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TECHNICAL NOTE—A Computational Approach for Optimal Joint Inventory-Pricing Control in an Infinite-Horizon Periodic-Review System

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Abstract

This note considers a joint inventory-pricing control problem in an infinite-horizon periodic-review system. Demand in a period is random and depends on the posted price. Besides the holding and shortage costs, the system incurs inventoryreplenishment costs that consist of both variable and fixed components. At the beginning of each period, a joint inventory and pricing decision is made. Under the long-run average profit criterion, we show that an optimal policy exists within the class of so-called 4s1 S1p5 policies. This is established based on our algorithmic development, which also results in an algorithm for finding an optimal 4s1 S1p5 policy. Subject classifications: joint pricing and inventory control; setup cost; price dependent demand; stochastic inventory model. Area of review: Manufacturing, Service, and Supply Chain Operations. History: Received May 2003; revisions received May 2004, August 2005, July 2007, May 2009; accepted April 2010.

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... In a multi-period problem setting with a fixed ordering cost, Chen and Simchi-Levi (2004a) establish the optimality of (s, S, p) policies for a finite horizon and for an infinite horizon (Chen and Simchi-Levi 2004b). Computational approach for finding the optimal joint inventory-pricing policies includes Feng and Chen (2011) and Wei and Chen (2011). There are also various extensions under the framework of joint pricing and inventory problem. ...
... Q β , r β and p β are the optimal policy parameters maximizing l β (n Q, r , p) for a given β. Following Chen (2005) and Feng and Chen (2011), without proof we propose the following lemma. ...
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... (2) Despite the observation above, the optimal price is not necessarily always decreasing with respect to the initial inventory level. In fact, the same phenomenon has been observed for the joint pricing and inventory control problem for nonperishables in the presence of fixed ordering cost (Chen and Feng 2010;Polatoglu and Sahin 2000). This can be explained as follows. ...
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