Inventory Models with Markovian Demands and Cost Functions of Polynomial Growth

Journal of Optimization Theory and Applications, Vol. 98, No. 2, pp. 281-323, August 1998

36 Pages Posted: 14 Feb 2008 Last revised: 21 Apr 2008

See all articles by Dirk Beyer

Dirk Beyer

M-Factor, Inc.

Suresh Sethi

University of Texas at Dallas - Naveen Jindal School of Management

Michael I. Taksar

University of Missouri at Columbia - Department of Mathematics (Deceased) ; State University of New York (SUNY), Stony Brook, College of Engineering and Applied Sciences, Department of Applied Mathematics and Statistics (Deceased)

Abstract

This paper studies stochastic inventory problems with unbounded Markovian demands, ordering costs that are lower semicontinuous, and inventory/backlog (or surplus) costs that are lower semicontinuous with polynomial growth. Finite-horizon problems, stationary and nonstationary discounted-cost infinite-horizon problems, and stationary long-run average-cost problems are addressed. Existence of optimal Markov or feedback policies is established. Furthermore, optimality of (s, S)-type policies is proved when, in addition, the ordering cost consists of fixed and proportional cost components and the surplus cost is convex.

Keywords: Dynamic inventory models - Markov chains - dynamic programming, finite horizon, infinite horizon , cyclic demand, (s, S)-policy, inventory models, Markov process, cost with polynomial growth, average cost, ergodic problem, base-stockpolicy, incomplete information, partial observations

JEL Classification: C61, M11, D81,D83

Suggested Citation

Beyer, Dirk and Sethi, Suresh and Taksar, Michael I., Inventory Models with Markovian Demands and Cost Functions of Polynomial Growth. Journal of Optimization Theory and Applications, Vol. 98, No. 2, pp. 281-323, August 1998 , Available at SSRN: https://ssrn.com/abstract=1093083

Dirk Beyer

M-Factor, Inc. ( email )

1400 Fashion Island Boulevard
Suite 602
San Mateo, CA 94404-2060
United States

Suresh Sethi (Contact Author)

University of Texas at Dallas - Naveen Jindal School of Management ( email )

800 W. Campbell Road, SM30
Richardson, TX 75080-3021
United States

Michael I. Taksar

University of Missouri at Columbia - Department of Mathematics (Deceased)

State University of New York (SUNY), Stony Brook, College of Engineering and Applied Sciences, Department of Applied Mathematics and Statistics (Deceased)

Do you have negative results from your research you’d like to share?

Paper statistics

Downloads
80
Abstract Views
1,097
Rank
551,501
PlumX Metrics