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Instability of Dynamic Inventory Systems

Author

Listed:
  • Jia Yan
  • John Liu

    () (School of Economic Sciences, Washington State University)

Abstract

We show in this paper that instability is an intrinsic cause of production variability in a dynamic inventory system. We first show that a unique stationary optimal policy exists for both full-backlog and lost-sales case and under the policy a firm replenishes its inventory to a constant target level. We then express the constant inventory target as the unique steady state of the Euler’s equation governing the dynamics of target inventories. We finally show that the Euler’s equation is locally instable at the steady state but a sufficiently large refund to unsold inventory in lost-sales case can stabilize the inventory system.

Suggested Citation

  • Jia Yan & John Liu, 2008. "Instability of Dynamic Inventory Systems," Working Papers 2008-23, School of Economic Sciences, Washington State University.
  • Handle: RePEc:wsu:wpaper:yan-4
    as

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    File URL: http://faculty.ses.wsu.edu/WorkingPapers/Yan/volatility_workpaper.pdf
    File Function: First version, 2008
    Download Restriction: no

    References listed on IDEAS

    as
    1. Fuente,Angel de la, 2000. "Mathematical Methods and Models for Economists," Cambridge Books, Cambridge University Press, number 9780521585293, October.
    2. Benveniste, L M & Scheinkman, J A, 1979. "On the Differentiability of the Value Function in Dynamic Models of Economics," Econometrica, Econometric Society, vol. 47(3), pages 727-732, May.
    3. Kandel, Eugene, 1996. "The Right to Return," Journal of Law and Economics, University of Chicago Press, vol. 39(1), pages 329-356, April.
    4. Alan S. Blinder & Louis J. Maccini, 1991. "Taking Stock: A Critical Assessment of Recent Research on Inventories," Journal of Economic Perspectives, American Economic Association, vol. 5(1), pages 73-96, Winter.
    5. Donald L. Iglehart, 1963. "Optimality of (s, S) Policies in the Infinite Horizon Dynamic Inventory Problem," Management Science, INFORMS, vol. 9(2), pages 259-267, January.
    6. James A. Kahn, 1992. "Why is Production More Volatile than Sales? Theory and Evidence on the Stockout-Avoidance Motive for Inventory-Holding," The Quarterly Journal of Economics, Oxford University Press, vol. 107(2), pages 481-510.
    7. Kahn, James A, 1987. "Inventories and the Volatility of Production," American Economic Review, American Economic Association, vol. 77(4), pages 667-679, September.
    8. Hall, George & Rust, John, 2000. "An empirical model of inventory investment by durable commodity intermediaries," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 52(1), pages 171-214, June.
    9. Ramey, Valerie A, 1991. "Nonconvex Costs and the Behavior of Inventories," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 306-334, April.
    10. Hau L. Lee & V. Padmanabhan & Seungjin Whang, 1997. "Information Distortion in a Supply Chain: The Bullwhip Effect," Management Science, INFORMS, vol. 43(4), pages 546-558, April.
    11. Alexandre Scheinkman, Jose, 1976. "On optimal steady states of n-sector growth models when utility is discounted," Journal of Economic Theory, Elsevier, vol. 12(1), pages 11-30, February.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    stability; production variability; dynamic inventory system; full-backlog; lost-sales;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D92 - Microeconomics - - Micro-Based Behavioral Economics - - - Intertemporal Firm Choice, Investment, Capacity, and Financing

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