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Instability of Dynamic Inventory Systems

  • Jia Yan
  • John Liu

    ()

    (School of Economic Sciences, Washington State University)

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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.

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File URL: http://faculty.ses.wsu.edu/WorkingPapers/Yan/volatility_workpaper.pdf
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File Function: First version, 2008
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Paper provided by School of Economic Sciences, Washington State University in its series Working Papers with number 2008-23.

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Length: 24 pages
Date of creation: Dec 2008
Date of revision:
Handle: RePEc:wsu:wpaper:yan-4
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Web page: http://faculty.ses.wsu.edu/

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  1. 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.
  2. 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.
  3. Kahn, James A, 1987. "Inventories and the Volatility of Production," American Economic Review, American Economic Association, vol. 77(4), pages 667-79, September.
  4. 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.
  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. Ramey, Valerie A, 1991. "Nonconvex Costs and the Behavior of Inventories," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 306-34, April.
  7. 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 727-32, May.
  8. Kandel, Eugene, 1996. "The Right to Return," Journal of Law and Economics, University of Chicago Press, vol. 39(1), pages 329-56, April.
  9. Kahn, James A, 1992. "Why Is Production More Volatile Than Sales? Theory and Evidence on the Stockout-Avoidance Motive for Inventory-Holding," The Quarterly Journal of Economics, MIT Press, vol. 107(2), pages 481-510, May.
  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.
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