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Optimal Control and Equilibrium Behavior of Production-Inventory Systems

  • Owen Q. Wu


    (Stephen M. Ross School of Business, University of Michigan, Ann Arbor, Michigan 48109)

  • Hong Chen


    (Sauder School of Business, University of British Columbia, Vancouver, British Columbia V6T 1Z2, Canada)

The relationship between commodity inventory and short-term price variations has received considerable attention, but the understanding has been limited to single-stage cross-sectional relation. In this paper, we aim to deepen our understanding of the inventory-price relationship in two dimensions: across time and across production stages. We first examine an individual firm controlling production and two stages of inventory under uncertain input and output prices and operating costs. We next establish and characterize the rational expectations equilibrium for an economy in which competitive production firms link a raw material market and a finished goods market, with uncertain and price-sensitive supply and demand. We characterize the dynamics of inventory, market price, and gross margin based on theoretical analysis, simulation, and empirical evidence from the petroleum industry. We find that inventory fluctuations lag behind price variations, and the length of the lags depend on how far the inventory is from the source of the supply or demand shocks. We also find that shocks are both dampened and delayed when propagating through the production stages, and that shocks have a prolonged effect on inventories and prices at both stages.

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Article provided by INFORMS in its journal Management Science.

Volume (Year): 56 (2010)
Issue (Month): 8 (August)
Pages: 1362-1379

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Handle: RePEc:inm:ormnsc:v:56:y:2010:i:8:p:1362-1379
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  1. Fama, Eugene F & French, Kenneth R, 1988. " Business Cycles and the Behavior of Metals Prices," Journal of Finance, American Finance Association, vol. 43(5), pages 1075-93, December.
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  6. Michael Ye & John Zyren & Joanne Shore, 2002. "Forecasting crude oil spot price using OECD petroleum inventory levels," International Advances in Economic Research, Springer;International Atlantic Economic Society, vol. 8(4), pages 324-333, November.
  7. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "An Intertemporal General Equilibrium Model of Asset Prices," Econometrica, Econometric Society, vol. 53(2), pages 363-84, March.
  8. Eduardo Schwartz & James E. Smith, 2000. "Short-Term Variations and Long-Term Dynamics in Commodity Prices," Management Science, INFORMS, vol. 46(7), pages 893-911, July.
  9. Deaton, Angus & Laroque, Guy, 1996. "Competitive Storage and Commodity Price Dynamics," Journal of Political Economy, University of Chicago Press, vol. 104(5), pages 896-923, October.
  10. Paul Zipkin, 1989. "Critical Number Policies for Inventory Models with Periodic Data," Management Science, INFORMS, vol. 35(1), pages 71-80, January.
  11. S. P. Sethi & H. Yan & H. Zhang & Q. Zhang, 2002. "Optimal and Hierarchical Controls in Dynamic Stochastic Manufacturing Systems: A Survey," Manufacturing & Service Operations Management, INFORMS, vol. 4(2), pages 133-170.
  12. Bryan R. Routledge & Duane J. Seppi & Chester S. Spatt, 2000. "Equilibrium Forward Curves for Commodities," Journal of Finance, American Finance Association, vol. 55(3), pages 1297-1338, 06.
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  14. repec:kap:iaecre:v:8:y:2002:i:4:p:324-333 is not listed on IDEAS
  15. Asche, Frank & Gjolberg, Ole & Volker, Teresa, 2003. "Price relationships in the petroleum market: an analysis of crude oil and refined product prices," Energy Economics, Elsevier, vol. 25(3), pages 289-301, May.
  16. Considine, Timothy J. & Larson, Donald F., 2001. "Uncertainty and the convenience yield in crude oil price backwardations," Energy Economics, Elsevier, vol. 23(5), pages 533-548, September.
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