Inventory Problems with Partially Observed Demands and Lost Sales

Journal of Optimization Theory & Applications, Vol. 136, No. 1, January 2008

33 Pages Posted: 24 Dec 2007 Last revised: 10 Apr 2014

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

Andrew Royal

University of Texas at Dallas

Suresh Sethi

University of Texas at Dallas - Naveen Jindal School of Management

Date Written: 2008

Abstract

This paper considers the case of partially observed demand in the context of a multi-period inventory problem with lost sales. Demand in a period is observed if it is less than the inventory level in that period and the leftover inventory is carried over to the next period. Otherwise, only the event that it is larger than or equal to the inventory level is observed. These observations are used to update the demand distributions over time. The state of the resulting dynamic program consists of the current inventory level and the current demand distribution, which is infinite dimensional. The state evolution equation for the demand distribution becomes linear with the use of unnormalized probabilities. We study two demand cases. First, the demands evolve according to a Markov chain. Second, the demand distribution has an unknown parameter which is updated in the Bayesian manner. In both cases, we prove the existence of an optimal feedback ordering policy.

Keywords: inventory models, partially observed systems, incomplete information, lost sales

JEL Classification: M11, C00

Suggested Citation

Bensoussan, Alain and Cakanyildirim, Metin and Minjarez-Sosa, J. Adolfo and Royal, Andrew and Sethi, Suresh, Inventory Problems with Partially Observed Demands and Lost Sales (2008). Journal of Optimization Theory & Applications, Vol. 136, No. 1, January 2008, Available at SSRN: https://ssrn.com/abstract=1078146

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

Andrew Royal

University of Texas at Dallas ( email )

2601 North Floyd Road
Richardson, TX 75083
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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