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Published online by Cambridge University Press:  30 July 2012

Xiuli Chao
Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, MI48109 E-mail:
Yifan Xu
School of Management, Fudan University, Shanghai 200433, China E-mail:
Baimei Yang
School of Management, Fudan University, Shanghai 200433, China E-mail:


One of the most fundamental results in inventory theory is the optimality of (s, S) policy for inventory systems with setup cost. This result is established under a key assumption of infinite ordering/production capacity. Several studies have shown that, when the ordering/production capacity is finite, the optimal policy for the inventory system with setup cost is very complicated and indeed, only partial characterization for the optimal policy is possible. In this paper, we consider a continuous review production/inventory system with finite capacity and setup cost. The demand follows a Poisson process and a demand that cannot be satisfied upon arrival is backlogged. We show that the optimal control policy has a very simple structure when the holding/shortage cost rate is quasi-convex. We also develop efficient algorithms to compute the optimal control parameters.

Research Article
Copyright © Cambridge University Press 2012

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