Optimal Ordering Policy for Inventory Systems with Quantity-Dependent Setup Costs

Shuangchi He (), Dacheng Yao () and Hanqin Zhang ()
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Shuangchi He: Department of Industrial and Systems Engineering, National University of Singapore, Singapore 117576
Dacheng Yao: Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
Hanqin Zhang: Department of Decision Sciences, National University of Singapore, Singapore 119245

Mathematics of Operations Research, 2017, vol. 42, issue 4, 979-1006

Abstract: We consider a continuous-review inventory system in which the setup cost of each order is a general function of the order quantity and the demand process is modeled as a Brownian motion with a positive drift. Assuming the holding and shortage cost to be a convex function of the inventory level, we obtain the optimal ordering policy that minimizes the long-run average cost by a lower bound approach. To tackle some technical issues in the lower bound approach under the quantity-dependent setup cost assumption, we establish a comparison theorem that enables one to prove the global optimality of a policy by examining a tractable subset of admissible policies. Since the smooth pasting technique does not apply to our Brownian inventory model, we also propose a selection procedure for computing optimal policy parameters when the setup cost is a step function.

Keywords: stochastic inventory model; quantity-dependent setup cost; ( s , S ) policy; base stock policy; impulse control; instantaneous control (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (8)

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