Inventory Problems with Partially Observed Demands and Lost Sales |
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Authors: | A Bensoussan M Çakanyıldırım J A Minjárez-Sosa A Royal S P Sethi |
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Institution: | (1) School of Management, University of Texas at Dallas, Richardson, Texas, USA |
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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.
Permanent address of J. Adolfo Minjárez-Sosa: Departamento de Matemáticas, Universidad de Sonora, Hermosillo, Sonora, México.
This project was partially supported by NSF Grant 0509278, ARPATP Grant 009741-0019-2006, and CONACYT (Mexico) Grant 46633-F. |
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Keywords: | Partially observed demand Markovian demand Bayesian update Inventory control Lost sales |
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