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Optimal control policy for a Brownian inventory system with concave ordering cost

Part of: Operations research and management science

Published online by Cambridge University Press:  30 March 2016

Dacheng Yao ,
Xiuli Chao  and
Jingchen Wu
Dacheng Yao*
Affiliation:
Chinese Academy of Sciences
Xiuli Chao*
Affiliation:
University of Michigan
Jingchen Wu
Affiliation:
University of Michigan
*
∗Postal address: Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China. Email address: [email protected]
∗∗Postal address: Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, MI 48109-2117, USA. Email address: [email protected]
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Abstract

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In this paper we consider an inventory system with increasing concave ordering cost and average cost optimization criterion. The demand process is modeled as a Brownian motion. Porteus (1971) studied a discrete-time version of this problem and under the strong condition that the demand distribution belongs to the class of densities that are finite convolutions of uniform and/or exponential densities (note that normal density does not belong to this class), an optimal control policy is a generalized (s, S) policy consisting of a sequence of (si, Si). Using a lower bound approach, we show that an optimal control policy for the Brownian inventory model is determined by a single pair (s, S).

Keywords

Brownian inventory system(s, S) policyconcave ordering cost

MSC classification

Primary: 90B05: Inventory, storage, reservoirs
Secondary: 90B30: Production models
Type
Research Papers
Information
Journal of Applied Probability , Volume 52 , Issue 4 , December 2015 , pp. 909 - 925
Copyright
Copyright © Applied Probability Trust 2015 

Footnotes

∗∗∗

Current address: 500 9th Ave N, Seattle, WA 98109, USA. Email address: [email protected]

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