Average Cost Optimality in Inventory Models with Markovian Demands and Lost Sales

Beyer, Dirk; Sethi, Suresh

Average Cost Optimality in Inventory Models with Markovian Demands and Lost Sales

ANALYSIS, CONTROL AND OPTIMIZATION OF COMPLEX DYNAMIC SYSTEMS, E.K. Boukas, R. P. Malhame, eds., Chapter 1, pp. 3-23, Springer, 2005

19 Pages Posted: 19 Sep 2008 Last revised: 30 Mar 2014

See all articles by Dirk Beyer

Suresh Sethi

University of Texas at Dallas - Naveen Jindal School of Management

Date Written: November 3, 2003

Abstract

This paper is concerned with long-run average cost minimization of a stochastic inventory problem with Markovian demand, fixed ordering cost, convex surplus cost, and lost sales. 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, lost sales, Markov chain, dynamic programming, infinite

JEL Classification: M11, C61

Suggested Citation: Suggested Citation

Beyer, Dirk and Sethi, Suresh, Average Cost Optimality in Inventory Models with Markovian Demands and Lost Sales (November 3, 2003). ANALYSIS, CONTROL AND OPTIMIZATION OF COMPLEX DYNAMIC SYSTEMS, E.K. Boukas, R. P. Malhame, eds., Chapter 1, pp. 3-23, Springer, 2005, Available at SSRN: https://ssrn.com/abstract=1269723