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 Chen, L. Articles by Plambeck, E. L. Search for Related Content

Dynamic Inventory Management with Learning About the Demand Distribution and Substitution Probability

TrueDemand, Inc., Los Gatos, California 95032
Graduate School of Business, Stanford University, Stanford, California 94305
li{at}tdemand.com
elp{at}stanford.edu

Awell-known result in the Bayesian inventory management literature is: If lost sales are not observed, the Bayesian optimal inventory level is larger than the myopic inventory level (one should "stock more" to learn about the demand distribution). This result has been proven in other studies under the assumption that inventory is perishable, so the myopic inventory level is equal to the Bayesian optimal inventory level with observed lost sales. We break that equivalence by considering nonperishable inventory. We prove that with nonperishable inventory, the famous "stock more" result is often reversed to "stock less," in that the Bayesian optimal inventory level with unobserved lost sales is lower than the myopic inventory level. We also prove that making lost sales unobservable increases the Bayesian optimal inventory level; in this specific sense, the famous "stock more" result of other studies generalizes to the case of nonperishable inventory.

When the product is out of stock, a customer may accept a substitute or choose not to purchase. We incorporate learning about the probability of substitution. This reduces the Bayesian optimal inventory level in the case that lost sales are observed. Reducing the inventory level has two beneficial effects: to observe and learn more about customer substitution behavior and (for a nonperishable product) to reduce the probability of overstocking in subsequent periods.

Finally, for a capacitated production-inventory system under continuous review, we derive maximum likelihood estimators (MLEs) of the demand rate and probability that customers will wait for the product. (Accepting a raincheck for delivery at some later time is a common type of substitution.) We investigate how the choice of base-stock level and production rate affect the convergence rate of these MLEs. The results reinforce those for the Bayesian, uncapacitated, periodic review system.

Key Words: Bayesian inventory management; unknown demand distribution; unobserved lost sales; substitution probability; Bayesian dynamic programming; optimal inventory control; maximum likelihood estimator; make-to-stock queue
History: Received: May 13, 2005; accepted: January 3, 2007.

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]

				K. S. Azoury and J. Miyaoka Optimal Policies and Approximations for a Bayesian Linear Regression Inventory Model Management Science, May 1, 2009; 55(5): 813 - 826. [Abstract] [PDF]

				W. T. Huh and P. Rusmevichientong A Nonparametric Asymptotic Analysis of Inventory Planning with Censored Demand Mathematics of Operations Research, February 1, 2009; 34(1): 103 - 123. [Abstract] [PDF]

				M. Armony, E. Plambeck, and S. Seshadri Sensitivity of Optimal Capacity to Customer Impatience in an Unobservable M/M/S Queue (Why You Shouldn't Shout at the DMV) MSOM, January 1, 2009; 11(1): 19 - 32. [Abstract] [PDF]

				N. DeHoratius, A. J. Mersereau, and L. Schrage Retail Inventory Management When Records Are Inaccurate MSOM, January 1, 2008; 10(2): 257 - 277. [Abstract] [PDF]