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Competitive and Cooperative Inventory Policies in a Two-Stage Supply Chain

Author

Listed:
  • Gérard P. Cachon

    (The Fuqua School of Business, Duke University, Durham, North Carolina 27708)

  • Paul H. Zipkin

    (The Fuqua School of Business, Duke University, Durham, North Carolina 27708)

Abstract

We investigate a two-stage serial supply chain with stationary stochastic demand and fixed transportation times. Inventory holding costs are charged at each stage, and each stage may incur a consumer backorder penalty cost, e.g. the upper stage (the supplier) may dislike backorders at the lower stage (the retailer). We consider two games. In both, the stages independently choose base stock policies to minimize their costs. The games differ in how the firms track their inventory levels (in one, the firms are committed to tracking echelon inventory; in the other they track local inventory). We compare the policies chosen under this competitive regime to those selected to minimize total supply chain costs, i.e., the optimal solution. We show that the games (nearly always) have a unique Nash equilibrium, and it differs from the optimal solution. Hence, competition reduces efficiency. Furthermore, the two games' equilibria are different, so the tracking method influences strategic behavior. We show that the system optimal solution can be achieved as a Nash equilibrium using simple linear transfer payments. The value of cooperation is context specific: In some settings competition increases total cost by only a fraction of a percent, whereas in other settings the cost increase is enormous. We also discuss Stackelberg equilibria.

Suggested Citation

  • Gérard P. Cachon & Paul H. Zipkin, 1999. "Competitive and Cooperative Inventory Policies in a Two-Stage Supply Chain," Management Science, INFORMS, vol. 45(7), pages 936-953, July.
  • Handle: RePEc:inm:ormnsc:v:45:y:1999:i:7:p:936-953
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    File URL: http://dx.doi.org/10.1287/mnsc.45.7.936
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    References listed on IDEAS

    as
    1. Fangruo Chen & Yu-Sheng Zheng, 1994. "Lower Bounds for Multi-Echelon Stochastic Inventory Systems," Management Science, INFORMS, vol. 40(11), pages 1426-1443, November.
    2. Andrew J. Clark & Herbert Scarf, 2004. "Optimal Policies for a Multi-Echelon Inventory Problem," Management Science, INFORMS, vol. 50(12_supple), pages 1782-1790, December.
    3. John A. Muckstadt & L. Joseph Thomas, 1980. "Are Multi-Echelon Inventory Methods Worth Implementing in Systems with Low-Demand-Rate Items?," Management Science, INFORMS, vol. 26(5), pages 483-494, May.
    4. John D. Sterman, 1989. "Modeling Managerial Behavior: Misperceptions of Feedback in a Dynamic Decision Making Experiment," Management Science, INFORMS, vol. 35(3), pages 321-339, March.
    5. Warren H. Hausman & Nesim K. Erkip, 1994. "Multi-Echelon vs. Single-Echelon Inventory Control Policies for Low-Demand Items," Management Science, INFORMS, vol. 40(5), pages 597-602, May.
    6. Barry Alan Pasternack, 1985. "Optimal Pricing and Return Policies for Perishable Commodities," Marketing Science, INFORMS, vol. 4(2), pages 166-176.
    7. Gérard P. Cachon & Colin F. Camerer, 1996. "Loss-Avoidance and Forward Induction in Experimental Coordination Games," The Quarterly Journal of Economics, Oxford University Press, vol. 111(1), pages 165-194.
    8. repec:inm:ormnsc:v:30:y:1984:i:12:p:1524-1539(2 is not listed on IDEAS
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