Partially Observed Inventory Systems: The Case of Zero-Balance Walk

SIAM Journal on Control & Optimization, Vol. 46, No. 1, pp. 176-209, 2007

37 Pages Posted: 12 Jan 2008 Last revised: 29 Oct 2009

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

Suresh Sethi

University of Texas at Dallas - Naveen Jindal School of Management

Abstract

In many inventory control contexts, inventory levels are only partially (i.e., not fully) observed. This may be due to nonobservation of demand, spoilage, misplacement, or theft of inventory. We study a partially observed inventory system where the demand is not observed, inventory level is noticed when it reaches zero, the unmet demand is lost, and replenishment orders must be decided so as to minimize the total discounted costs over an infinite horizon. This problem has an infinite-dimensional state space, and for it we establish the existence of a feedback policy when single-period costs are bounded or when the discount factor is sufficiently small. We also provide an approximately optimal feedback policy that uses a finite state representation.

Keywords: inventory models, incomplete information, partially observed systems, optima control, zero-balance walk, inventory control, feedback policy, lost sales case

JEL Classification: M11, C61

Suggested Citation

Bensoussan, Alain and Cakanyildirim, Metin and Sethi, Suresh, Partially Observed Inventory Systems: The Case of Zero-Balance Walk. SIAM Journal on Control & Optimization, Vol. 46, No. 1, pp. 176-209, 2007, Available at SSRN: https://ssrn.com/abstract=1082935

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

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

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