Article ID: | iaor20108817 |
Volume: | 56 |
Issue: | 12 |
Start Page Number: | 2265 |
End Page Number: | 2281 |
Publication Date: | Dec 2010 |
Journal: | Management Science |
Authors: | Semple John, Ramachandran Karthik, Bhaskaran Sreekumar |
Keywords: | backorders |
We consider a dynamic inventory (production) model with general convex order (production) costs and excess demand that can be accepted or refused by the firm. Excess demand that is accepted is backlogged and results in a backlog cost whereas demand that is refused results in a lost sales charge. Endogenizing the sales decision is appropriate in the presence of general convex order costs so that the firm is not forced to backlog a unit whose subsequent satisfaction would reduce total profits. In each period, the firm must determine the optimal order and sales strategy. We show that the optimal policy is characterized by an optimal buy‐up‐to level that increases with the initial inventory level and an order quantity that decreases with the initial inventory level. More importantly, we show the optimal sales strategy is characterized by a critical threshold, a