Dynamic Inventory Management with Learning About the Demand Distribution and Substitution Probability
AbstractAwell-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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoArticle provided by INFORMS in its journal Manufacturing & Service Operations Management.
Volume (Year): 10 (2008)
Issue (Month): 2 (May)
Bayesian inventory management; unknown demand distribution; unobserved lost sales; substitution probability; Bayesian dynamic programming; optimal inventory control; maximum likelihood estimator; make-to-stock queue;
You can help add them by filling out this form.
reading list or among the top items on IDEAS.Access and download statisticsgeneral information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Mirko Janc).
If references are entirely missing, you can add them using this form.