Partially Observed Inventory Systems: The Case of Rain Checks

SIAM Journal of Control and Optimization, 47(5), 2008, 2490-2519

27 Pages Posted: 30 Jan 2008 Last revised: 24 Jun 2020

See all articles by Alain Bensoussan

Alain Bensoussan

University of Texas at Dallas - Naveen Jindal School of Management

M. Çakanyıldırım

University of Texas at Dallas - Naveen Jindal School of Management

J. Adolfo Minjarez-Sosa

University of Sonora - Department of Mathematics

Suresh Sethi

University of Texas at Dallas - Naveen Jindal School of Management

Ruixia (Sandy) Shi

University of Richmond - Robins School of Business, Management Department

Date Written: February 8, 2008

Abstract

In many inventory control contexts, inventory levels are only partially (i.e., not fully) observed. This may be due to non-observation of demand, spoilage, misplacement, or theft of inventory. We study a periodic review inventory system where the unmet demand is backordered. When inventory level is nonnegative, the inventory manager does not know the exact inventory level. Otherwise, inventory shortages occur and the inventory manager issues rain checks to customers. The shortages are fully observable via the rain checks. The inventory manager determines the order quantity based on the partial information on the inventory level. The objective is to minimize the expected total discounted cost over an infinite horizon. The dynamic programming formulation of this problem has an infinite dimensional state space. We use the methodology of the unnormalized probability to establish the existence of an optimal feedback policy when the periodic cost has linear growth. Moreover, uniqueness and continuity of the solution to dynamic programming equations are proved when the discount factor is sufficiently small.

Keywords: Partially Observed Systems, inventroy control, Rain Checks, incomplete information, lost sales, optimal control, incomplete information, feedback policy, dynamic programming, unnormalized probability, infinite dimensional space

JEL Classification: C61, M11, D81, D83

Suggested Citation

Bensoussan, Alain and Cakanyildirim, Metin and Minjarez-Sosa, J. Adolfo and Sethi, Suresh and Shi, Ruixia, Partially Observed Inventory Systems: The Case of Rain Checks (February 8, 2008). SIAM Journal of Control and Optimization, 47(5), 2008, 2490-2519, Available at SSRN: https://ssrn.com/abstract=1087812 or http://dx.doi.org/10.2139/ssrn.1087812

Alain Bensoussan

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

800 West Campbell Rd
SM 30
Richardson, TX 75080-3021
United States
9728836117 (Phone)

HOME PAGE: http://www.utdallas.edu/~axb046100/

Metin Cakanyildirim

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

P.O. Box 830688
Richardson, TX 75083-0688
United States

J. Adolfo Minjarez-Sosa

University of Sonora - Department of Mathematics ( email )

C.P. 83000, Hermosillo, Son.
Mexico

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

Ruixia Shi

University of Richmond - Robins School of Business, Management Department ( email )

1 Gateway Road
University of Richmond
Richmond, VA 23173
United States

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

Paper statistics

Downloads
127
Abstract Views
1,494
Rank
402,428
PlumX Metrics