This Article Full Text (PDF) References Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via HighWire Citing Articles via Google Scholar Google Scholar Articles by Bensoussan, A. Articles by Sethi, S. P. Search for Related Content

A Multiperiod Newsvendor Problem with Partially Observed Demand

Alain Bensoussan, Metin Çakanyldrm, Suresh P. Sethi

International Center for Decision and Risk Analysis, School of Management, P.O. Box 830688, University of Texas at Dallas, Richardson, Texas 75083
School of Management, P.O. Box 830688, University of Texas at Dallas, Richardson, Texas 75083
Center for Intelligent Supply Networks, School of Management, P.O. Box 830688, University of Texas at Dallas, Richardson, Texas 75083
alain.bensoussan{at}utdallas.edu, http://www.utdallas.edu/alain.bensoussan
metin{at}utdallas.edu, http://www.utdallas.edu/metin
sethi{at}utdallas.edu, http://www.utdallas.edu/sethi

We consider a newsvendor problem with partially observed Markovian demand. Demand is observed if it is less than the inventory. Otherwise, only the event that it is larger than or equal to the inventory is observed. These observations are used to update the demand distribution from one period to the next. The state of the resulting dynamic programming equation is the current demand distribution, which is generally infinite dimensional. We use unnormalized probabilities to convert the nonlinear state transition equation to a linear one. This helps in proving the existence of an optimal feedback ordering policy. So as to learn more about the demand, the optimal order is set to exceed the myopic optimal order. The optimal cost decreases as the demand distribution decreases in the hazard rate order. In a special case with finitely many demand values, we characterize a near-optimal solution by establishing that the value function is piecewise linear.

Key Words: unobserved unmet demand; Markovian demand; newsvendor problem
History: Received: May 26, 2006;

This article has been cited by other articles:

				A. Bensoussan, M. Cakanyildirim, and S. P. Sethi Technical Note--A Note on "The Censored Newsvendor and the Optimal Acquisition of Information" Operations Research, May 1, 2009; 57(3): 791 - 794. [Abstract] [PDF]