the year; • speculations on price patterns; • backing up for some logistics inefficiencies (e.g. poor coordination of supply and

demand); • coping with random customer demand and lead times; this reason, actually, gives

birth to what are called safety stocks. Second, another quick look at the costs relevant to the determination of an inventory policy:

• procurement cost, incurred to acquire a good; • order cost, incurred to process and order; • manufacturing cost; • transportation costs; • handling costs; • inventory holding costs, incurred as opportunity cost (the loss of returns provided

by the most profitable alternative investment of the money spent on inventory) and warehousing cost (cost of space and equipment for stocking goods);

• shortage costs, which come as penalty costs for lost sales and for back orders; • obsolescence costs, for loss of value of goods in inventory.

Inventory management models can be classified according to various criteria, the most interesting of which, in the context of this document, are

• deterministic versus stochastic, depending on whether demand, prices and lead times are assumed known in advance or are considered as uncertain variables;

• instantaneous versus non instantaneous replenishment of the goods to be stocked.

5.1.1 Deterministic models The problem of determining an optimal inventory policy, with a deterministic model, can be summarized to - choosing the quantity q* to be periodically reordered and the shortage s*, to incur before reordering, that minimize the total inventory cost, assumed as the sum of acquisition costs, holding costs and shortage costs. The model assumes that inventory I(t) goes with time t as in the figure below




The analytical solution to this problem is given by the following results:

( )( )( )vhhud

rdh

kdv

vhq+

−−

+=

2*

12

( )( )

( )vhr

dudhqs

+

−−=

1**

where h= holding cost v= shortage cost per unit of product and per unit of time k= fixed component of order cost u= component of shortage cost per unit of product but independent on time of shortage d= (constant) demand rate r= replenishment rate In case of instantaneous replenishment (1/r = 0) and shortage not allowed, the results is the classical Economic Order Quantity (EOQ) given by

hkdq 2* =

with total (minimum) inventory cost, TC, given by

cdkdhTC += 2



e-MENSA – SSA Project where c is the value of the unit of product. In the above model, demand is assumed constant; in case of demand variable with time, things get more complex and one has to resort to linear programming. Analytical solutions are also provided in cases where quantity discounts are offered by suppliers, whereas multi-commodity inventory models are solved through non linear programming or heuristic procedures. 5.1.2 Stochastic Models As to stochastic models, the most significant are the reorder level method, the reorder cycle method, the (s,S) policy and the two bin technique. But it is worth giving first a quick look at the so called “Newsboy Problem” which paves the road to a rapid appreciation of these policies. 5.1.2.1 Newsboy Problem In the Newsboy problem, one-shot order decision is to be made, at the beginning of the sale period, on the quantity of product (newspapers in this particular instance) to purchase and resell over the same period; there is no initial inventory and no fixed order cost; the demand d is a random variable of which the cumulative density distribution function, Pr(d≤q) , is known (for each level q , of the quantity of product to purchase, it gives the probability that the demand d will be no larger than q). Given p as the selling price, c as the purchase price and u as the salvage value, the quantity S, that the newsboy should purchase in order for him to maximize his profit, is such that holds the following

( )Pr p cd Sp u−

≤ =−

The problem solution also provides the newsboy profit Π as function of quantity q purchased:

( ) ( ) ( ) ( ) ( )0 0

min , max 0,q p q f d u q f d cδ δ δ δ δ δ∞ ∞

Π = + − −∫ ∫ q

[ ] ( ) ( ) ( ) ( )0

q

q

pE d p q f d u q f d cδ δ δ δ δ δ∞

= + − + − −∫ ∫ q

in the above, E[d] is the expectation of demand d , δ is the current variable, corresponding to possible demand values, and f(δ) is the probability density function of demand (the derivative of Pr(d≤q) ). The maximum profit is then given by the above formula with q=S.



e-MENSA – SSA Project 5.1.2.2 (s,S) policy for a single period An extension of the newsboy problem deals with those cases, still one-shot order decision at the beginning of a single period, where there is an initial inventory q0 and a fixed order cost k. If q0 ≥ S (S calculated as in the newsboy problem), no order is needed. Otherwise, the best policy is to order S- q0 , as long as this order provides a profit larger than that achievable ordering nothing. Hence, if the expected profit Π(S)-k-cq0 is larger than Π(q0)-cq0 , S- q0 units will be ordered. Otherwise, no order is to be placed. As a consequence, if q0 < S , the optimal policy consists of ordering S- q0 units if Π(q0)≤ Π(S)-k . In other words, defined s as the inventory level such that Π(s)= Π(S)-k , the optimal policy is to order S-q0 units if the initial inventory level q0 ≤ s ; otherwise , order nothing. The parameter s has the function of order point , while S is called order-up-to-level , which accounts for the name assigned to this policy. 5.1.2.3 Reorder Point Policy In this policy, the inventory level I(t) is kept under continuous observation, and as soon as it reaches a reorder point l, a constant quantity q is ordered, as in the figure below



e-MENSA – SSA Project The best quantity to order is provided by the procedures applicable with deterministic demand, provided that the expected value d of demand is used; in particular, if EOQ hypotheses apply

hdkq 2* =

The reorder point l is obtained by requiring that the inventory level be non negative during the lead time tl, with probability α (this probability is, to all effects, equivalent to a specified service level). This requirement is the same as saying that demand is not to exceed l during the interval tl . In the reorder point policy the following assumptions are made:

• the demand rate d is normally distributed with expected value d and standard deviation σd;

• d and σd are constant in time; • the lead time tl is deterministic or is normally distributed with expected value lt

and standard deviation σtl ; • the demand rate and the lead time are statistically independent.

Under the above assumptions the reorder point l is given by ldl tztdl σα+= if lead time is constant (deterministic)

or 222 dtztdl tlldl σσα ++= if lead time is a random variable

αz is the normal deviate, referred to the demand distribution, corresponding to the specified service level α . As shown above, the randomness of the demand (as well as of the lead time, when is the case) is fully transferred to the determination of the reorder point l, rather than to the determination of the best quantity q*. The reorder point l minus the average demand in the reorder period tl constitutes a safety stock Is . In case of constant lead time, the safety stock is ldls tztdlI σα=−= 5.1.2.4 Reorder Cycle Policy In the reorder cycle policy (also called Periodic Review Policy) the stock level is kept under observation only periodically, with period of observation T. At each observation time ti , units are ordered , as in the figure below ( )ii tISq −=




The parameter S , again called the order-up-to-level , represent the maximum inventory level if the lead time tl is negligible. The review period T can be determined using procedures analogous to those used for determining q* in the deterministic models. For instance, when EOQ hypotheses apply

dhkT 2

=

The parameter S is determined in such a way that the probability that the inventory level becomes negative does not exceed (1- α ), where α is the specified service level. Since the risk interval is equal to T plus tl , S is required to be greater than or equal to the demand in ltT + with probability α . If the lead time is deterministic, then ( ) ldl tTztTdS +++= σα

where ( ltTd + ) and ld tT +σ are respectively the expected value and the standard deviation of the demand in . ltT +

The difference between S and the average demand in ltT + makes up a safety stock Is . If lead time is constant: lds tTzI += σα The comparison of this safety stock, with that of the reorder point policy, shows that the reorder cycle policy involves a higher level of safety stock. Against that, one should consider the advantage of monitoring the inventory level only periodically.



e-MENSA – SSA Project 5.1.2.5 The (s, S) Policy The (s, S) policy, for multi-period planning horizons, is a natural extension of the (s, S) policy already illustrated for one-shot case. At time , it ( )itIS − items are ordered if , as in the figure below ( ) stI i <

If s is large enough , the (s, S) policy is similar to the reorder cycle inventory method. On the other hand, if s is small

( Ss → )( )0→s , the (s, S) policy is similar to a

reorder point policy, with reorder point equal to s and reorder quantity . Sq ≅Hence, the (s, S) policy can be seen as a good compromise between the reorder point and the reorder cycle policies. Unfortunately, the parameters s, S and T are difficult to be determined analytically. Therefore, simulation is often used in practice. 5.1.2.6 The two-bin policy The two-bin policy can be seen as a variant of the reorder point policy where no demand forecast is needed and the inventory level does not need to be monitored continuously. The items in stock are assumed to be stored in two identical bins. When one of the two bins becomes empty, an order is issued for an amount equal to the bin capacity.



e-MENSA – SSA Project 5.1.3 Choice of inventory policy In large inventories it is reasonable that more valuable goods receive more attentive cares than less valuable goods which get managed with simpler and inexpensive approaches. A heuristic approach called ABC technique is often used and consists of clustering the goods in stock into three categories, indicated as A, B and C, depending on their impact on the total stock value. For instance, when the classic approach 80-20 is followed, the types of items, which together account for about 80% of the stock value, are put into category A, those which account for about 15% are put into category B and the others into category C. Then, the stock in category A is managed with more engaging techniques that require demand forecasting and continuous inventory control, such as reorder point policy; stock in category B may require a less engaging technique, such as reorder cycle policy, and stock in cat. C may be submitted to the simpler and inexpensive two-bin policy. 5.1.4 Implications for Supply Chains Made up of SME’s In a supply chain made up of many independent members, one of the main issues is to what extent inventory should be managed with a decentralized approach (i.e. any member freely provides to its own inventory) or with a centralized approach where a specific member provides the service of inventory management for the other members. As usual, the factors the influence such decisions are multifold: one should consider geographic locations and nature of the activities of the members, as well as their mutual relationships. We have, here, an example of the need to optimize concurrently the activities of the SC members: it does not make much sense optimizing the sole inventory management without accounting for the other kinds of activities. However, in these efforts of optimization one has to bare in mind what are the economic consequences of the different choices: in the case of inventory management, simple analyses tell us that a centralized approach is more efficient than a decentralized one; hence, somehow incentives should be sought for a centralized solution, taking, however, into account all other relevant factors. In order to provide a simplified proof of the above statement, let us consider a case in which the EOQ hypotheses apply. If a centralized solution is implemented, the average inventory (equal to half the best order quantity) is given by

hkd2

21 where d is the demand

we refer to this average value, since on this depends the inventory cost. If a decentralized solution is implemented for the same total demand d, with n different inventories which serve each 1/nth of the demand, the average inventory would be




( ) nhkd

hndkn 2

21/2

21

=

In other words the decentralized solution is n times more expensive than the centralized one. This is usually referred to as the square-root law. 5.2 Collaborating through Contracts Optimal supply chain performance requires the execution of a precise set of actions. Unfortunately, those actions are not always in the best interest of the supply chain as a whole, as long as the supply chain members are primarily concerned with optimizing their own objectives and that self serving focus results in poor performance of the supply chain. However, optimal performance is achievable if the SME’s members coordinate by contracting on a set of transfer payments such that each member’s objective becomes aligned with the supply chain’s objective. This section goes through a review of studies on contract management. Numerous supply chain models are presented; in each model the supply chain optimal actions are identified. In each case the enterprises could implement those actions, i.e., each firm has access to the information needed to determine the optimal actions and the optimal actions are feasible for each firm. However, often firms lack the incentive to implement those actions. To create that incentive the firms can adjust their terms of trade via a contract that establishes a transfer payment scheme. A number of different contract types are analyzed and their benefits and drawbacks are mentioned. The first references are to contract forms of the so called “newsvendor model”, which, despite only an elementary model, provides the chance to highlight three important questions in supply chain coordination. First, which contracts coordinate the supply chain? A contract is said to coordinate the supply chain if the set of supply chain optimal actions is a Nash equilibrium, i.e. no firm has a profitable unilateral deviation from the set of supply chain optimal actions. Ideally, the optimal actions should also be a unique Nash equilibrium, otherwise the firms may “coordinate” on a sub-optimal set of actions. In the newsvendor model, the action to coordinate is the retailer’s order quantity (and in some cases the supplier’s production quantity also needs coordination). Second, which contracts have sufficient flexibility (by adjusting parameters) to allow for any division of the supply chain’s profit among the firms? If a coordinating contract can allocate rents arbitrarily, then there always exists a contract that Pareto dominates a non coordinating contract, i.e. each member’s profit is no worse off and at least one member is strictly better off with the coordinating contract. Third, which contracts are worth adopting? Although coordination and flexible rent allocation are desirable features, contracts with



e-MENSA – SSA Project those properties tend to be costly to administer. As a result, the contract designer may actually prefer to offer a simple contract even if that contract does not optimize the supply chain’s performance. A simple contract is particularly desirable if the contract’s efficiency is high (i.e. is high the ratio of supply chain profit, with that contract, to the supply chain’s optimal profit) and if the contract designer captures the lion’s share of supply chain profit. Only the short description of the newsvendor model reports some analytical details, just to illustrate the methodology of analysis being adopted. 5.2.1 Newsvendor model This model considers a supply chain made up of only two members: a supplier (she) and a retailer (he) . The retailer faces the newsvendor’s problem: he must choose an order quantity before the start of a single selling season that has stochastic demand. Let be the demand during the selling season. Let F be the cumulative distribution function of demand and f be its probability density function: F is differentiable, strictly increasing and F(0) = 0. Let

0>D

( ) ( )xFxF −= 1 and [ ]DE=µ be the expectation of the demand. The retail price is p. The supplier’s production cost per unit is cs and the retailer’s marginal cost per unit is cr,

s rc c p+ < . The retailer’s marginal cost is incurred upon procuring a unit (rather than upon selling a unit). For each demand the retailer does not satisfy, the retailer incurs a goodwill penalty cost gr and the analogous cost for the supplier is gs. For notational convenience, let and rs ccc += rs ggg += . The retailer earns cv < per unit unsold at the end of season, where v is net of any salvage expenses. Assume the supplier’s net salvage value is no greater than v, so it is optimal for the supply chain to salvage left over inventory at the retailer. For a detailed description of the newsvendor model see [Silver, E., D. Pyke and R. Peterson. 1998. Inventory Management and Production Planning and Scheduling. John Wiley and Sons. New York]. The following sequence of events, in a “game” fashion, is expected to occur : the supplier offers the retailer a contract; the retailer accepts or rejects the contract; assuming the retailer accepts the contract, the retailer submits an order quantity q to the supplier; the supplier produces and delivers to the retailer before the selling season; season demand occurs; and finally transfer payments are made between the firms, based upon the agreed contract. If the retailer rejects the contract, the game ends and each firm earns a default payoff. Each SC member is risk neutral, so each firm maximizes expected profit. There is full information, which means that both firms have the same information at the start of the game, i.e. each firm knows all costs, parameters and rules. The retailer could assume the supplier operates under voluntary compliance, which means the supplier delivers the amount (not to exceed the retailer’s order) that maximizes her profit, given the terms of the contract. Alternatively, the retailer could believe the



e-MENSA – SSA Project supplier never chooses to deliver less than the retailer’s order because the consequences for doing so are sufficiently great, e.g., court action or a loss of reputation. This case is referred to as forced compliance. Any contract that coordinates the supply chain with voluntary compliance surely coordinates with forced compliance, but the reverse is not true (because the contract may fail to coordinate the supplier’s action). Hence, voluntary compliance is the more conservative assumption. In the following, forced compliance is assumed (it simplifies problem analysis). Since sales are the minimum between quantity q ordered by the retailer and demand D, the expected sales S(q) are provided by


)

)

( ) ( )( ) (∫+−=q

dyyyfqFqqS0

1

where is the product between the quantity q and the probability that sales

equal q (which occurs when the demand is larger than q). While is the “sum”

of the products between demand values y and the relative probabilities f(y)dy , when these values y are lower than the quantity q.

( )( qFq −1

( )∫q

dyyyf0

The above relation is simplified, integrating by parts:

( ) ( )∫−=q

dyyFqqS0

Let be the expected left over inventory, ( )qI ( ) ( ) ( )qSqDqqI −=−= + . Let be the lost sales function, ( )qL ( ) ( ) ( )qSqDqL −=−= + µ . Let T be the expected transfer payment from the retailer to the supplier. The retailer’s profit function is

( ) ( ) ( ) ( ) ( ) ( ) ( ) TgqvcqSgvpTqcqLgqvIqpSq rrrrrr −−−−+−=−−−+= µπ The supplier’s profit function is

( ) ( )( ) TqcqSgq sss +−−−= µπ The supply chain’s expected profit is ( ) ( ) ( ) ( ) ( ) ( ) µππ gqvcqSgvpqqq sr −−−+−=+=Π

Since F is strictly increasing, is strictly concave; hence, there is a unique optimal order quantity , for which the expected supply chain profit

Πoq ( )oqΠ is maximum and

which can be achieved zeroing the derivative of the previous relation. This procedure, in turn, provides the following:

( ) ( )gvp

vcqFqS oo +−−

=='


e-MENSA – SSA Project Let be the retailer’s optimal order quantity, i.e. *

rq ( )qq rr πmaxarg* = . The retailer’s order clearly depends on the chosen transfer payment scheme T (nothing is to be said about the supplier for the assumption made of forced compliance). In the next sections the above relations will be used to analyze various forms of contract. The analytical approach for all of these contracts is the same: determine the set of contract parameters that coordinate the retailer’s action; then evaluate the possible range of profit allocations between the firms; and then check whether the contract coordinates under voluntary compliance, i.e. whether the supplier has no incentive to deliver less than the retailer’s order quantity. 5.2.2 The wholesale price contract With a wholesale price contract the supplier charges the retailer w per unit purchased; hence . ( ) qwwqT =,

( wqr , )π is strictly concave in q, so the retailer’s unique optimal order quantity satisfies the following relation (achieved differentiating

*rq

rπ with respect to q) a) ( ) ( ) ( ) 0*' =−+−+− vcwqSgvp rrr Since is a decreasing function in q, only when ( )qS '

or qq =*

( ) ( vcvcgvpgvpw r

r −−−⎟⎟⎠

⎞⎜⎜⎝

⎛+−+−

= )

It is straightforward to confirm that this optimum price charged to the retailer is not larger than the supplier cost , i.e. . Hence, the wholesale price contract coordinates the supply chain only if the supplier earns a non-positive profit. So the supplier clearly prefers a higher wholesale price.

scw ≤

Despite that, this contract is commonly observed in practice and, hence, deserves some more analyses, if only for the purpose of investigating on the behavior of the two supply chain members. One reason for its usage is that the wholesale price contract is simple to administer. As a result, a supplier may prefer the wholesale price contract over a coordinating contract if the additional administrative burden associated with the coordinating contract exceeds the supplier’s potential profit increase. From condition a), above written, that must satisfy, it follows that *

rq

( )r

rr gvp

vcwqF+−−+

−=1*

Since F is strictly increasing and continuous, there is a one-for-one mapping between w and . This map is a sort of demand curve of the retailer versus the supplier; something like in the following figure:

*rq





w

*rq

Hence, let be the unique wholesale price that induces the retailer to order unit (i.e. for each w charged by the supplier, there is a unique optimum quantity, ordered by the retailer, which maximizes his profit with that w). From the above relation, this

( )qw *rq

( )qw is given by ( ) ( ) ( ) ( )vcqFgvpqw rr −−+−= The supplier’s profit function can now be written as ( )( ) ( ) ( )( ),s s sq w q g S q w q c q gsπ µ= + − − It is immediately apparent that the compliance regime does not matter with this contract: for a fixed wholesale price no less than , the supplier’s profit is non-decreasing in q, so that the supplier surely produces and delivers whatever quantity the retailer orders, since she has no interest in delivering less than ordered.

sc

In addition one can verify that the above supplier’s profit function has a unique maximum (if the demand is an IGFR function , as it is in most cases). Hence there is a unique sales quantity, , that maximizes the supplier’s profit (what occurs is that the supplier sets the wholesale price to

*sq

( )*sqw , knowing quite well the retailer then orders

units, given the strict meaning of w). Given this uniqueness of , **sr qq = *

sq ( )( )**, sss qwqπ is the best profit the supplier can hope for. But the retailer may actually hope for more than ( )( )**, ssr qwqπ . As a matter of fact, whereas the supplier has a best with which she determines w ( the “game” foresees that she makes the first move setting up w), the retailer has a whole set (a whole map) of w and ; actually he could hope to sell more than and earn more; why ? because does not represent the maximum profit for the supply chain (for which, we have seen it, the supplier gets no profit); hence there is still margin for the retailer to sell a higher quantity, i.e. a higher corresponding to a lower w in the map w- and so increasing his profit, as demonstrated by the following:

*sq

*rq

*sq **

sr qq =

*rq

*rq

( )( ) ( ) ( ) ( )',

0rr

q w qw q q p v g f q q

qπ∂

= − = − + >∂


e-MENSA – SSA Project Of course the retailer has to be able to get the supplier to lower her requested price w, so reducing the supplier’s profit. If the retailer has enough contracting power, he can push the supplier to lower w, at the limit, down to the value for which the supplier gets no profit at all; at that point, the SC profit is all for the retailer and is the maximum achievable by the retailer and by the supply chain. So the “game” ends up exactly where it was anticipated with the procedure to identify the optimum SC profit . oqThis behavior can actually be observed in agrifood supply chains, where the primary producers fail to join, for instance, into a cooperative and get subjected to the power of a large retailer (e.g a supermarket chain). From the above it gathers that the increase in retail power can actually improve supply chain performance, but at the expenses of the supplier. The two performance measures applied to the wholesale price contract are the efficiency of the contract, ( ) ( )os qq ΠΠ /* , and the supplier’s profit share, ( )( ) ( )*** /, ssss qqwq Ππ . From the supplier’s perspective the wholesale price contract is an attractive option if both of those measures are high: the product of these ratios is the supplier’s share of the supply chain’s optimal profit : ( )( ) ( )osss qqwq Π/, **π . Simulations have shown that as demand gets less volatile, the supplier’s share of supply chain profit increases more quickly than supply chain efficiency. One explanation for this pattern is that the retailer’s profit represents compensation for bearing risk: with the wholesale price contract there is no variation in the supplier’s profit, but the retailer’s profit varies with the realization of demand. As the demand gets less volatile, the retailer faces less demand risk and therefore his compensation is reduced. Various researches have studied extensions to this model that are beyond the scope of this document. Let’s now move to another simple contract type. 5.2.3 The buyback contract With a buy back contract the supplier charges the retailer wb (“wholesale price”) per unit purchased, but pays the retailer b (“buyback rate”) per unit remaining at the end of the season. This contract does not necessarily imply that the units remaining at the end of the season are physically returned to the supplier. That does occur if the supplier’s net salvage value is greater than the retailer’s net salvage value. However, if the retailer’s salvage value is higher, the retailer salvages the units and the supplier credits the retailer for those units, which is sometime referred to as “markdown money”. In the buyback contract, the transfer payment is ( ) ( ) ( ) ( )qbwqbSqbIqwbwqT bbb −+=−=,, The retailer’s profit is ( ) ( ) ( ) ( ) µπ rrbrbr gqvcbwqSbgvpbwq −−+−−−+−=,, We can now consider the set of buyback parameters { }bwb , such that , for ,0≥λ




( )gvpbgvp r +−=−+− λ ( )vcvcbw rb −=−+− λ

It is to be highlighted that, for each given value of λ, these two equations identify one sole couple of values of wb and b. With the above position, we can proceed with a procedure similar to that of the wholesale contract, writing that ( ) ( ) ( ) ( ) µλλπ rbr gqvcqSgvpbwq −−−+−=,, ( ) ( )rggq −+Π= λµλ From the above last relation, we notice that the value of q which zeros the derivative (with respect to q) of the first and the second member is the same; this value is, then, the optimum for the retailer as well as for the supply chain: or qq =*

The supplier’s profit is simply : ( ) ( ) ( ) ( ) ( ) ( )( )rsbsbs ggqbwqqbwq λλµλππ −−−Π−=−Π= 11,,,, Since , the buyback contract coordinates the supply chain with voluntary compliance, as long as

or qq =*

1≤λ . Actually, some ambiguity arises with 0=λ (or 1=λ ) because then is indeed optimal for the supplier (or the retailer), but so is every other quantity; hence, coordination is possible, but the optimal solution is no longer the unique Nash equilibrium.

oq

Beyond the mathematics in the above, what is the meaning of λ ? It is roughly the splitting factor, of the supply chain profit, between the retailer and the supplier. The higher λ, the higher the retailer’s quota of the supply chain profit. The retailer earns the

entire supply chain profit, i.e. ( ) ( )obor qbwq Π=,,π , when ( )( ) 1≤

+Π+Π

=gqgq

o

ro

µµλ ,

Whereas, the supplier earns the entire supply chain profit, i.e. ( ) ( )obos qbwq Π=,,π ,

when ( ) 0≥+Π

=gq

g

o

r

µµλ

So every possible profit allocation is feasible with this set of coordinating contracts, assuming λ = 0 and λ = 1 are considered feasible. It is important to recall that to each value of λ (still between 0 and 1) corresponds a well defined couple of values of wb and b, as already mentioned above. Hence not all values of wb and b are suitable for this contract to coordinate the supply chain, but only those which are consistent with one value of λ , in agreement with the two equations above written to define it. That implies that in the negotiation process, between supplier and retailer, wholesale price and buyback rate have to be chosen concurrently and consistently with their relationship with λ; in other words, it is the value of λ (the splitting factor) which is to be the very object of the negotiation process.



e-MENSA – SSA Project As a matter of fact, if the negotiation process would proceed differently, this contract wouldn’t coordinate the supply chain. For instance, let us suppose the firms agree, first, to a particular (but whatever) wholesale price. Given any fixed wholesale price, the coordinating buy back rate could be different from the one that maximizes the retailer’s or the supplier’s profit. In other words, both players could have an incentive to argue for a non-Pareto optimal (i.e., non-coordinating) contract. It would be a waste if the players then agreed upon an non-Pareto optimal contract because then, by definition, there would exist some coordinating contract that could make both players better off. However, that coordinating contract would have a different wholesale price. The key lesson for managers is that they should never negotiate the two parameters wb and b sequentially (i.e., agree on one parameter and then consider the second parameter). Instead, negotiations should always allow concurrent decisions on both the wholesale price and the buy-back rate. To conclude the treatment of this contract, we notice that the buyback contract coordinates the supply chain with voluntary compliance: that increases the robustness of the supply chain. As a matter of fact, suppose the retailer is not rational and orders

. Since the supplier is allowed to deliver less than the retailer’s order quantity, the supplier can correct the retailer’s mistake by delivering only units. However, because the retailer can refuse to accept more than he ordered, the supplier cannot correct the retailer’s mistake if he orders less than .

oqq >

oq

oq 5.2.4 The revenue-sharing contract With a revenue sharing contract the supplier charges per unit purchased and, in addition, the retailer gives the supplier a percentage of his revenue. We can assume that all revenue is shared, i.e. salvage revenue is also shared between the firms, but it is also possible to design coordinating revenue sharing contracts in which only regular revenue is shared. Let be the fraction of supply chain revenue the retailer keeps, so ( )

rw

Φ Φ−1 is the fraction the supplier earns. Revenue sharing contracts have been applied, for instance, in the video cassette rental industry with much success. The transfer payment with revenue sharing is ( ) ( ) ( ) ( ) ( )( )vqSqqpSqwwqT rrr −Φ−+Φ−+=Φ 11,,

The retailer’s profit function is

( ) ( )( ) ( ) ( ) µπ rrrrrr gqvcwqSgvpwq −Φ−+−+−Φ=Φ,, The above relation shows that we can follow a procedure fully similar to that used in the buyback contract, again introducing a splitting factor λ , so that to get to fully analogous conclusions.



e-MENSA – SSA Project The optimal order quantity for the supply chain, , is also the retailer’s optimal quantity as well as the supplier’s. So the revenue-sharing contract coordinates the supply chain, but, again, for λ holds the condition

oq

10 ≤≤ λ . Again the decision variables and cannot assume whatever values but are to be consistent with the equations that

connect them with λ and are to be chosen concurrently in negotiations. rw Φ

5.2.5 The quantity-flexibility contract With a quantity-flexibility contract the supplier charges per unit purchased but then compensates the retailer for his losses on unsold units. To be specific, the retailer receives

qw

a credit from the supplier at the end of the season equal to ( ) ( )min ,q rw c v I t q+ − The first term (between parentheses) is the retailer’s loss per unsold unit, the second term is the minimum between the leftover inventory I and a fraction [ ]1,0∈t of the quantity q purchased by the retailer; hence, a (maximum) threshold, equal to the product t q, is set by the supplier on the quantity of goods to be considered for compensation. Hence, the quantity-flexibility contract fully protects the retailer on a portion of his order, whereas the buyback contract gives partial protection on the retailer’s entire order. (The retailer continues to salvage left over inventory, which is why the salvage value is not include in each unit’s credit.) If the supplier does not compensate the retailer for the processing cost per unit, then the retailer will receive only partial compensation on a limited number of units; this condition is called “backup agreement” and is analyzed by more than one research study.

rc

With a mathematical approach similar to those of the previous sections (first write the transfer payment, then the retailer’s profit and look for the quantity which makes it maximum, then check on whether this value can be equal to ) one gets to a necessary condition on the wholesale price as a function of t, i.e.

oq( )twq .

A second condition is that should also maximize the supplier profit. In checking on this condition, one finds that it cannot be granted in a regime of voluntary compliance.

oq

Hence, supply chain coordination is achieved but with forced compliance since, in this case, the supplier’s action is no longer relevant (the supplier is explicitly forced by contract to provide the quantity the retailer has asked for). As to the allocation of the SC profits between the two members, one finds that, when t=0, the retailer earns at least the supply chain optimal profit ( )oqΠ . On the contrary, when t=1, it is the supplier that earns at least ( )oqΠ . Given that the profit functions are continuous in t, it follows that all allocations of ( )oqΠ are possible.



e-MENSA – SSA Project 5.2.6 The sales-rebate contract With a sales rebate contract the supplier charges per unit purchased but then gives the swretailer a rebate r per unit sold above a threshold t. The transfer payment with this contract is built as in the following if qws tq ≤ ( ) =trwqT ss ,,,

( ) if ( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛++− ∫

q

ts dyyFtrqrw tq >

the payment schema, if , can be built considering that the retailer pays for every unit purchased, an additional r per unit for the first t units purchased (no rebate on these) and an additional r per unit for the units above the threshold t , but only for those

which are not sold and expected to be as numerous as , because is

the expected number of the unsold units (see the newsvendor model) and then

are the expected unsold units beyond the threshold t.

tq ≥ rws −

( )∫q

t

dyyF ( )∫q

o

dyyF

( )∫q

t

dyyF

As usual, for this contract to achieve SC coordination, the retailer’s profit is to be maximum for . oqq = The retailer profit is: ( ) ( ) ( ) ( ) ( trwqTgqvcqSgvptrwq ssrrsr ,,,,,, − )−−−+−= µπ The maximum condition in oqq = , also recalling from the newsvendor model that

( ) ( )qFqS =' , is : ( ) ( ) ( ) ( ) ( )

0,,,,,,

=∂

∂−−−+−=

∂∂

qtrwqT

vcqFgvpq

trwq sosror

sorπ

If , since T , the above condition becomes oqt ≥ qwss =

( ) ( ) ( ) ( )vcqFgvprw rors −−+−=recalling (from the newsvendor model) that the maximum supply chain profit occurs

when : ( ) ( )gvp

vcqFqS oo +−−

==' , and also recalling that and

, the above condition can again be written as

rs ggg +=

rs ccc +=

( ) ( ) ( ) ( ) ( ) ( ) sossosos cqFgcvcqFgqFgvprw +−=+−−−+−=Then, if , we have oqt ≥ ss cw < , a condition which is clearly unacceptable to the supplier. On the other hand, this contract makes only sense if oqt < (otherwise no rebate would take place).



e-MENSA – SSA Project And if , with a mathematical processing analogous to the above, we get the corresponding condition for :

oqt <( )rws

( ) ( ) ( ) ( ) ( ) ( ) ( )ososorors qFrcqFgqrFrvcqFgvprw ++−=−+−−+−=

( ) ( ) sos cqFgr +−= From the above relations, one can demonstrate that there is a value of t , in the range

, such that the retailer’s profit evaluated at is maximum (with respect to other values of quantity q). Hence this contract coordinates the supply chain. [ oq,0 ] oq

As to the allocation of the SC profit between retailer and supplier, any possible allocation can be achieved with the appropriate choice of the decision parameters t, r, : the sales rebate contract is parameter rich and these three parameters are more than sufficient to coordinate one action and to redistribute rents. For instance, even intuition suggests that lowering the value of t shifts the SC profits towards the retailer, whereas lowering r shifts those profits towards the supplier. However, also for this kind of contract, the triplets of values for these decision parameters cannot be whatever, but must be consistent with the relations written above.

sw

If we consider the supplier’s profit function, written for a coordinating sales-rebate contract:

( )( ) ( )( ) ( )( )trrwqTqcqSgtrrwq ssssss ,,,,,, +−−−= µπ where, in the second member, the first term is the goodwill loss, the second term is the production cost and the third one is the transfer payment. For , tq >

( )( ) ( ) ( ) ( )qrFrrwcqFg

qtrrwq

sssss +−+−=

∂∂ ,,,π

replacing ( ) ( ) ( ) soss cqFgrrw +−= we get

( )( ) ( ) ( ) (( )os

ss qFqFgrq

trrwq−−=

∂∂ ,,,π )

For , the above derivative is positive only if oqq ≤ sgr < (since ( ) ( )( ) 0<− oqFqF ); we check on this derivative to be positive, in order to tell if there is no incentive for the supplier to provide the retailer with a quantity less that , in which case the supply chain will be coordinated with voluntary compliance.

oq

But, if , from the above relation sgr < ( ) ( ) ( ) soss cqFgrrw +−= , we see that ss cw < , i.e. the supplier cannot earn a positive profit. Hence, it will have to be and the above derivative will be negative, signaling that the supplier does have an incentive to provide the supplier less than . As a matter of fact, means the supplier loses money on each unit delivered to the retailer above t: the retailer effectively pays the

sgr >

oq sgr >



e-MENSA – SSA Project supplier for each unit sold above the threshold t and, from the above relation on

, we can tell that ( ) rrw −

( )rws

( ) ( ) ( ) sooss cqrFqFgrrw +−−=− i.e. ( ) ss crrw <− As a consequence, the sales-rebate contract is coordinated only with forced compliance: the supplier is to be forced to provide no less than what the retailer orders; that, in turn, requires some relative strength on the side of the retailer 5.2.7 The quantity-discount contract There are many types of quantity-discount contracts. Here we consider an “all unit” discount, i.e., the transfer payment is ( ) ( ) qdwqT dd = where is the per-unit wholesale price which decreases with q. The retailer’s profit function is then

( )qwd

( )( ) ( ) ( ) ( )( ) µπ rrdrdr gqvcqwqSgvpqwq −−+−+−=, One technique to obtain coordination is to choose the payment schedule such that the retailer’s profit equals a constant fraction λ of the supply chain’s profit. If we impose this condition we get

( ) ( )( )( ) ( ) ( ) vcvcqqSggvpqw rsd +−−+−+−−= λλ1

Since ( )qqS decreases with q, the above discount schedule also decreases with q as long

as λλ ≤ , where

gvpgvp r

+−+−

=λ

The retailer profit function can now be written as ( )( ) ( ) ( ) ( ) µλλπ rdr gqvcqSgvpqwq −−−+−=, ( )( ) µµλ rggq −+Π= This contract coordinates the supply chain with voluntary compliance. As a matter of fact, in the above relation, we see that the value of q (i.e. ), which maximizes the supply chain profit

oq( )qΠ , also maximizes the retailer’s profit, as well as,

as a consequence, the supplier’s profit. As with the buyback and revenue-sharing contracts, the parameter λ acts to allocate the supply chain’s profit between the two SC members. However, the upper bound on λ prevents too much profit from being allocated to the retailer. Technically, the schedule continues to coordinate even if ( )qwd λλ > , but then ( )qwd is increasing in q . In that case the retailer pays a quantity premium.



e-MENSA – SSA Project 5.2.8 Conclusions on contracts analysis We have briefly analyzed five basic contract schemes, in order to provide some insights on the potentials for supply chain optimization through collaboration of members by selecting and managing contracts among SC members; we have referred to these potentials as “coordination” capability of these contracts. We have seen that two of these contracts are equivalent (revenue-sharing and buyback contracts) to coordinate the newsvendor and to divide the supply chain’s profit. Each contract coordinates by inducing the retailer to order more than he would with just a wholesale price contract (which is also advantageous to consumers). Revenue-sharing and quantity-flexibility contracts do this by giving the retailer some downside protection: if demand comes up to be lower than ordered quantity q, the retailer gets some refund. The sales-rebate contract does this by giving the retailer upside incentive: if demand is greater than a threshold t , the retailer effectively purchases the units sold above t for less than their cost of production. The quantity-discount coordinates by adjusting the retailer’s marginal cost curve so that the supplier earns progressively less on each unit. Some notes follow on why one contract form should be observed over another. The various coordinating contracts may not be equally costly to administer. The wholesale-price contract is easy to describe and requires a single transaction between the SC members. The quantity-discount also requires only a single transaction, but it is more complex to describe. The other coordinating contracts are more costly to administer: the supplier must monitor the number of units the retailer has left at the end of the season, or the remaining units must be transported back to the supplier, depending on where the units are salvaged. Hence, the administrative cost argument does not explain the selection among buy-back, revenue-sharing and quantity-flexibility contracts, but may explain the selection of a quantity-discount or a wholesale price contract. The risk neutrality assumption notwithstanding, the contracts do differ with respect to risk. With the exception of the quantity-discount contract, each of the coordinating contracts shifts risk between the two firms: as the retailer’s share of profit decreases, his risk decreases and the supplier’s risk increases. Hence, these contracts could provide some insurance to a risk averse retailer, but would be costly to a risk averse supplier. The supplier’s exposure to demand uncertainty with some of the coordinating contracts could matter to the supplier if the retailer chose an order quantity other than . For example, if the supplier offers a generous buy-back to the retailer, then the supplier will not want the retailer to order too much product. Under voluntary compliance the supplier can avoid this excessive ordering error by shipping only . But with forced compliance the supplier bears the full risk of an irrational retailer, a risk that even a risk

oq

oq



e-MENSA – SSA Project neutral supplier may choose to avoid. However, with voluntary compliance the supplier may ship less than the retailer’s order even if everyone is quite rational: revenue-sharing and quantity-discount always coordinate the supplier’s action with voluntary compliance, quantity-flexibility contracts generally, but not always, coordinate the supplier’s action and sales rebate contracts never do. An issue of particular interest for supply chains made up of SME’s is the following. Consider the application of these contracts in a setting with heterogeneous retailers that do not compete, i.e. the action of one retailer has no impact on any other retailer, for instance because of geographic dispersion. In general, suppliers are legally obligated to offer the same contractual terms to their retailers, hence, it is desirable for the supplier to offer the same contract to all retailers, or, at the very least, the same menu of contracts. If only one contract is offered, then it coordinates all of the retailers as long as the set of coordinating contracts does not depend on something that varies across the retailers. For example, the coordinating revenue-sharing contracts do not depend on the demand distribution, but do depend on the retailer’s marginal cost. Hence, a single revenue-sharing contract can coordinate retailers with heterogeneous demands, but not necessarily retailers with different marginal costs. However, in some cases, heterogeneity can be accommodated with a single contract. The independence of a contract on some parameter is also advantageous if the supplier lacks information regarding that parameter. For example, a supplier does not need to know a retailer’s demand distribution to coordinate the supply chain with a revenue-sharing contract, but would need to know the retailer’s demand distribution with a quantity-flexibility, sales-rebate or quantity-discount contract. However, there may also be situations in which the supplier wishes to divide the retailers by offering a menu of contracts. A case may be that of a supplier which tries to exert efforts on two retailers to improve their demand forecast. He may consider whether it is useful to offer two types of contracts, one for a retailer that exerts effort and one for a retailer that does not. Since coordinating buy back contracts are independent of the demand distribution, this separation requires the supplier to offer non coordinating buyback contracts, i.e., supply chain efficiency must be sacrificed to induce forecasting. Quantity-flexibility contracts do depend on the demand distribution, so a menu can be constructed with two coordinating quantity-flexibility contracts, i.e., supply chain efficiency need not be sacrificed. In summary, while it is possible to identify some differences among the contracts (e.g., different administrative costs, different risk exposures, etc.) none of them is sufficiently compelling to explain why one form should be adopted over another 5.2.9 Need for further research effort on collaborating through contracts In the newsvendor model the retailer impacts sales only through his stocking decision, but in reality a retailer may influence sales through many different actions. Some of them are listed in the following:



e-MENSA – SSA Project • retailer’s decision on setting product price to consumers; • retailers efforts on spurring demand with better consumer service and promotion. Besides, in the real world business, orders are often issued not in one shot, so that there are chances to review order scheduling on the bases of the most recent updating of demand forecast. In addition, different supply chains configurations, for instance with regard to stocking, can make a difference on the features of the contracts we have analyzed. A model like SMEC certainly requires further research to investigate on how the above factors impact on the coordinating capability within the various forms of contract. But on the subject of different supply chain configuration, it is worth mentioning, here, the impact of more complex structures of supply chains, in particular of multi-echelon or of multiple-members in the same SC segment. Multi-echelon supply chains refers to SC structures which include more than two segments, i.e. more than two type of activities as those we have modeled in the previous sections, where we’ve only had the supplier segment and the retailer segment (and which is referred to as “single echelon”). In actual supply chains of the agrifood business we usually have more than two segments such as primary production, transportation (usually more than one segment), transformation, wholesaling (usually more than one segment) and retailing. As to coordinating with contracts, multi-echelon supply chains can be dealt with through the same approach we’ve seen for single echelon in the previous sections. In practice any couple of segments of activities that interface with each other constitute a single echelon which can be coordinated with contracts as those we have analyzed. Having other supply chain members as upstream suppliers or as downstream customers only influences parameters such as ( the marginal product cost to the supplier of the echelon being considered) and

scµ (the expected demand of the “retailer” of the single echelon being

considered, a “retailer” which will sell his products to the downstream segment of the supply chain). Besides that, the conclusions of the analyses of the previous sections still apply. As a matter of fact, the problem we have dealt with is that of checking whether the optimum SC profit is also the optimum of the SC members (in particular of the “retailer”), so that to be confident that the SC members, pursuing their own optimums , act in favor of the SC optimum. But our analyses haven’t sough to determine the value of the optimum of the echelon being considered: it is certainly this determination which depends on having other supply chain members upstream and downstream of the echelon and which is to be done concurrently for all the echelons that make up the supply chain, as we have already mentioned at the beginning of section 5. As to multiple members in the same SC segment, we shortly consider two models with one supplier and multiple competing retailers. For the sake of brevity , demonstrations are not shown, but the methodology is still the same we have seen in previous sections.



e-MENSA – SSA Project The first model has a fixed retail price and competition occurs by allocating demand among the retailers proportional to their inventory. In this model the retailers are biased towards ordering more inventory than optimal, because of the so called demand stealing effect: each retailer fails to account for the decrease in the other retailer’s demands when he increases his order quantity. As a result, with just a wholesale price contract the supplier can coordinate the supply chain and earn a positive profit. Nevertheless, there are limitations to that coordinating contract: it provides for only one division of supply chain profit and it is not even the supplier’s optimal wholesale price contract. A buyback contract does not share those limitations: with a buyback contract the supplier can coordinate the supply chain and earn more than with the optimal wholesale price contract. The second model with retail competition yields qualitatively very different results. In this model the following sequence of events occurs: the retailers order inventory, market demand is observed and then the market clearing price is set. The market clearing price is the price at which consumers are willing to purchase all of the retailers’ inventory. Hence, retailers might incur a loss on each unit when the market demand realization is low. The retailers anticipate that possibility and respond by ordering less than the optimal amount. As a result, in contrast to the quantity allocation competition of the first model, now the supplier needs an instrument to increase retail inventory. Two are considered: resale price maintenance and buyback contracts. With either one the supplier can coordinate the supply chain and extract all of the supply chain’s profit. Given the relevance of the multiple members case for the supply chain made up of SME’s, the related illustration is shown in appendix A to this document. 5.3 Dynamic pricing In recent years there has been an increasing interest on innovative pricing strategies in an effort to improve supply chain operation. Firms are employing methods of dynamically adjusting price over time based on inventory levels, production schedules, customer segmentations based on their sensitivity on price and lead time. As known, dynamic pricing has always been common practice in the agrifood industry, especially for fresh food. Approaches of dynamic pricing require coordination among production, distribution and marketing decisions (in particular, decisions on pricing) which are made, in a supply chain of independent SME’s, by different SC member enterprises and could be made at different times; hence the strong need of considering dynamic pricing within a comprehensive collaboration process as that being studied in the SMEC model. A research study, conducted in 2002, has analyzed the problem of dynamic pricing for an organizational set (i.e. a generic firm) with a whole lot of assumed operational features which, however, can be deemed as very common, so that the study results are significant



e-MENSA – SSA Project also in the real world [Chen, X., D. Simchi-Levi. Coordinating inventory control and pricing strategies with random demand and fixed ordering cost: the finite horizon case. Working Paper. Massachusetts Institute of Technology. 2002]. The study aims at providing the best inventory policy and pricing definition which, together, maximize the firm profits. Some of the assumptions made are the following: • the firm makes inventory and pricing decisions over a finite time horizon with T

periods ; • demands dt in different periods ( t = 1, 2, 3…T) are independent from each other and

are of the following form: dt = Dt(p) + βt where p is the price, Dt(p) is the demand shape as function of price (“additive demand function”) and βt is a random variable;

• the firm incurs both fixed and variable ordering costs (which include production costs if the firm is a producer); the order is only made at the beginning of each period;

• the firm incurs inventory holding costs; unsatisfied demand (if any, in the period) is backlogged and penalty costs are incurred for lost sales.

The study results are that, in the above operational context, there exists an optimal inventory policy referred to as “(s, S, P) policy”. This is a very simple policy which consists of • checking, at the beginning of each period t, on whether the inventory level xt (which

has been passed over from the previous period t-1) is lower than the level st ; • if the above is the case an order sized (St - xt) is to be placed and the price is to be set,

at the beginning of period t, as pt = pt (St ); • otherwise no order is to be placed and the price is to be set, at the beginning of period

t , as pt = pt (xt ). The above means that the price is set dynamically on each period depending on the inventory level xt faced at the period beginning. Given that the optimum exists, it can be sought for with numerical techniques implemented by the Decision Support System which the firm avails of. pt (St ) (or respectively pt (xt ) ) is that price that maximizes the expectation of the profit of period t calculated accounting for the random demand and the associated revenues generated by the price pt and also accounting for the holding (or penalty) cost associated to the initial inventory St (or respectively xt ). This result is not tautological; as a matter of fact, it has to be notice that the objective of the pricing policy being considered is that of maximizing profits for the whole set of the T periods, whereas the result of the study is that the above objective is met just maximizing profits over every single period t, with a simple standard (s,S) policy associated to an ad hoc setting of the price in every period, based on the initial inventory level. This approach appears to be particularly useful in agrifood, especially in fresh food markets where the periods t may just be one day lasting. The same study reports very similar results in cases where the demand is “multiplicative” (i.e. of the form Dt (p) = at p-b ) instead of additive. Also similar results are achieved in the case of infinite planning horizon (T very large) as for products with long life cycle.



e-MENSA – SSA Project The above refers to pricing policies considered along with inventory policies; other studies have considered pricing policies along with inventory and production policies. Two different strategies have been studied [Chan L. M. A., D, Simchi-Levi, J. Swann. Effective Dynamic Pricing Strategies with Stochastic Demand. Working Paper. Massachusetts Institute of Technology. 2001]: • Delayed Production, where decisions about pricing policies are determined at the

beginning of the planning horizon, while production and inventory decisions are made period by period (to be noticed that this decision on pricing does not correspond to a fixed pricing policy, but to an anticipated setting of price over the various periods t of the planning horizon);

• Delayed Pricing, where decisions about production levels are made at the beginning of the planning horizon, while planning and inventory decisions are made period by period.

The study assumes a stochastic demand Dt(p, et(pt )) , where et(pt ) is a random variable and a limited production capacity qt ,in each period, with only variable production costs, inventory holding costs charged on inventory carried from one period to the next and freedom for the decision maker to leave demand unsatisfied, or just produce more than demand, and forgo immediate revenue for potentially higher revenue in the future (e.g. when future prices are expected higher or production costs are known will be higher). As to the Delayed Production strategy, the result has been that, given a vector of prices P (i.e. the whole set of prices p1 , p2 … pT over the periods of planning horizon), there exists an optimal policy consisting of an optimal order-up-to-level (inventory policy) and an optimal save-up-to-level (production policy). The above means that, at the beginning of each period t, the amount produced should be such that • to raise the inventory, inherited from the previous period, to the optimum level

evaluated for the same single period (and called the “optimal order-up-to level”) or as close as possible if the capacity production constraint is reached,

• to leave an amount of product in storage equal to the optimal save-up-to-level for the same single period, i.e. the level which maximizes future returns over sales lost in the current period.

The reference to the single period is underlined, to highlight the important fact that both the optimal order-up-to level and the optimal save-up-to-level do not depend on the level of inventory carried over from the previous period. Again, then, the result is not tautological, because the optimization problem, to be performed over the whole set of periods which make up the planning horizon, is broken down into manageable maximization problems of every single period. Unfortunately, for the Delayed Pricing strategy, the study has produced more complex results, on which it may suffice, here, to say that: • the save-up-to-level in a specific period depends upon the initial inventory level of

that period; • price does not necessarily increase as inventory decreases.



e-MENSA – SSA Project Extensive numerical simulations performed by the study, as well by other studies, shows the following. On the whole, the benefits of dynamic pricing are the higher : • the smaller the available production capacity, • the higher the degree of demand uncertainty, • the higher the level of demand seasonality, • the shorter the planning horizon. Expected profit increases can be of the order of a few percents (significant in sectors which operate with small profit margins). In the simulations, Delayed Pricing usually outperformed Delayed Production.



e-MENSA – SSA Project 6. QUALITY CONSISTENCY CRITERIA In a supply chain, the final product or service is the aggregation of the results of the activities of its members and to these different activities are entrusted the various quality features that the product/service must provide. The global quality level is just a composite of those features which then must to be consistent with each other. As a matter of fact, as the strength of a chain is that if its weaker ring, the product quality level is as low as that of its worst quality feature. The problem of ensuring quality consistency in a supply chain owned or controlled by a large enterprise is usually solved by the same large enterprise, which sets le quality specifications that each member must grant, under penalty of rejection of its output or its expulsion from the supply chain.. But in a decentralized supply chains of SME’s, this management approach cannot be adopted, by definition of “decentralized” , and the global product quality rests on the specific quality features which are defined by each of the bilateral contracts which govern the exchanges between supplier members and client members. As for other criteria considered in the SMEC model, if a member can be placed in the position of the supply chain coordinator, he/she may wield the power to impose consistent quality requirements to all other members. But in a supply chain made up of SME’s this is more like a theoretic conditions, easy to fall down when there are serious disagreements among members. Again the approach pursued by the SMEC management model is that of looking for incentives to place in the bilateral contracts that govern the transactions among SC members. In order to give a closer look at the problem, consider the contract between a retailer and his supplier (who is unlikely to be a primary producer, in the agrifood business). The retailer is the most aware of the whole set of quality features which are sought by consumers; but when he negotiates with the supplier, he can only impose conditions on features which are directly under the control of the supplier (for the product acquired and for the processing executed). Features that are out of the supplier’s control and not self evident at the time of the exchange, are likely to be out of the contractual agreement. For instance, this may be the case for conservation time of fruit and vegetable, which is not self evident at the time of the exchange and may depend on the processing features in earlier stages of the supply chain. On the other hand, conservation time is unlikely to be in the contractual agreement of this supplier (say, he is just a wholesaler) with his own upstream supplier, who in turn could be a primary producer or even another wholesaler, just because he is not interested in conservation time as long as he will hold the product for short a time as possible.



e-MENSA – SSA Project In addition, when the contractual quality specifications are not met, the product will be rejected by the retailer and redirected by the supplier to a secondary market of lower level or to waste disposal; but should not to occur in a highly functional supply chains. It is clear, from the above, that the full set of quality features is to be well known and carefully considered by all SC members, both to prevent consumer disappointment and product waste. In principle, the contractual quality features in the exchanges at the supply chain tail should include also the features applicable at the SC head. But what incentives may have the SC members in engaging in such agreements, where no member wields the power to impose them ? Can an “external quality premium” have a significant role? (for instance a discount granted by each member to his supplier which, in turn, assumes liability for those quality features that are outside his control). Can this contractual device grant larger profits to all members? (in which case a condition of Nash equilibrium would be met) or can, however, grant higher profits to the supply chain, even though these higher profits are enjoyed by only some of the members? (in which case a Pareto improvement would be achieved). The problems deserves quite an effort of research, because various SC conditions of operations and forms of contractual agreements should be considered. However, just to give a short look at the terms of feasibility of the approach, let’s consider just the following simple model of supply chain: a primary producer providing quantity and sell it at price aq ap ; an intermediary who tries to resell the same quantity to a retailer at price aq bp ; a retailer who will accept only the quantity aq w− , because w units are out of specifications. Without external quality premium, the retailer costs are ( )b ap q w wg− + where g is the cost of lost sales With external quality premium, the retailer costs are ( )b ap e q+

because he accepts and sells the whole and e is the external quality premium. aq For the retailer to incur less cost with the external quality premium, it is to be ( ) ( )b a b ap e q p q w wg+ < − +

which gives b

a

g pe wq−

<



e-MENSA – SSA Project The intermediary’s cost is a ap q without external quality premium. With external quality premium he can afford to pay ap e+ to the producer (and still earn a profit larger than before, assuming b ap p> ) . The producer, in turn, will be subjected to a more stringent quality schedule on his production and, hence, will incur an extra cost of production x. So as long as

b

a

g px e wq−

< <

every one will earn a larger profit and a Nash equilibrium condition is met. All the above refers to a very simplified SC condition and configuration, but it is just to show that there is ground for conducting a deep study of the problem.



e-MENSA – SSA Project 7. OPERATION ANALYSIS CRITERIA Purpose of Operation Analysis is to check on whether: • the supply chain operations are really pursuing the objectives set in the strategic plan; • the strategic plan matches a realistic and updated picture of the reference market. As to the former, specific checks are to be conducted on: the forecasting process; the optimization process; the exception conditions. As to the latter, it is necessary to monitor the characteristics of the market, assumed as the reference, and the consumer group assumed as the target in the strategic plan. 7.1 Analyses of operations versus objectives The sales forecasted over the time period being considered are to be checked against the sales realization over the same period. Differences should find sensible explanations, otherwise the forecasting process is to be reviewed to pinpoint and change unrealistic hypotheses. In an context like our supply chains, featured by the exchange of information and hence by collaborative forecasting, one should check whether misleading forecasts have been provided by some members: despite our efforts to optimize SC operation through optimized conditions of its members, there may still be someone that deems (erroneously in the long run) advantageous for him/her to detour from the collectively planned course of actions. The optimization process of a supply chain is based, as seen in sections 4 and 5, on the exchange of information on the cost structures of each member, but these are to be about the true and updated costs of any single firm of the supply chain. There is a tendency in each entrepreneur to provide an optimistic picture of his/her firm, so it is necessary to monitor the operations results of the supply chains, in terms of the actual costs that are supported by each member and are manifested in the prices charged on the transactions with the other SC members. Another reason for monitoring is that enterprises may rapidly change and so their costs structures, so these changes are to be highlighted as soon as possible to review consistently the optimization process. “Exception conditions” is the term, borrowed by CPFR, to indicate mismatches between the volume of activities assigned to each member by the optimization process and the activity volume accepted by the same members. There are many reasons for an exception condition to occur: enterprises may rapidly change in time so that the restraints on maximum and minimum volume of activities may equally change. There is nothing implicitly wrong in this, but it is necessary to understand whether these changes are temporary or permanent, because, if the former is true, only the distribution of activities among SC members is to be changed for the



e-MENSA – SSA Project current planning period. But if the latter is true, are the terms of the optimization process that need to be changed, otherwise the same mismatch will reoccur over the future planning periods and the optimum conditions will punctually be missed. The terms to be reviewed consist of the performance parameters of the member which rises the exception condition, such as his costs , his minimum and maximum volume of activities .. and the like. There is a tendency in each entrepreneur to negate that changes for the worst, in his/her firm, have occurred permanently, if only because his/her job is also that of inverting negative trends. Hence, the supply chain should endow itself of an objective judgment process, that must be accepted by all members when joining the SC, on whether a change is to be assumed as either permanent or temporary. An analytical (Bayesian) approach is available to this purpose: the approach provides the probability that, given a change has occurred more than once, the same change is to be deemed as permanent. Only the probability boundary is to be set to tune the approach which, afterwards, can be applied as an objective measurement device. Another reason for exception conditions to occur is the request to a member to increase his/her volume of activities beyond the relative restraint. That request can either come from external conditions (e.g. major new market opportunities) or from internal conditions, such as the one, mentioned above, of a member unable to provide his/her part of the activities and then someone else being asked to backup for it. Usually this condition implies that the member, being asked to increase activities, needs to restructure his/her productive facilities to gain a new optimum configuration. That triggers the whole process of financing the restructuring process (see the next section 8) and sheds light on the importance of making sure that the change of other members, which cause the restructuring, are indeed permanent. 7.2 Analyses of strategic plan versus actual market conditions Firms and supply chains are unlikely to be born at the same time: usually supply chains are established with firms that may have been operating for quite a time (in other supply chains). That implies different outlooks of the market from the various SC members and requires the definition of what is the market to be assumed as the reference for the supply chain as well as the group of consumers to be targeted. These definitions must occur at the onset of the SC operation as part of the strategic planning. However, in a rapidly changing environment, such as the global market, these initial definitions must be continuously checked in order to ascertain whether they keep consistency with the current, varying, market conditions. In the following it is suggested that the above check be conducted repeating periodically the same process of initial definition of the reference market and the target group of consumers, in order to ensure there is no mismatch with the SC current strategy. This suggestion is justified by the choice to adopt, for this process, a segment of the wider process of identification and development of new products for the supply chain. As long as new product development is to be seen as a permanent process in order for the SC to readily exploit new market opportunities, it might as well be convenient to use part



e-MENSA – SSA Project of it to check also on whether the right strategy is currently used for the products the supply chain already offers to the market. The following shortly describes the segment of new product development devoted to the definition of reference market and target group of consumers; the procedures proposed in the following are also to be understood as technical support to the process of Quality Function Deployment (see section 3.1). 7.2.1 Reference market definition It should first be recalled what are the desirable characteristics of markets: • Potential, measured by size of the market and sales growth rate; • Penetration, measured by vulnerability of competitors; • Scale, measured by share of market and cumulative sales volume; • (low) Input, measured by the investment necessary to enter and penetrate the market; • Reward, measured by profits; • (low) Risk, measured by instability and probability of losses. The above six criteria are used to evaluate the desirability of a particular market. However this evaluation is usually not so straightforward, because it is very rare that a market will dominate all others in all six criteria. So a supply chain must have some procedure by which to select markets to enter based on these conflicting objectives. There are numerous sophisticated procedures for this evaluation. However, in the first phase of market definition, a simpler procedure is used to screen out from the numerous possible markets a smaller set to be better evaluated. This simpler procedure is called “Market Profile Analysis” and consists of the following steps: • Enumerate the criteria that are important to the supply chain, starting from the ones

listed above (which could be further refined), through a discussion among the SC members to get on a list on which there is general consensus.

• Assign weights to these criteria as a measure of their relative importance to the supply chain.

• For each alternative market, rate each criterium (typically five possible rates are used, such as “much worse=-2”, “worse=-1”, “average=0”, “better=+1”, “much better=+2”).

• Provide an overall evaluation of each possible market simply adding the products (weight x rate) over all criteria.

• Eliminate those market that exhibit a low overall evaluation (so that to leave just a few for further analyses).

The effort of narrowing the area of interest for further analyses allows the next step of definition of the market to be assumed as the reference for the supply chain. Defining a market basically means describing the features of a set of products that have some relationship with each other, typifying those relationships so that to spot which are the products that compete with each other to provide similar benefits to the buyers.



e-MENSA – SSA Project There are a few different procedures available to define a market; such as the following: • Traditional approaches, with which a generic type of product is broken down into

subtypes by physical properties ( such as autos, described as sub compact, compact….etc) or by channels of distributions (products sold directly by manufactures or through independent distributors) or by other similar criteria. The problem with these definitions is that they do not mirror how consumers view the market.

• Cross elasticity, with which two products A and B are in the same market if a reduction of the price of A causes a reduction of the sales of B (and vice versa), i.e. if the two products are “substitutes” (and, then, competitors). This is a very rational definition but cross elasticity is difficult to measure.

• Homogenous uses, with which different products are defined as substitutes because they lend themselves to the same use by the buyers.

• Hierarchical definition based on product substitutability, with which the hierarchy is defined observing the sequence of issues considered and decision made by consumers (e.g. light constructions could be chosen as made of wood, or of steel or of concrete; then, for those made of wood, one should decide about the roof cover which could by metal or by tar… and so on).

• Perceived similarity, based on observed consumer behavior of switching from one product to another and with which the products in the same market can be clustered into “perceptual maps”.

• Mixed procedures which are the most interesting and integrate more of the above approaches, such as hierarchical definition followed by perceived similarity, with perceptual maps on the final branches of the hierarchy. The following figure illustrates an example for coffee market.



e-MENSA – SSA Project 7.2.2 Selection of target group of consumers This selection is most effectively conducted through techniques of segmentation. Market segments can be defined in many ways. The more common criteria are • demographics • attitudes • usage rate • specific benefit sought ( and then specific preferences or choices, such as preference

on reliability or on durability… and so on). There are analytic methods for market segmentation, which identify clusters of consumers that are homogeneous with respect to the criteria selected to represent similarities. One simple technique is the following, supported by available computer programs (which may be part of the e-platform adopted by the supply chain). Suppose the following: S is the set of individuals to be partitioned into segments ( )1 2, ,....., pS S S

{ }1 2, ,......., mY Y Y Y= are the variables adopted for clustering

Let i index the individuals and let ( )1 2, ....i i i imy y y y= be the values Y takes on for individual i . Define the dissimilarity, , between individuals i and h, as the square of the Euclidean distance between and , that is:

2ihd

iy hy

( )222

1

m

ih i h ik hkk

d y y y y=

= − = −∑

The total variance , , of Y can be divided into a “between-group variance”, , and a “within-group variance” , such that

TV BV

wV B wV V VT+ = . Where 2

1 12

m m

T ii h

nV y= =

= −∑∑ hy n = total number of consumers

2

2j

j j

jS i hy

i S h S

nV y

∈ ∈

= −∑∑ jn = number of consumers in group jS

1j

p

w Sj

V V=

= ∑

Specific computer programs, adopting a heuristic procedure, will find the partition in segments which minimizes the within-group variance ( so finding the segments with the most homogeneous consumers in them, i.e. the segments we are looking for).

wV

Of course the computer results must be examined to interpret the meaning of each segment, i.e., what kind of consumer each segment identifies in terms of the segmenting variables that have been used.



e-MENSA – SSA Project 7.2.3 Strategy check Market definition, for instance through the hierarchical description of products , and target group segmentation, through the above identification of consumers , represent the two needed elements of a product and market strategy. Assuming that the above elements are obtained through the collection of fresh data from the market, the check to be periodically performed for the supply chain is the following: does the supply chain strategy still match one or more couples of products-consumers as was set in the initial definition of the strategic plan or there is some mismatch denoting that something has changed in the market, either in terms of available products (from competitors) or in terms of consumers tastes and preferences? When mismatches are highlighted, they have to be submitted to the coral analysis and decision making process of the Quality Function Deployment process, in order to undertake the appropriate corrective actions. However, when mismatches are large and/or non-marginal corrective actions appear necessary, it is time to devote efforts to some new product development in order to provide new breath to the supply chain (but this development, which requires quite a number of pages to be treated, is out of the scope of this document).



e-MENSA – SSA Project 8. CRITERIA OF FINANCING IMPROVEMENT PROJECTS First we should briefly state what is the problem to deal with. With a world rapidly changing, frequent are the occasions for improving business organizations. If this is true for a generic enterprise, it is certainly truer for a supply chain: one after the other, its enterprise members will need to incur some change, so that, almost continuously, a supply chain will be facing the problem of implementing and financing those necessary changes, in particular when these consist of technological improvements which require to have access to the right amount of financial resources to manage as investment capitals. Within supply chains owned or controlled by large enterprises, is the large enterprise which eases or grants the access to the necessary financial resources; as a matter of fact, the large enterprise has all the interests in making the members of “its” supply chain work at their best. But in a decentralized supply chain, made up of SME’s, the small size of the SC members turns into a limited access to financial resources, making it bitter the problem of implementing projects of improvement of the supply chain. More often than not, investment projects are to be undertaken by one or few members of the supply chain at a time: today, transportation means or warehousing facilities are to be updated and tomorrow it will be the turn of production or transformation. So the recurrent problem, in a supply chain made up of SME’s, is that of large amounts of investment capitals needed by SC members with low power to access them. On the other hand, whereas the improvement project costs fall on few members, the future benefits granted by these improvements are collected by all members, because, by definition, these projects turn into high efficiency and/or effectiveness of the supply chain operation. One way to get around this problem is that of resorting to collaborative financing of the supply chain improvement projects, i.e. all SC members contributing to the financing of the project. In principle, the collaboration might come in two forms: • contributing capitals; • sharing liability. the latter being of value only when it is recognized by the financing institution which will grant the loan. The usual approach, that we have adopted in other collaboration criteria, holds here. There is to be a business reason why all the SC members collaborate in the financing effort of one or few members; after all, the improvements, such as new transformation plants, will rest with the owner member.



e-MENSA – SSA Project These reasons can only be provided by a specific “business plan” developed for the improvement project. To be noticed that, as opposed to the CPFR guidelines which suggest the SC members join their business plans, in the SMEC model a business plan is to be set up only for each improvement project, the financing of which is beyond the capabilities of the interested members. Needless to say, the business plan is to be developed with reference to the whole supply chain, identifying costs to be incurred by all members, within their financing capabilities, and future returns (e.g. in terms of higher revenues) also collected by all members and granted by the better SC operation which is made possible by the improvement. The business plan will be tuned so that to show a balance of costs and benefits for each SC member, meeting the restrains posed by the limited financing capability of each member. Hence, as with the operations optimization criteria, an analytical approach, which makes use of Linear Programming techniques, needs to be adopted. Just to provide a perception on how these techniques will be used, the following provides a simplified scheme of the equations which should be met with the expected benefits evaluated by the business plan.

ii

c C=∑

,max0 i ic c≤ ≤

i ic k b= 0 1k< <

( ),1

n

i it

b pv p=

=∑ t

)

ii

b C≥∑

Where:

ic is the contribution to the financing provided by the SC member i C is the total cost of the improvement project

,maxic is the financing maximum capability of member i

ib is the benefit expected on member i from the improvement project k is the cost/benefit ratio, assumed equal for all members of the SC

( ,i tpv p is the present value (the value discounted to the time (year) t=0 when the project cost is incurred) of the extra profit expected to be gained by member i over the year t :

( )( )

,, 1

i ti t t

ppv p

r=

+



e-MENSA – SSA Project where the interest rate r is the largest between the cost of the loan granted for the capital investment and the opportunity cost (the annual rate of return of the best alternative investment for the supply chain). In case of profits expected to be equal every year ( ,i t ip p= ) :

( )11

1i

i n

pbr r

⎡ ⎤= −⎢ ⎥

+⎢ ⎥⎣ ⎦

Where n is the expected commercial life of the improvement to be implemented. It is to be noticed that (,i t i )p or p is the extra profit expected on enterprise member i from its doing business with the supply chain; that applies to all members but those who will be the owners of the improvement; for those owners the related value to use for

,i t ip or p will be the extra profit expected from its doing whatever business, i.e. both within and outside the supply chain. So, if one of those owners participate to the supply chain with a fraction f (f < 1) of its total business, the profit value to use in the above equations will be :

,i t ip porf f⎛ ⎞⎜ ⎟⎝ ⎠

The above provides to ask for a larger contribution to the members owners of the improvement. When the contribution is made as investment capitals (each member is granted a loan as part of total investment), each member will pay back for his own loan with the extra profits that will be afforded by the improvement. But also when the contribution is made in form of liability (on a fraction of the total investment), each member, who only provided liability, is to contribute to pay back for the same fraction of the whole loan (granted to the member owner) with the extra profits afforded by the improvement. The above evaluation procedure makes the implicit assumption that the SC members are risk neutral. More often than not, SME entrepreneurs may have a risk adverse behavior. When this is the case the above evaluation should be done for a scenario that corresponds to conservative values of the uncertain parameters. If these parameters are multifold, the evaluation is to be repeated many times with different values of those parameters achieved from random extractions by the relative distributions (Montecarlo approach). The various results of the evaluation will, in turn, be organized so that to show the probability distribution of the result of interest ( for instance, of the total benefit );

from that distribution, one can, for instance, evaluate the likelihood that the condition is not met, so that the decision on whether to undertake the improvement with

a collaborative financing can also be made with information about the impact of adverse events.

ii

b∑

ii

b C≥∑



e-MENSA – SSA Project In case the uncertainties are only due to randomness of the demand for the product or service of the supply chain, the above evaluation can be certainly done for the expected values of annual sales

(see sect. 5.2.1) ( ) ( ) ( )0

,q

S t q t F t y dy= − ∫


)Where q(t) is the annual quantity of product that the supply chain puts on the market at year t and ( ,F t y is the probability distribution of demand at year t. In this case the above procedure will be executed with the expected values of profits ,i tp calculated subtracting costs from the revenues allowed by the expected sales. Again, in case of risk adverse members, it may be required to perform the above evaluation for a (subjective) “worst case” scenario. One way of doing this is that of selecting a value of probability that we want to assume for the worst case scenario; for instance 0.25 (25%). In the calculation of expected sales, we then consider only the initial part of the probability function F(y), from 0 to 0.25. Then apply the above procedure with this value of expected sales and find the expected values of profits and benefits, which will be lower or even negative this time, providing the worst case scenario expected with that probability assumed above.


e-MENSA – SSA Project 9. EXECUTION CRITERIA

Execution of the processes proposed by the SMEC model is enabled by the adoption of the right tool for each of the elements of the model.

For the tools that are available to this purpose, the reader is referred to the document “BRIEFING ABOUT E-PLATFORMS AND SUPPLY CHAINS” as part of the WGMAP activities of e-Mensa project.

In addition to the tools mentioned in the above document, it is worth here mentioning a new powerful tool that has recently gained the attention of supply chain managers and practitioners and that is called “Business Process Management” or BPM.

This tool has evolved from an initial concept of, so called, Business Process Reengineering (BPR), a kind of methodological approach for restructuring the business processes to fit them to the new information and communication technologies. But, over time, this methodological approach has evolved towards being a tool, in addition to a method, for managing the whole lifecycle of the business processes which occur in a supply chain.

According to GARTNER GROUP, “Business Process Management or BPM, is the practice of improving the efficiency and effectiveness of any organization by automating the organization's business processes. BPM used to be also know as Business Process Reengineering (BPR)“. In this simple definition, the keywords are “automation” and “business processes” However, the added value of BPM is not limited to business process automation, even tough that is certainly a notable result.

The e-Mensa document “BRIEFING ABOUT E-PLATFORMS AND SUPPLY CHAINS” reports on e-business platforms which can be provided with the various functionalities which are needed to the supply chain. Basically, that document states that the typical platform provides, for these functionalities, - the right execution environment, the right interfaces with other functionalities (for

instance provided by an ERP) that are executed within the computing facilities of the enterprise members of the supply chain,

- the right interfaces with the human operator when he/she requests a direct service over the internet (i.e. using only a browser, like explorer), such as visiting the catalogue of a supplier,

- the right access to data repositories of the supply chain. As explained in that document, e-platforms are already well equipped to support automated business transactions between supply chain members. However, the same document, written a year ago, states that, in an approach such as the one suggested by the SMEC model, high levels of collaboration are necessary among the SC members and not all the functionalities required to implement this collaboration are inherently provided by the available e-platforms.

However, the recent availability of BPM platforms has made this statement less true, today.




As a matter of fact, a BPM tool is concocted to widely support a whole set of collaboration activities, through the design, the simulation, the implementation, the monitoring, and the control of processes which require the interventions of many human operators. To this extent a BPM platform is the best alley to the supply chain managers who want to increase the level of collaboration of their supply chain.

Within the SMEC model, BPM is the right tool to set up the collaborative strategic planning through the full support to the Quality Function Deployment, which can be instantiated as a web process, i.e. a process which can be participated by all SC members through the internet.

The same is true for the SCOR Roadmap, as it is for the whole work flow of processes that implement the complex conditions of supply contracts which can coordinate the supply chain, as seen in section 5.2. Still the same applies to information sharing, quality consistency, collaborative financing.. and the like.

In other words, BPM, today, is the last piece of technology that can turn collaboration models, such as SMEC, into real world operational practices for supply chains made up by SME’s. A few words about BPM may be worth here.

In order to use BPM effectively, organizations must stop focusing exclusively on data and data management, and adopt a process-oriented approach that makes no distinction between work done by humans and by computers. The idea of BPM is to bring processes, people and information together.

The vision of the supply chain as a whole set of processes requires separation of flows (of activities and of information), business rules and services that support those flows.

Identifying the business processes is relatively easy. Breaking down the barriers between business areas and finding owners for the processes is difficult.

BPM not only involves managing business processes within the enterprise members of the Supply Chain but also involves real-time integration of the processes of each member with those of the other SC partners. A simple example of BPM functionality can be the following.

When an SC member needs some inventory, he can log into the web site, built with the BPM platform, and order the required inventory. A message will be generated and sent to another member enterprise that can supply the inventory. Regardless the physical location of that enterprise and its adopted computer system, the supervisor of that enterprise receives the message and releases his approval to the inventory shipment, provided that the applicable rules are met by the member requesting the inventory. The check on whether those rules are met is done automatically by the BPM tool. The requesting member will then be notified of the allocation and the inventory will be shipped.

It is important to underscore that a BPM tool provides a so called IDE (Integrated Development Environment) for designing a whole set of processes and for defining the



e-MENSA – SSA Project rules that must be met. This design is accomplished without writing computer code but through simple operations of click and drag on icons that represent the basic components of processes and rules.

When the design operation is through, the whole net of processes can be simulated, to verify its consistency, and is “released” and deployed, ready to get into action as soon as a SC member initiates the starting action. The BPM will so issue the appropriate messages and will send them to the other SC members involved in the process; it will also provide to check on the applicable rules before proceeding to the next steps of the process as far as to the foreseen end action.

A further capability of a BPM tool is that of monitoring the SC processes, taking measurements of the actual performances and comparing them with pre-defined target performances. Whenever actual vs target performances are unsatisfactory, alarm messages are generated and sent to the involved SC members, so that corrective actions can be taken.

Another outstanding feature of a BPM tool is in-line reconfiguration: whenever the above corrective actions consist of modifying some process, this change can be implemented without “stopping the train”; the whole flow of SC processes does not need to be stopped and only the affected process will be submitted to some change of the applicable rules with seamless progression of the supply chain operation. A Business Process Management Solution has Six Components: BPM IDE, i.e. the integrated design environment used to design processes, rules, events and exceptions. Creating a structured definition of each process is very important to any business and the IDE enables a business user to design all processes with no programming knowledge. Process Engine, which keeps track of the states and variables for all of the active processes. Within a complex system, there could be thousands of processes with interlocking records and data. User Directory. Administrators define people in the system by name, department, role and even potential authority level. This directory will enable tasks to be sent automatically to the defined resources. Workflow. This is the communication infrastructure that forwards tasks to the appropriate users of the Supply Chain members. Process Monitoring & Reporting. Enables users to track the performance of their current processes and the performance of those who are executing these processes. Integration. Devices of Enterprise Application Integration (EAI) and/or Web services make up this component which is critical to BPM, as long as business processes of the Supply Chain require data from the disparate computer systems of the various SC



e-MENSA – SSA Project members. The above mentioned Process Monitoring component is usually referred to as BAM (Business Activity Monitoring) which is devoted to the automated monitoring of the SC business processes. BAM requires the Supply Chain to identify its Key Performance Indicators (KPIs) so that to concoct a system that enables fast, even real time, response to changes, whether they are threats or new business opportunities. Hence BAM is particularly suitable to implement SCOR Roadmap guidelines. BAM provides Graphical Key Performance Indicators & Analysis and enables zoom in on cross-process metrics with real-time analysis to determine which processes are creating bottlenecks or which customer is most profitable. Among the most recognized advantages of BPM, are the following: BPM is excellent for processes that extend beyond the boundaries of an enterprise and communicate with processes of the partners, customers, suppliers and vendors; so BPM is born as the process management tool of Supply Chains. BPM makes it easy for companies to program their current processes, automate their execution, monitor their current performance and make on-the-fly changes to improve the current processes. A BPM software enables the automation of those tasks that are currently being performed manually. Many of these tasks require some type of application process, approval or rejection process, notifications and status reports. A BPM solution can make these tasks automatic up to the request for human decision. Handling exceptions is an area where BPM really shines. Organizations have few problems when their processes run smoothly, that is ninety percent of the time. However, it's that ten percent of exceptions that dominate the majority of the organization's time and resources. BPM gives businesses the agility to stay competitive, reduces the time elapsed in a business process and increases the productivity per person. Usually a business process consists of many steps. A typical BPM initiative reduces the number of steps by 50%. A Business Process needs many people and resources. A good BPM is able to reduce the number of resources needed for the same process. BPM helps improve coordination across SC members. About the BPM Solutions available on the market, they may be sorted into two categories:




- complete solutions, developed as native BPM tools (such as TIBCO solution); - composites of e-business platforms, applications of process management (so

called Business Process Execution Language - BPEL systems) and applications of Business Rules Management, installed on top of the e-platform and integrated with each other. That is the case, for instance, of the ORACLE‘s e-business platform integrated with its BPEL system and with the ILOG‘s Business Rules Management System.



e-MENSA – SSA Project APPENDIX A

Coordination with contracts in supply chains with multiple retailers Two cases will be examined: competing retailers with fixed consumer price and competing retailers with market clearing price. A.1 competing retailers with fixed consumer price We need first to take the single retailer newsvendor model (described in section 5.2.1) and make the following modifications:

• set ; 0==== vggc srr

• increase the number of retailers to ; 1>n• interpret D as the total consumer demand to our retailers; • let F continue to be the distribution function for D;

• assume the consumer demand be divided between the n retailers proportionally to their stocking quantity, i.e. the demand of retailer i is iD

Dqq

D ii ⎟⎟

⎠

⎞⎜⎜⎝

⎛=

where . In addition, let’s state ∑=

n

iiq

1ii qqq −=− .

Demands at the retailers are perfectly correlated with the proportional allocation model. Hence, either every firm has excess demand (when ) or every firm has excess inventory (when ). That could be a reasonable model when customers have low search costs; a customer that desires a unit finds it if there is a unit in the system. That search need not involve an actual physical inspection of each store by every customer. For example, information regarding availability could be exchanged among customers through incidental social interactions that naturally occur with daily activities. The model also presumes consumers do not care from which retailer they make their purchases, i.e. there are no retail brand preferences.

qD >qD <

Given the proportional allocation rule, in practice the integrated supply chain faces a single newsvendor problem. Hence the optimal order quantity is defined by the familiar

( )gvp

vcqF o +−−

= which, with our assumptions, gives ( )pcqF o = or ( )

pcpqF o

−=

Because the integrated solution remains a single location newsvendor problem, the multiple retailer model with proportional allocation is a nice generalization of the single retailer model. In the decentralized system we want to investigate retail behaviour with either a wholesale price contract or a buy back contract (since the retail price is fixed, in this case there exists a revenue sharing contract that is equivalent to the buy back contract.) Retailer i’s profit function with a buyback contract is :




( ) ( )0

q qi i

i i i i io

q qp q F y dy wq b q q F y dyq q

π⎡ ⎤⎛ ⎞ ⎛

= − − − + − −⎞

⎢ ⎥⎜ ⎟ ⎜⎜ ⎟ ⎜ ⎟⎟⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦∫ ∫

the above profit is taken from the newsvendor model. In the second member, the firs term is the expected sales of retail i, having taken into account that F is the probability function for the demand of the whole set of retailers and the probability function for each

retailer is achieved multiplying the former by iqq

, i.e. the fraction of demand that is

allocated to retailer i, according to the assumption of proportional allocation. The above profit can be rewritten as

( ) ( ) ( ) ( ),q

ii i i i

o

qq q p w q p b F y dyq

π −

⎛ ⎞= − − − ⎜ ⎟

⎝ ⎠∫

Setting b=0, the above also provides the retailer’s profit with a wholesale price contract The second order condition confirms each retailer’s profit function is strictly concave in his order quantity. Hence, there exists an optimal order quantity for retailer i for each iq− . In game theory parlance, retailer i has a unique optimal response to the other retailers’ strategies (i.e. their order quantities). Let ( )i iq q− be retailer i’s response function, i.e., the mapping between and retailer i’s optimal response. Since the retailers have

symmetric profit functions, iq−

( ) ( ) ,j j i iq q q q i j− −= ≠ .

A set of order quantities,{ }* *1 ,..... nq q , is a Nash equilibrium of the decentralized system, if

each retailer’s order quantity is a best response, i.e., for all i, , where

and . There may not exist a Nash equilibrium, or there may be

multiple Nash equilibria. If there is a unique Nash equilibrium, then that is taken to be the predicted outcome of the decentralized game.

(*i i iq q q−= )*

* q* *i iq q q− = − *

1*

n

jj

q=

= ∑

Any Nash equilibrium must satisfy each retailer’s first order condition: ( ) ( ) ( )

*

* * * **

0

, 1 0q

i i ji i

i

q q p wq q F q q F y dyq p b q

π−

⎛ ⎞∂ ⎛ ⎞−⎜ ⎟= − −⎜ ⎟ ⎜ ⎟∂ −⎝ ⎠ ⎝ ⎠

∫ =

*i

Substituting into the above equation and solving for given a fixed : * *iq q q− = − *

iq *q

( ) ( ) ( ) ( )

( ) ( ) ( )

*

*

*

0* *

* *

0

/ 1/

1/

q

i q

p w p b q F y dyq q

F q q F y dy

⎡ ⎤− − −⎢ ⎥⎣ ⎦=−

∫

∫

The above gives each retailer’s equilibrium order conditional on being the equilibrium total order quantity. Hence, the above describes an equilibrium only if

. Substituting this into the above equation and simplifying:

*q

*iq nq= *




( ) ( )*

** 0

1 1 1 qn pF q F y dyn n q p

⎛ ⎞− −+ =⎜ ⎟

wb−⎝ ⎠

∫

The left hand side of this equation increases with from 0 (when = 0) to 1 (when ). Hence, when b<w<p, there exists a unique that satisfies the above equation.

In other words, in there exists a unique Nash equilibrium in which the total order quantity, , is implicitly given by the above equation and each retailer’s order quantity equals .

*q *q*q = ∞ *q

*q* * /iq q= n

Let’s consider how the equilibrium order quantity changes in n. The left hand side of the above equation is decreasing in n. Hence, is increasing in n for fixed contractual terms: a single retailer that faces market demand D purchases less than multiple retailers facing the same demand (with proportional allocation, but other studies show that this effect generalizes beyond just the proportional allocation).

*q

In other words, competition makes the retailers order more inventory, because of the demand stealing effect: each retailer ignores the fact that ordering more means the other retailers’ demands stochastically decrease. However, other studies have shown that this effect does not apply universally, in that competition may lead some retailers to understock when there are more than two retailers and demands are not symmetric. Furthermore, those studies show that if retailers sell complements, rather than substitutes, then the demand stealing effect is reversed: each retailer tends to understock because it ignores the additional demand it creates for other retailers. The above effects of overstocking and understocking appear as negative potentials of competition and are in essence due to how and to what extent information is shared. Appropriate information sharing, among SC members, should favour the best stocking level for the supply chain, without violating competition basic rules, at least in this context with a fixed price. Due to the demand stealing effect the supplier can coordinate the supply chain and earn a positive profit with just a wholesale price contract. As a matter of fact, let ( )w q be the wholesale price that induces the retailers to order q units with a wholesale price contract (i.e. with b=0). Still from the above equation, we get

( ) ( ) ( )0

1 1 11qnw q p F q F y dy

n n q⎡ ⎤−⎛ ⎞ ⎛ ⎞= − −⎜ ⎟ ⎜ ⎟⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦

∫

By definition, ( )ow q is he coordinating wholesale price. Given that

( ) ( ) /oF q p c c= − and ( ) ( )0

1 qF y dy F q

q<∫

it can be shown that ( )w q c> when n>1 . Hence, Hence, the supplier earns a positive profit with that coordinating contract. Let’s recall that, with the single retailer, model SC coordination is only achieved when the supplier earns zero profit, i.e. marginal cost



e-MENSA – SSA Project pricing, ( )w q c= . As a consequence, competition among multiple retailers, when compared to one strong retailer, favours the supplier (with no surprise!). Although the supplier can use the wholesale price contract to coordinate the supply chain, that contract is not optimal for the supplier. The supplier’s profit function with a wholesale price contract is

( )( ) ( )( ),s q w q q w q cπ = −

Assuming n>1, if we differentiate ( )( ),s q w qπ with respect to q and evaluate at ( )ow q ,

we get the coordinating wholesale price:

( )( ) ( ),0

o o o os q w q q p f q

q n

π∂= − <

∂

Hence, rather than coordinating the supply chain with the wholesale price ( )ow q , the supplier prefers to charge a higher wholesale price and sell less than when n>1. oqAlthough the supplier does not wish to use a wholesale price contract to coordinate the supply chain, it is possible the supplier’s profit with a coordinating buyback contract can exceed her profit with the optimal wholesale price contract. Let ( )bw b be the wholesale price that coordinates the supply chain given the buyback rate. Since the buy back rate provides an incentive to the retailers to increase their order quantity, it must be that

( ) ( )bw b w q> o , i.e., to coordinate the supply chain the supplier must use a wholesale price that is higher than the coordinating wholesale price contract, which, recall, is lower

than the supplier’s optimal wholesale price. Taking into account that ( )p

cpqF o−

= and

that ( ) ( )*

** 0

1 1 1 qn pF q F y dyn n q p

⎛ ⎞− −+ =⎜ ⎟

wb−⎝ ⎠

∫ , we get

( ) ( )0

1 1 1 oq

bo

p c nw p p b F y dyn p n q⎡ ⎤⎛ ⎞⎛ ⎞− −

= − − +⎢ ⎥⎜ ⎟⎜ ⎟⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦

∫

given that , retailer i’s profit , with a coordinating buyback contract, is : * * /iq q n=

( ) ( )( ) ( ) ( )* * 1, /o

i i

q

i oo

q q p w b q n p b F y dyn

π−

⎛ ⎞= − − − ⎜ ⎟⎝ ⎠ ∫

( )2

oq

oo o

p b pq p c F y dypn q

⎡ ⎤⎛ ⎞−= − −⎢ ⎥⎜ ⎟

⎢ ⎥⎝ ⎠ ⎣ ⎦∫

( )2 op b qpn

⎛ ⎞−= Π⎜ ⎟⎝ ⎠

The supplier’s profit with the coordinating contract is




( )( ) ( ) ( ) ( ) ( )* * 1, , ,o

s o i i i

p n bq w b b q n q q q

pnπ π −

⎡ ⎤− += Π − = Π⎢ ⎥

⎣ ⎦o

Hence, the supplier can extract all supply chain profit with b=p. As shown earlier, the coordinating contract with b=0 provides a lower bound for the supplier’s profit (because the supplier could do even better with a higher wholesale price than ). The ratio of

the supplier’s lower bound to the supplier’s maximum profit ( )0bw

( )oqΠ , provides a measure of how much improvement is possible by using a coordinating buyback contract:

( )( )

( ), 0 ,0 1s o b

o

q w nq n

π −=

Π

Hence, as n increases, the supplier’s potential gain decreases from using a coordinating buyback contract rather than her optimal wholesale price contract. In fact, the supplier can use a wholesale price contract to capture most of the supply chain’s optimal profit with a relatively few number of retailers: for n = 5 the supplier captures at least 80% of the optimal profit and for n = 10 the supplier captures at least 90%. In practice, that suggests that downstream competition can mitigate the need for coordinating contracts, showing a significant advantage in getting numerous members to join in supply chain segments. A.2 Competing retailers with market-clearing prices In the previous model retail competition influences the allocation of demand. In this model, competition influences the retail price. Specifically, the market price depends on the realization of demand and the amount of inventory purchased. Suppose demand can take on one of two states, high or low. Let q be the retailers’ total order quantity. Let’s refer to an elastic linear demand and adopt normalized levels for quantity and for price (so that the price of the first unit made available on the market is 1). When demand is low, the market clearing price is ( ) ( )1lp q q += − .

When demand is high, the market clearing price is ( ) 1hqp qθ

+⎛= −⎜⎝ ⎠

⎞⎟ with 1θ > . Suppose

either demand state is equally likely. There is a continuum of retailers, indexed on the interval [0,1]. Retailers must order inventory from a single supplier before the realization of the demand is observed. After demand is observed the market clearing price is determined. Perfect competition is assumed, which means the retailers continue to order inventory until their expected profit is zero. Left over inventory has no salvage value and the supplier’s production cost is zero. Some studies have shown that the qualitative insights from this model continue to hold with a continuous demand state space, a general supplier cost function and a general demand function. In addition, they have shown that the qualitative insights also hold if the retailers choose their prices before the realization of demand (making reference to a



e-MENSA – SSA Project model in which all demand is allocated to the retailer with the lowest price, and any residual demand is subsequently allocated to the retailer with the second lowest price, ..and so on). To set a benchmark, suppose a single monopolist controls the entire system (suppose she sells directly to consumers) . In this situation the monopolist can choose how much of her inventory to sell on the market after demand is observed. At that point the cost of inventory is sunk, so the monopolist maximizes revenue pq (instead of profit): in the low demand state the monopolist sells q=1/2 at price ( )1/ 2 1/ 2lp = and in the high demand

state sells / 2q θ= still with price ( )1/ 2 1/ 2hp = . So the inventory order should be one of those two quantities. Assuming the production cost is zero, ordering / 2θ units is optimal. Furthermore, the monopolist sells her entire stock in the high demand state, but in the low demand state the monopolist does not sell some of her inventory (she sells 1/2 versus / 2θ ) . The monopolist’s expected profit is

( ) ( ) ( ) ( ) ( ) ( ) 11/ 2 1/ 2 1/ 2 1/ 2 / 2 / 28o l hp p θθ θ +

Π = + =

Now consider the system in which the supplier sells to the perfectly competitive retailers with just a wholesale price contract. The retailer’s expected profit is

( )1 1 12

qq q wθ

⎡ ⎤⎛ ⎞− + − −⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦q 1q ≤

( ) ( )1 12 2l hp q q p q q wq+ − =

1 12

qqθ

⎛ ⎞− −⎜ ⎟⎝ ⎠

wq 1

w

q >

Let q be the quantity that sets the above profit to zero when( )1 1q ≤ , which is the equilibrium outcome due to perfect competition:

( ) ( )12 1

1q w wθ

θ= −

+

For to hold, it must be that ( )1 1q w ≤ ( ) ( )1/ 2 1/ 2w θ≥ − .

Let q be the quantity that sets the above profit to zero when : ( )2 w 1q >

( ) ( )2 1 2q w wθ= −

For to hold, it must be that ( )2 1q w > ( ) ( )1/ 2 1/ 2w θ< − .

Let be the supplier profit. From the above results, ( )s wπ

( )1q w w ( ) ( )1/ 2 1/ 2w θ≥ −


( )s wπ =

q w otherwise ( )2 w


e-MENSA – SSA Project Let ( )*w θ be the supplier optimum wholesale price:

12

3θ ≤


( )*w θ =

14

otherwise

and

( )2 1θθ+

3θ ≤

( )( )*s wπ θ =

18θ otherwise

So when 3θ ≤ the retailers order

( )( )*1 1

q w θθθ

=+

and the market clearing prices are

( )( )( )*1

11lp q w θ

θ=

+ ( )( )( )*

1 1hp q w θθθ

=+

When 3θ > the retailers order

( )( )*2 2

q w θθ =

and the market clearing prices are

( )( )*2 0lp q w θ = ( )( )( )*

212hp q w θ =

No matter the value of θ , ( )( )*

s owπ θ < Π so the supplier does not capture the maximum


e-MENSA – SSA Project possible profit with a wholesale price contract. When 3θ ≤ the supplier falls short because the retailers sell too much in the low demand state. To mitigate those losses the retailers order less than the optimal quantity, but then they are unable to sell enough in the high demand state. When 3θ > the supplier falls short because the retailers sell too much in the low demand state even though they sell the optimal amount in the high demand state. Hence, in either case the problem is that competition leads the retailers to sell to much in the low demand state. Recall, the monopolist does not sell all of her inventory in the low demand state, but the perfectly competitive retailers cannot be so restrained. To earn a higher profit the supplier must devise a mechanism to prevent the low demand state market clearing price from falling below 1/2. In short, the supplier must curtail the destructive competition that results from having more inventory than the system needs. In one study it has been proposed that the supplier implements resale price maintenance: the retailers may not sell below a stipulated price. Let p be that price. When p is above the market clearing price the retailers have unsold inventory, so demand is allocated among the retailers. Assume demand is allocated so that each retailer sells a constant fraction of his order quantity, i.e. we have proportional allocation. Given the optimal market clearing price is always 1/2, the search for the optimal resale price maintenance contract should begin with 1/ 2p = . Let be the order quantity of the tth retailer and let be the tth retailer’s expected profit. Assume the retailers’ total order quantity equals

tq

( )r tπ/ 2θ i.e.,

( )1

01q t dt =∫

Hence, the market price in either demand state is ½. We later confirm that the retailers indeed order / 2θ in equilibrium. Evaluate the tth retailer’s expected profit:

( ) ( ) ( ) ( )1 1/ 2 12 / 2 2r t q t w q t p q tπ

θ⎛ ⎞= − + +⎜ ⎟⎝ ⎠

p

)

the retailer sells in the low-demand state and sells q(t) in the high-demand state. Simplifying the above profit:

( ) ( ) (1/ 2 / / 2q t θ

( ) ( ) 14r t q t wθπθ+⎛ ⎞= − −⎜ ⎟

⎝ ⎠

so the supplier can charge 14

w θθ+

=

We must now confirm the retailers indeed order / 2θ given that wholesale price. Say the retailers order 1/2 <q < / 2θ , so the tth retailer’s expected profit is

( ) ( ) ( )1 1/ 2 1 12 2

qq t w q t p q tq θ

⎛ ⎞ ⎛ ⎞− + + −⎜ ⎟ ⎜ ⎟⎝ ⎠⎝ ⎠

The above is decreasing in the relevant interval and equals 0 when the wholesale price is w . So with the ( , )p w resale price maintenance contract the retailers order q= / 2θ , the

optimal quantity is sold in either state and the retailers’ expected profit is zero.

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e-MENSA – SSA Project Hence, the supplier earns with that contract. oΠ Resale price maintenance prevents destructive competition in the low demand state, but there is another approach to achieve the same objective. Suppose the supplier offers a buy back contract with b=1/2. Since retailers can earn b=1/2 on each unit of inventory, the market price cannot fall below 1/2: for the market price to fall below 1/2 it must be that some retailers are willing to sell below ½, but that is not rational if the supplier is willing to give 1/2 on all unsold units. Therefore, the retailers sell at most 1/2 in the low demand state and / 2θ in the high demand state. The retailers’ profit with a buyback contract is

( )( ) ( )( ) ( )( )1 11/ 2 1/ 2 1/ 22 2l hp b q p q q qw+ − + −

which simplifies to 34 2

qq wθ

⎛ − −⎜⎝ ⎠

⎞⎟ (this profit assumes 1/2 <q < / 2θ ).

The supplier wants the retailers to order q= / 2θ . From the above equation the retailers earn a zero profit with q= / 2θ when w=1/2. Hence, the supplier maximizes the system’s profit with a buyback that offers a full refund on returns. Although resale price maintenance and thebuy back contract achieve the same objective, the supplier sets a higher wholesale price with the buyback contract, i.e. ( )1/ 2 1 4θ θ> + ; so retailers do not incur the cost of excess inventory in the low demand states with a buy back contract, but they do with resale price maintenance. A buyback contract is also not the same as a revenue sharing contract in this situation. (section 5.2.4 demonstrates the two contracts are equivalent in the single newsvendor model). The buy back contract prevents the market clearing price from falling below 1/2 in the low demand state, but revenue sharing does not prevent destructive competition: in the low demand state the retailers have no alternative use for their inventory, so they still attempt to sell all of it in the market. Those contracts are also different in the single newsvendor model with price dependent demand (not treated in this document). However, in that model the revenue sharing contract coordinates the supply chain and the buyback contract does not. The key distinction is that in the single newsvendor model the retailer controls the market price, whereas in this competitive model the retailers do not. It is interesting that a buyback contract coordinates the supply chain in either competitive model even though in the first one the supplier must discourage the retailers from ordering too much and in the second one the supplier must encourage the retailers to order more. To explain this apparent contradiction, the wholesale price component of the contract always reduces the retailer’s order quantity and the buyback component always increases the retailer’s order quantity. Thus, depending on the relative strength of those two components, the buyback contract can either increase or decrease the retailers’ order quantities. In conclusion, retail competition introduces several challenges for supply chain coordination. There may exist a demand stealing effect which causes each retailer to



e-MENSA – SSA Project order more than the supply chain optimal quantity because each retailer ignores how he reduces his competitors’ demand. For coordination, the supplier needs to reduce the retailers’ order quantities, which can be done with just a wholesale price contract above marginal cost. But that wholesale price contract only provides for one division of the supply chain’s profit and it is not even the supplier’s optimal wholesale price contract. The supplier can do better with a buyback contract and coordinate the supply chain. However, the incremental improvement over the simpler wholesale price contract decreases quickly as retail competition intensifies. In contrast to the demand stealing effect, in the presence of the destructive competition effect, the supplier needs to increase the retailers’ order quantities. This occurs when demand is uncertain and the retail price is set to clear the market. When demand is high the retailers earn a profit, but when demand is low, deep discounting to clear inventory leads to losses. The retailers anticipate this problem and respond by curtailing their inventory purchase. Both resale price maintenance and buyback contracts prevent deep discounting, and therefore alleviate the problem. There are several studies conducted on supply chain coordination with competing retailers.



supply chains made up with sme’s: basic requirements of ...5.1.2.1 newsboy problem ... 5.2.1...

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