Average Cost Optimality in Inventory Models with Markovian Demands

Beyer, Dirk; Sethi, Suresh

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Average Cost Optimality in Inventory Models with Markovian Demands

Journal of Optimization Theory and Applications: Vol. 92, No. 3, pp. 497-526, MARCH 1997

30 Pages Posted: 6 Jun 2008 Last revised: 10 May 2017

See all articles by Dirk Beyer

Suresh Sethi

University of Texas at Dallas - Naveen Jindal School of Management

Date Written: 1987

Abstract

This paper is concerned with long-run average cost minimization of a stochastic inventory problem with Markovian demand, fixed ordering cost, and convex surplus cost. The states of the Markov chain represent different possible states of the environment. Using a vanishing discount approach, a dynamic programming equation and the corresponding verification theorem are established. Finally, the existence of an optimal state-dependent (s, S) policy is proved.

Keywords: Dynamic inventory model, Markov chain, dynamic programming, infinite horizon, long-run average cost, ergodic cost, (s, S) policy

JEL Classification: M11, C61

Suggested Citation: Suggested Citation

Beyer, Dirk and Sethi, Suresh, Average Cost Optimality in Inventory Models with Markovian Demands (1987). Journal of Optimization Theory and Applications: Vol. 92, No. 3, pp. 497-526, MARCH 1997, Available at SSRN: https://ssrn.com/abstract=1141523