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
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: Suggested Citation
Do you have negative results from your research you’d like to share?
Recommended Papers
-
On the Optimal Control of Partially Observed Inventory Systems
By Alain Bensoussan, M. Çakanyıldırım, ...
-
Partially Observed Inventory Systems: The Case of Zero-Balance Walk
By Alain Bensoussan, M. Çakanyıldırım, ...
-
A Multiperiod Newsvendor Problem with Partially Observed Demand
By Alain Bensoussan, M. Çakanyıldırım, ...
-
Optimality of Base-Stock and (s, S) Policies for Inventory Problems with Information Delays
By Alain Bensoussan, M. Çakanyıldırım, ...
-
Optimal Ordering Policies for Inventory Problems with Dynamic Information Delays
By Alain Bensoussan, M. Çakanyıldırım, ...
-
Optimal Ordering Policies for Stochastic Inventory Problems with Observed Information Delays
By Alain Bensoussan, M. Çakanyıldırım, ...
-
Economic Evaluation of Systems that Expedite Inventory Information
By Alain Bensoussan, M. Çakanyıldırım, ...
-
A Note on 'The Censored Newsvendor and the Optimal Acquisition of Information'
By Alain Bensoussan, M. Çakanyıldırım, ...
-
If the Inventory Manager Knew: Value of Visibility and RFID under Imperfect Inventory Information
By Aykut Atali, Hau L. Lee, ...
-
Censored Newsvendor Model Revisited with Unnormalized Probabilities
By Alain Bensoussan, M. Çakanyıldırım, ...