ABSTRACT
The decentralized transshipment problem is a two-stage decision making problem where the companies first choose their individual production levels in anticipation of random demands and after demand realizations they pool residuals via transshipment. The coordination will be achieved if at optimality all the decision variables, i.e. production levels and transshipment patterns, in the decentralized system are the same as those of centralized system. In this paper, we study the coordination via transshipment prices. We propose a procedure for deriving the transshipment prices based on the coordinating allocation rule introduced by Anupindi et al. [1]. With the transshipment prices being set, the companies are free to match their residuals based on their individual preferences. We draw upon the concept of pair-wise stability to capture the dynamics of corresponding matching process. As the main result of this paper, we show that with the derived transshipment prices, the optimum transshipment patterns are always pair-wise stable, i.e. there are no pairs of companies that can be jointly better off by unilaterally deviating from the optimum transshipment patterns.
- R. Anupindi, Y. Bassok, and E. Zemel. A general framework for the study of decentralized distribution systems. Manufacturing & Service Operations Management, 3(4):349, 2001. Google ScholarDigital Library
- M. Baiou and M. Balinski. Erratum: The stable allocation (or ordinal transportation) problem. Mathematics of Operations Research, 27(4):662--680, 2002. Google ScholarDigital Library
- X. Chen and J. Zhang. A stochastic programming duality approach to inventory centralization games. Operations Research, 57(4):840, 2009. Google ScholarDigital Library
- D. Granot and G. Sošić. A three-stage model for a decentralized distribution system of retailers. Operations Research, pages 771--784, 2003. Google ScholarDigital Library
- B. Hezarkhani and W. Kubiak. A coordinating contract for a two location supply chain. European Journal of Operational Research, 2010. Submitted.Google Scholar
- X. Hu, I. Duenyas, and R. Kapuscinski. Existence of coordinating transshipment prices in a two-location inventory model. Management Science, 53(8):1289--1302, 2007. Google ScholarDigital Library
- X. Huang and G. Sošić. Repeated Newsvendor Game with Transshipments. Technical report, Working paper, Marshall School of Business, University of Southern California, Los Angeles, CA, 2008.Google Scholar
- X. Huang and G. Sošić. Transshipment of Inventories: Dual Allocations vs. Transshipment Prices. to appear in Manufacturing & Service Operations Management, 2009. Google ScholarDigital Library
- M. Jackson. A survey of models of network formation: Stability and efficiency. Game Theory and Information, 2003.Google Scholar
- G. Owen. On the core of linear production games. Mathematical programming, 9(1):358--370, 1975.Google Scholar
- J. Sánchez-Soriano. Pairwise solutions and the core of transportation situations. European Journal of Operational Research, 175(1):101--110, 2006.Google ScholarCross Ref
- G. Sošić. Transshipment of inventories among retailers: Myopic vs. farsighted stability. Management science, 52(10):1493, 2006. Google ScholarDigital Library
Index Terms
- Transshipment prices and pair-wise stability in coordinating the decentralized transshipment problem
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