A Multiperiod Newsvendor Problem with Partially Observed Demand
Mathematics of Operations Research, Vol. 32, No. 2, pp. 322-344, May 2007
23 Pages Posted: 4 Feb 2008 Last revised: 29 Apr 2014
Abstract
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.
Keywords: unobserved unmet demand; Markovian demand; newsvendor problem, dynamic programming, inventroy models, partially observed systems, incomplete information, base stock policy, myopic policy
JEL Classification: C61,M11,D81, D83
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, ...
-
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, ...
-
Inventory Problems with Partially Observed Demands and Lost Sales
By Alain Bensoussan, M. Çakanyıldırım, ...