Report of the 6th ISIR Summer School on
“Quantitative Models for Supply Chain Management”

Technische Universiteit Eindhoven, The Netherlands, August 18-22,2003

Sponsored by Beta Research School and
 Netherlands Organization for Scientific Research (NWO)

The sixth ISIR summer school was organized at the Technische Universiteit Eindhoven in The Netherlands, with “Quantitative Models for Supply Chain Management” as central theme. Around this theme we had tutorials and presentations by Ph.D. students on recent research. For the tutorials we invited Refik Güllü, Yale Herer, Fikri Karaesmen, and Ulrich Thonemann (also Kaj Rosling was invited, but unfortunately he had to cancel). Further, Ton de Kok and Geert-Jan van Houtum gave a tutorial. We had 18 presentations by Ph.D. students. A new element was that each presentation by a Ph.D. student was followed by comments of 2 discussants: one other Ph.D. student and one senior researcher. Discussants received complete working papers in advance of the summer school so that they were well prepared.

Many of the participants expressed their appreciation for the focus of the summer school on Ph.D. students, the inclusion of tutorials in the program, and the role of the discussants. Many people were pretty much satisfied with the level of the Ph.D. presentations, and the level of the tutorials was even judged as very good.

As social events we had a golf clinic followed by a BBQ, and a factory visit to Océ Technologies followed by the summer school dinner. The golf clinic gave a lot of fun and also had a competitive element. Winner of the exercise part became Roger Hill. After that we walked a 9-holes course in groups of 4 persons. The group consisting of Brenda Ho, Pär Brander, Simone Zanoni, and Roger Hill won that part. At Océ, we first had a tour in a factory where high-end copiers were assembled. Océ’s products range from 5000 EURO machines (low-end copiers) to machines of 1 million EURO (advanced high-speed printing systems). After the tour, an interesting presentation was given about several supply chain issues that play at Océ.

Below, a list of participants and abstracts of all talks are given. For further information, see www.tm.tue.nl/beta. At this site, several presentations and presented papers are available.

Organization committee,Eindhoven, October 11, 2003

Impression of the golf players (Photographer: Kai Hoberg)

Awards for the winners (Photographer: Kai Hoberg)

LIST OF PARTICIPANTS

Tutorial speakers		
-	Refik Güllü, Middle East Technical University, Ankara, Turkey, gullu@ie.metu.edu.tr
-	Yale Herer, Technion, Haifa, Israel, yale@technion.ac.il
-	Fikri Karaesmen, Koç University, Istanbul, Turkey, fkaraesmen@ku.edu.tr 
-	Ulrich Thonemann, Münster University, Germany, 	                ulrich.thonemann@uni-muenster.de
Ph.D. students		
-	Pär Brander, Luleå University of Technology, Sweden, Par.Brander@ies.luth.se
-	Xavier Brusset, Université Catholique de Louvain, Belgium, xavier@brusset.com
-	Umut Corbacioglu, Erasmus University, The Netherlands, ucorbacioglu@fbk.eur.nl
-	Roland Deme, Eötvös Lórán University of Science, Budapest, Hungary, demeroland@freemail.hu
-	Mustafa Doğru, Technische Universiteit Eindhoven, The Netherlands, m.k.dogru@tm.tue.nl
-	Brenda Ho, Tamkang University, Taipei, Taiwan, chho@mcu.edu.tw
-	Kai Hoberg, Münster University, Germany, Kai.Hoberg@uni-muenster.de
-	Bram Kranenburg, Technische Universiteit Eindhoven, The Netherlands, a.a.kranenburg@tm.tue.nl
-	Johanna Laine, Luleå University of Technology, Sweden, Johanna.Laine@ies.luth.se
-	Hussein Naseraldin, Technion, Haifa, Israel, nhussein@TECHUNIX.technion.ac.il
-	Fredrik Olsson, Lund University, Sweden, fredrik.olsson@iml.lth.se
-	Deniz Özdemir, INSEAD, Fontainebleau, France, deniz.OZDEMIR@insead.edu
-	Ulas Özen, Technische Universiteit Eindhoven, The Netherlands, u.ozen@tm.tue.nl
-	Patrik Tydesjö, Lund University, Sweden, patrik.tydesjo@iml.lth.se
-	Bas Verheijen, Erasmus University, The Netherlands, bverheijen@fbk.eur.nl
-	Ying Xie, Coventry University, United Kingdom, Y.Xie@coventry.ac.uk
-	Banu Yüksel, Bilkent University, Ankara, Turkey, ybanu@bilkent.edu.tr
-	Simone Zanoni, University of Brescia, Italy, zanoni@ing.unibs.it
Senior researchers		
-	Derek Atkins, The University of British Columbia, Canada, atkins@oldadm.ubc.ca
-	Attila Chikán, Budapest Univ. of Econ. Sciences and Public Adm., Hungary, Chikana@axelero.hu
-	Israel David, Ben-Gurion University of the Negev, Beer-Sheva, Israel, idavid@bgumail.bgu.ac.il
-	Roger Hill, University of Exeter, United Kingdom, R.M.Hill@exeter.ac.uk
-	Gudrun Kiesmüller, Technische Universiteit Eindhoven, The Netherlands, G.P.Kiesmueller@tm.tue.nl
-	Roelof Kuik, Erasmus Universiteit, The Netherlands, rkuik@fbk.eur.nl
-	Erwin van der Laan, Erasmus Universiteit, The Netherlands, E.Laan@fbk.eur.nl
-	Ravi Ravichandran, Indian Institute of Management, Ahmedabad, India, nravi@iimahd.ernet.in
-	Jacob Wijngaard, University of Groningen, The Netherlands, j.wijngaard@bdk.rug.nl
-	Henk Zijm, University of Twente, The Netherlands, zijm@CS.UTWENTE.NL
Organizers		
-	Karel van Donselaar, Technische Universiteit Eindhoven, The Netherlands, k.h.v.donselaar@tm.tue.nl
-	Geert-Jan van Houtum, Technische Universiteit Eindhoven, The Netherlands, G.J.v.Houtum@tm.tue.nl
-	Ton de Kok, Technische Universiteit Eindhoven, The Netherlands, A.G.d.Kok@tm.tue.nl
-	Mieke Rossou, Technische Universiteit Eindhoven, The Netherlands, M.E.H.A.Rossou@tm.tue.nl (Beta office)
ABSTRACTS (IN CHRONOLOGICAL ORDER)

Tutorial 1: ‘On the Relation between Cost and Service Models for General Inventory Systems’ by Geert-Jan van Houtum  

In this talk, a systematic overview is presented of possible relations between cost and service models for fairly general single- and multi-stage inventory systems. In particular, we relate various types of penalty costs in pure cost models to equivalent types of service measures in service models. We show how an optimal policy for a service model may be obtained from cost-optimal policies in a related pure cost model. Pure cost models have been studied extensively in the literature. By these results it seems possible to transform many of the known optimal solutions for pure cost models to service models, which are more appropriate from a practical point of view. A number of examples is discussed to show the generality of the results.

Ph.D. Presentation 1: ‘Analyzing the Bullwhip Effect of Installation-Stock and Echelon-Stock Policies with Linear Control Theory’ by Kai Hoberg. Discussants: Roland Deme and Roelof Kuik.

We analyze the dynamic behavior of various inventory policies from a control theoretic perspective. We consider several categories of inventory policies and focus on the comparison of installation stock and echelon stock policies in a two-echelon supply chain and derive their transfer functions. For each policy category we present two different policy types: the original order-up-to policy and a policy that is partially adjusted according to the error between the target installation or echelon stock and the actual level. We use eight performance measures relating to stationary and non-stationary demand to investigate the effects of the policies on the supply chain. We show that even in the presence of information delay the echelon stock policy with partial adjustment shows superior behavior.

Ph.D. Presentation 2: ‘When Competitors Agree to Cooperate: The Case of Transshipment in Supply Chains’ by Derek Atkins (replaced his Ph.D. student Xuan Zhao). Discussants: Xavier Brusset and Refik Güllü.

It is a commonplace observation that even the most competitive firms often find it in their best interests to cooperate. Taking the special case of competitive supply chains, there is a long history of cooperation when it helps both parties. Long-term examples are joint supply arrangements such as flower or vegetable markets/auctions and recently e-auctions for parts or components have sprung up in many industries. One simple example of cooperation is when two supply chains agree in advance to transship or `pool' surplus product for use by another. The alternative is to let their customers switch unsatisfied demand to a competitor. Now which is preferable, and how does such a preference depend on the many parameters, prices, the nature of competition, the degree of competition, wholesale prices etc. Simply when should competitive retailers transship? To get answers we study a stylized model under three market environments: a market with an exogenous retail price, an endogenous retail price, and with price competition. The summary answer is that strong price competition between substitutable goods should lead to caution in signing transshipment contracts. But with little price competition and particularly where retailers are free to set the transshipment price, then transshipment is probably the way to go. However this simple summary is tempered by both the many parameters in play and the nature of the stylized model studied.

Tutorial 2: ‘Game Theoretic Supply Chain Models’ by Refik Güllü.

In this presentation we intend to accomplish two objectives: (1) to present a brief introduction to game theoretic concepts, and (2) to outline some specific supply chain related models that are analyzed using game theoretic tools and techniques. To achieve the first objective, we discuss Nash equilibrium, existence and uniqueness issues by posing a simple model of stock competition between two retailers. We also present examples where an equilibrium either does not exist, or there are multiple equilibriums. For the second part of the talk, two supply chain models under different competition schemes are presented. We present and discuss leader-follower games in supply chain context and related coordination issues. The talk is concluded by outlining some potential research opportunities in game theoretic supply chain modeling.

Ph.D. Presentation 3: ‘A Strategy for Vendor Managed Inventory: Analytical Approach and Performance Evaluation’ by Simone Zanoni. Discussants: Patrik Tydesjö and Roger Hill.

This research investigates an industrial policy based on the principle of a vendor-managed inventory. The strategy, known as Consignment Stock (CS), may lead to successful results for both buyer and supplier. The study presents the analytical model developed for the CS policy in the deterministic case, referring to the single-vendor and single-buyer situation. Afterwards, the CS policy is compared with the traditional approach available in literature. Analytical results allowed the identification of the benefits introduced by the CS approach, referring to environments affected by uncertain demand and variable delivery lead times. The results obtained enhance the conclusions of the previous contributions (the last is going to be published). They also allow a more comprehensive understanding of the Consignment Stock mechanism and potentialities, identifying the stochastic environments where CS may be successfully adopted.

Ph.D. Presentation 4: ‘Consolidation and Accumulation Opportunities as a Driver for VMI’ by Bas Verheijen. Discussants: Simone Zanoni and Gudrun Kiesmüller.

Under an arrangement called Vendor Managed Inventories (VMI), the vendor and buyer can achieve either equal or lower costs for the total supply chain than in the traditional case. The vendor controls the timing and quantity of goods to ship and has thus the ability to optimize the shipment of goods to his buyers and lower the costs of the supply chain. In this paper, we have reviewed different models from literature that aim to optimize inventory and transport of goods from vendor to buyer. We present models describing situations of single vendor with a single buyer shipping one or multiple products as well as models describing the situation of one vendor with multiple vendors. We propose a generalization of the model by Syam and Shetty [1996], which describes the situation of one vendor with multiple buyers, to include multiple items. This method can be implemented by methods that are fairly standard in the field of mixed-integer programming. This approach seems promising, but numerical experiments are still necessary.

Ph.D. Presentation 5: ‘The Integrated Inventory Models with Defective Items’ by Brenda Ho. Discussants: Banu Yüksel and Attila Chikán.

Integrated inventory management has recently received a great deal of attention.  Through the Japanese experience of using Just-in-Time (JIT) production, it shows that cooperation between vendor and buyer is helpful in determining economic order quantity and achieving better benefits in cost saving.  Previous researches on the integrated vendor-buyer inventory problem mainly focused on the production shipment schedule in terms of the number and size of batches transferred between both parties under deterministic demand and perfect quality.  In fact, the production process may temporarily out of control and produce defective items, or good quality items might be damaged during the transportation.  Therefore, defective items should be considered in the integrated inventory model for reality. In this research, we assume that an arrival order lot may contain some defective items, and the number of defective items is a random variable.  Upon arrival of an order, all the items are inspected and defective items in each lot will be discovered and returned to the vendor at the time of delivery of the next lot.  Also, lead-time is controllable and reducible by adding extra crashing cost.  We derive a modified mixture inventory model with backorders and lost sales, in which the order quantity, reorder point, lead-time and the number of shipment between buyer and vendor are decision variables.  In this proposal, we first assume that the lead-time demand follows a normal distribution, and then relax the assumption about the form of the distribution function of the lead time demand and apply the minimax distribution-free procedure to solve the problem.  Iterative procedures will be developed to obtain the optimal ordering/shipping strategy.  Furthermore, the effects of parameters will also be discussed.

Ph. D. Presentation 6: ‘The Selection Rule of the Place and the Quantity of the Production in the Case of a Global Company’ by Roland Deme. Discussants: Umut Corbacioglu and Yale Herer.

The theory of the multinational corporation has traditionally sought to explain why a firm can successfully invest in overseas operations. This multi-facility structure with production units in different geographical regions gives a firm the flexibility to exploit the uncertainty over future changes in exchange rates, competitive moves, or government policies. n this paper we modeled this coordination as the operating flexibility to shift production between two manufacturing plants located in different countries. A parametric linear programming model treats explicitly this flexibility. We studied the optimal policies for a firm operating plants in two countries, and making two different products that can substitute one another. If a global company has factories in several countries, it can select the place and the quantity of the production according to the global demand and the exchange rate of the currencies. The optimal decision is modeled by a parametric linear programming problem in case of products that substitute each other. The structure of the possible optimal solutions was analyzed with the help of simplex algorithm and found some very exiting connections between the mathematical and economic meanings of the results.

Tutorial 3: ‘Inventory Control Systems for Spare Parts’ by Ulrich Thonemann.

We show how spare-part inventories are managed optimally and how spare-part systems are used and implemented in practice. We also highlight some challenges of spare-part management systems. One of the challenges is the estimation of the optimization potential. We present approximate analytical models to quantify the expected improvement in inventory investment when using a system approach to control inventory as opposed to a simpler item approach. A system approach ensures that a demand-weighted average fill rate is achieved at low inventory investment by assigning low fill rates to parts with high costs and high fill rates to parts with low costs. An item approach does not vary fill rates by parts but assigns identical fill rates to all parts. Using single-parameter functional representations of the skewness of unit costs and average demand across all parts in the system, simple approximate analytical expressions for the required inventory investment are derived for both approaches. The accuracy of the approximations is validated using data from a distribution center for
computer spare parts.

Ph.D. Presentation 7: ‘Handling Direct Upstream Demand in Multi-Echelon Inventory Systems’ by Fredrik Olsson and Patrik Tydesjö. Discussants: Brenda Ho and Fikri Karaesmen.

This paper considers a two-echelon distribution inventory system with a central warehouse and a number of retailers. There is direct customer demand also at the warehouse. If this upstream demand requires a high service, it may be advantageous to give higher priority to customer orders compared to retailer replenishments. We suggest and evaluate two techniques for handling this situation. One technique means that we have an extra separate stock point for the direct customer demand at the warehouse.  The other technique means that we apply a so-called critical level policy at the warehouse, i.e., if the stock on hand at the warehouse is less than or equal to the critical level, retailer replenishments are backordered.
Ph.D. Presentation 8: ‘The Impact of Information and Coordination on Transport Procurement’ by Xavier Brusset. Discussants: Bas Verheijen and Ulrich Thonemann.

In industry, transport cost is second in importance after production cost. It is the purpose of the present paper to study the impact of information sharing and procurement contractual parameters between a supply chain and its transport suppliers. After reviewing the literature, we propose a model to measure the benefits in terms of transport cost and standard deviation of transport cost. We evaluate three scenarios over one period for a shipper carrier single-echelon model with a mix of long-term and short-term procurement strategies: perfect information, asymmetric information and private information. We propose solutions for the contract parameters that optimize cost and reduce standard deviation. We quantify the rent transfer between shipper and carrier according to available information.

Tutorial 4: ‘Production/Inventory Systems with Advance Demand Information’ by Fikri Karaesmen.

Standard stochastic models of production/inventory systems usually incorporate future demand information only through the probability distribution of demand (or of the demand process). In most practical cases, however, advance demand information (ADI) is available in various forms such as early orders from customers or demand forecasts (and their updates). The first part of this talk describes the effects of ADI (in the form of early customer orders) in three single-stage inventory systems: a single-period newsvendor type system, a continuous review (uncapacitated) inventory system, and a (capacitated) production/inventory system. The second part of the talk presents examples of modeling the advance demand information structure and its evolution. The structure of optimal replenishment policies under ADI is also briefly discussed. Finally, some future research perspectives are presented.

Ph.D. Presentation 9: ‘Lot Scheduling in Disassembly Processes’ by Pär Brander. Discussants: Bram Kranenburg and Erwin van der Laan.

Due to environmental and legislative reasons, the importance of recycling is steadily increasing. Ecologically harmless recycling of used technical consumer products is or will become mandatory for their producers. In a collaborative research center in Germany, prototypical disassembly facilities are designed by systematic research of disassembly processes. In the context of this collaborative research project, lot scheduling in a disassembly-process is investigated. The investigated process is characterized by sequence-dependent set-up times. The purpose of this paper is to develop a lot scheduling policy for the disassembly of different products. Two different policies are introduced and compared in a simulation study.

Ph.D. Presentation 10: ‘The Multi-Location Transshipment Problem with Capacitated Production’ by Deniz Özdemir. Discussants: Mustafa Doğru and Jacob Wijngaard.

We consider coordination among stocking locations through replenishment strategies that explicitly consider lateral transshipments. The basic contribution of our research is the incorporation of capacity concerns to the traditional transshipment model. We formulate the case where the supplier has limited production as a capacitated network flow problem embedded in a stochastic optimization problem. We develop a solution procedure based on infinitesimal perturbation analysis (IPA) to solve the stochastic optimization problem numerically. We prove the validity of our sample-path-based optimization procedure for the setting with limited production. We analyze the impact on system behavior and on performance measures of the stocking locations. We find that depending on the production capacity, system behavior can be distorted. In a production-inventory system, either capacity flexibility or transshipment flexibility is required to provide a certain level of service.

Ph.D. Presentation 11: ‘A Numerical Study of the Effect of the Balance Assumption on System Performance in Distribution Systems’ by Mustafa Doğru. Discussants: Fredrik Olsson and Israel David.

The two-echelon distribution system consisting of a single warehouse serving N retailers facing the stochastic demand of the customers, is a well-studied model in the inventory literature. In this numerical study, we consider a two-echelon distribution system with continuous i.i.d. demand and average cost criterion under periodic review. For the expected cost of the system, we define a lower bound based on the relaxed version of the problem where the balance assumption holds and an upper bound obtained by simulating the solution of this relaxed problem. This brackets the optimal cost value within an interval. Finally, a test bed is developed and the impact of the balance assumption on the expected cost of the system is investigated. 

Ph.D. Presentation 12: ‘Cooperation between Multiple Newsvendors with Warehouses’ by Ulas Özen. Discussants: Hussein Naseraldin and Henk Zijm.

This study considers a supply chain that consists of n retailers, each of them facing a newsvendor problem, w warehouses and a supplier. Each retailer is associated with some warehouses, where the ordered amount of goods of this retailer becomes available after some lead-time at its associated warehouses. At the time that the goods arrive at the warehouses, demand realizations become known by the retailers. For this setting, we consider the associated cooperative game between the retailers, in which cooperating retailers can coordinate their orders and they are allowed to make reallocations to increase their expected joint profit. We analyze the characteristics of the associated cooperative game (like non-emptiness of the core, etc.). Furthermore, we study some variants of the model above.    

Ph.D. Presentation 13: ‘Fitting Gamma and Erlang Distribution on Varying Demand Patterns’ by Johanna Laine. Discussants: Kai Hoberg and Geert-Jan van Houtum.

This paper considers the difficulty of estimating a statistical distribution on demand data, especially when demand is intermittent. The purpose is to test the hypotheses of three moments and three parameters, respectively, to possibly gain a better approximation describing the pattern of real demand data. Using the empirical demand data and fitting its relative frequency of demand rates to the gamma distribution using two and three parameters and also the Erlang by three moments (adding another measure describing the spread of the data), respectively, the best approximation is found. The test study shows that no general suppositions can be made regarding the benefits of the three moments Erlang or three parameter gamma.    

Ph.D. Presentation 14: ‘Supply Chain Design with Lateral Transshipments’ by Hussein Naseraldin. Discussants: Deniz Özdemir and Derek Atkins.

In this paper we describe our current research in the management approach that quantitatively combines strategic and operational decisions.  This approach, integrating decisions from various horizons, is new (only a handful of articles have tackled it), but it is increasingly attracting attention due to the potential benefits it offers.  The environment that we will examine can be depicted as a multi-echelon supply chain. Managing such a system entails different decisions on different horizons.  Decisions such as the number and location of facilities and assignment of end-customer to retail outlet are part of the strategic design of a supply chain.  Inventory control decisions, on the other hand, belong to the operational side of the traditional decision hierarchy.  Integrating these decisions, along with lateral transshipment decisions as an operational recourse, has the potential to improve system performance. We model a system that contains customers and retail outlets.  Decisions that should be determined in such a context include: the number of retail outlets, the location of each, the assignment of customers to retail outlets, the lateral transshipments policy to be followed (this recourse will be explained in later sections) and inventory quantities to be maintained at each retail outlet in order to retain a certain level of service.

Tutorial 5: ‘Distribution Systems with Lateral Transshipments’ by Yale Herer.

In this tutorial we will discuss transshipments, the monitored movement of stock between two locations at the same echelon level of the inventory distribution system. Transshipments is an
emerging inventory recourse that is facilitated by the newest information technologies. We will begin by defining transshipments and then we will give examples from industry. We will discuss several papers that have been written on the subject with a two-fold purpose. The first purpose is to get an overall picture of the research done in the area of transshipments. The second and more important purpose is to obtain an understanding of why transshipments are beneficial and how they impact on the supply chain.

Ph.D. Presentation 15: ‘A Multi-Item Spare Parts Inventory Model with Customer Differentiation’ by Bram Kranenburg. Discussants: Johanna Laine and N. Ravichandran.

We consider a single warehouse, where spare parts of multiple SKU-s are kept on stock to serve customers with (close-to-)identical machines. Customers are divided into multiple customer groups, and a target (overall) fill rate is set per group. In order to get differentiated service levels, critical-level policies are assumed. We formulate a multi-item, single-stage spare parts inventory model for this problem, with the objective to minimize the inventory investment under the condition that all target fill rates are met. Based on Lagrange relaxation, we develop a lower and an upper bound for the optimal costs. The upper bound represents the costs of a heuristic solution that is generated. Computational results show that the gap between the lower and upper bound is small in general.

Ph.D. Presentation 16: ‘Comparison of Two Joint Replenishment Policies Two-Echelon Inventory System’ by BanuYüksel. Discussants: Ying Xie and Karel van Donselaar.

In this study, we consider a single item, two-echelon inventory system with a single central warehouse and N non-identical retailers under a new type of ordering policy. In particular, we propose a special type of joint replenishment policy for the retailers which aims to coordinate the orders given to the warehouse and the warehouse employs a regular one-for-one ordering policy. We provide the exact expressions for the key operating characteristics of the model. We present numerical results that compare the proposed policy to another recently proposed joint replenishment policy by Cheung and Lee (2002).  

Tutorial 6: ‘Multi-Echelon Inventory/Production Systems: Theory and Practice’ by Ton de Kok.

In this presentation we discuss the implementation of a supply chain planning system between two companies in the high volume electronics supply chain. The system supports the generation of a joint agreed supply plan. The output of the planning process is weekly release decisions of wafers, dies, IC's, PCB's and final products. The planning logic generating release proposals is based on a class of echelon order-up-to-level policies called Synchronized Base Stock policies, that apply to general multi-echelon inventory systems (i.e. each item may have multiple child items and multiple parent items). We discuss the essentials of SBS policies and the modifications required to apply the SBS policies to a non-stationary demand and random yield situation. We report about empirical results of the implementation of the planning system, both in terms of supply chain performance and user satisfaction.

Ph.D. Presentation 17: ‘An NPV and AC Analysis of a Multi-Source, Multi-Product Remanufacturing System’ by Umut Corbacioglu. Discussants: Pär Brander and Gudrun Kiesmüller.

The net present value (NPV) or discounted cash flow approach is generally considered to be the right approach for determining optimal policies. Due to simpler structure average cost (AC) approach is more frequently employed. Such an approximation leads to good results under certain conditions. However, recent studies show that such an approximation is not that straightforward in models with reverse logistics. This study addresses the issue of setting the holding cost parameters in a multi-source, multi-product remanufacturing environment such that the average cost approach gives near optimal results.

Ph.D. Presentation 18: ‘Fuzzy Two-Level Coordination of Distribution Supply Chains in the Presence of Uncertainty in Customer Demands’ by Ying Xie. Discussants: Ulas Özen and Ton de Kok.

This paper considers a distribution supply chain (DSC), which consists of one warehouse and a number of spatially, distributed retailers. Each inventory point is controlled by a fixed period, order-up-to level review policy. The distribution system operates in the presence of uncertainty in customer demands. Customer demands are expressed, based on subjective managerial judgements and experiences, by imprecise linguistic terms such as ‘demand is about  products’, ‘demand is much higher than products’, etc. They are modeled by the corresponding fuzzy sets. The warehouse and retailers operate with objectives that are conflicting in nature. In order to minimize its own cost, the warehouse requests all the retailers to place their replenishment orders at the same time. However, this does not necessarily lead to the minimum costs for the retailers. There is a need to introduce a coordination function. This paper presents a new fuzzy two-level decision making approach to coordinate warehouse and retailers review policies. It includes two levels of control: a leader level and a follower level. The leader level is responsible for determining an optimal review policy for the warehouse and for the overall coordination; while at the follower level, local optimal retailer review policies are determined taking into consideration coordination instructions given by the leader level.