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Title: Optimal Ordering Policy for Inventory Systems with Quantity-Dependent Setup Costs
Authors: He, Shuangchi 
Yao, Dacheng
Zhang, Hanqin 
Keywords: stochastic inventory model
quantity-dependent setup cost
(s, S) policy
base stock policy
impulse control
instantaneous control
Issue Date: 1-Nov-2017
Publisher: INFORMS
Citation: He, Shuangchi, Yao, Dacheng, Zhang, Hanqin (2017-11-01). Optimal Ordering Policy for Inventory Systems with Quantity-Dependent Setup Costs. MATHEMATICS OF OPERATIONS RESEARCH 42 (4) : 979-1006. ScholarBank@NUS Repository.
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.
ISSN: 0364-765X
DOI: 10.1287/moor.2016.0833
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