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Optimal Control and Equilibrium Behavior of Production-Inventory Systems

Author

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  • 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)

Abstract

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.

Suggested Citation

  • Owen Q. Wu & Hong Chen, 2010. "Optimal Control and Equilibrium Behavior of Production-Inventory Systems," Management Science, INFORMS, vol. 56(8), pages 1362-1379, August.
    • Handle: RePEc:inm:ormnsc:v:56:y:2010:i:8:p:1362-1379
    DOI: 10.1287/mnsc.1100.1186
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    References listed on IDEAS

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    4. Lingxiu Dong & Panos Kouvelis & Xiaole Wu, 2014. "The Value of Operational Flexibility in the Presence of Input and Output Price Uncertainties with Oil Refining Applications," Management Science, INFORMS, vol. 60(12), pages 2908-2926, December.
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    6. Sripad K. Devalkar & Ravi Anupindi & Amitabh Sinha, 2011. "Integrated Optimization of Procurement, Processing, and Trade of Commodities," Operations Research, INFORMS, vol. 59(6), pages 1369-1381, December.
    7. YuJan Shen & KuanFu Shen & ChihTe Yang, 2019. "A Production Inventory Model for Deteriorating Items with Collaborative Preservation Technology Investment Under Carbon Tax," Sustainability, MDPI, vol. 11(18), pages 1-18, September.
    8. Nicola Secomandi & Guoming Lai & François Margot & Alan Scheller-Wolf & Duane J. Seppi, 2015. "Merchant Commodity Storage and Term-Structure Model Error," Manufacturing & Service Operations Management, INFORMS, vol. 17(3), pages 302-320, July.
    9. Avi Herbon & Konstantin Kogan, 2014. "Time-dependent and independent control rules for coordinated production and pricing under demand uncertainty and finite planning horizons," Annals of Operations Research, Springer, vol. 223(1), pages 195-216, December.
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