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Volume 4, Number 2, 2014, Pages 197-220                                                                DOI:10.11948/2014009
Optimal control of a finite-capacity inventory system with setup cost and lost sales
Baimei Yang,Yiqian Huang,Yifan Xu
Keywords:Inventory System, Finite Capacity, Poisson Demand, Markov Decision Process, Lost Sales.
Abstract:
      One of the most fundamental results in inventory theoryis the optimality of (s, S) policy for inventory systems withsetup cost. This result is established based on a key assumptionof infinite production/ordering capacity. Several studies haveshown that, when there is a finite production/ordering capacity,the optimal policy for the inventory system is very complicatedand indeed, only partial characterization for the optimal policyis possible. In this paper, we consider a continuous reviewinventory system with finite production/ordering capacity andsetup cost, and show that the optimal control policy for thissystem has a very simple structure. We also develop efficientalgorithms to compute the optimal control parameters.
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