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April  2009, 5(2): 391-402. doi: 10.3934/jimo.2009.5.391

Censored newsvendor model revisited with unnormalized probabilities

Alain Bensoussan 1, , Metin Çakanyildirim 2, and  Suresh P. Sethi 3,

1. 

International Center for Decision and Risk Analysis, School of Management, P.O.Box 830688, SM 30, University of Texas at Dallas, Richardson, TX 75083-0688, United States
2. 

School of Management, P.O.Box 830688, SM 30, University of Texas at Dallas, Richardson, TX 75083-0688, United States
3. 

Center for Intelligent Supply Networks, School of Management, P.O.Box 830688, SM 30, University of Texas at Dallas, Richardson, TX 75083-0688, United States

Received  April 2008 Revised  October 2008 Published  April 2009

This paper revisits the model of the censored newsvendor presented by Ding, Puterman and Bisi [8], We analyze that model in an infinite-horizon context by using the interesting concept of unnormalized probabilities. The unnormalized probabilities considerably simplify the dynamic programming equation and facilitate the proof of the existence of an optimal policy. They can also be used to give a simple, alternative proof to Ding et al.'s claim that the myopic order quantity is always less than or equal to the optimal order quantity. Importantly, the concept of unnormalized probabilities can be used to treat other important operations research problems with partial observations.
Keywords: Unnormalized probabilities, unobserved unmet demand, newsvendor problem..
Mathematics Subject Classification: Primary: 93C41, 93C41; Secondary: 49L2.
Citation: Alain Bensoussan, Metin Çakanyildirim, Suresh P. Sethi. Censored newsvendor model revisited with unnormalized probabilities. Journal of Industrial and Management Optimization, 2009, 5 (2) : 391-402. doi: 10.3934/jimo.2009.5.391
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