Instability of Dynamic Inventory Systems
AbstractWe 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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Bibliographic InfoPaper provided by School of Economic Sciences, Washington State University in its series Working Papers with number 2008-23.
Length: 24 pages
Date of creation: Dec 2008
Date of revision:
stability; production variability; dynamic inventory system; full-backlog; lost-sales;
Find related papers by 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 - - Intertemporal Choice - - - Intertemporal Firm Choice, Investment, Capacity, and Financing
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-01-03 (All new papers)
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- Kahn, James A, 1987. "Inventories and the Volatility of Production," American Economic Review, American Economic Association, vol. 77(4), pages 667-79, September.
- George Hall & John Rust, 1999.
"An Empirical Model of Inventory Investment by Durable Commodity Intermediaries,"
- 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.
- George J. Hall & John Rust, 1999. "An Empirical Model of Inventory Investment by Durable Commodity Intermediaries," Cowles Foundation Discussion Papers 1228, Cowles Foundation for Research in Economics, Yale University.
- 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.
- 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.
- 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.
- Kandel, Eugene, 1996. "The Right to Return," Journal of Law and Economics, University of Chicago Press, vol. 39(1), pages 329-56, April.
- 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.
- 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.
- 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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