Optimal control policy for a Brownian inventory system with concave ordering cost. (December 2015)

• Record Type: Journal Article
• Authors: Yao, Dacheng; Chao, Xiuli; Wu, Jingchen
• Is Part Of: Journal of applied probability. Volume 52:Number 4(2015)
• Page Start: 909
• Page End: 925
• Publication Date: 2015-12
• Subjects: Brownian inventory system, -- (s, S) policy, -- concave ordering cost; 90B05, -- 90B30; 519.2
• DOI: 10.1239/jap/1450802743
• Languages: English
• ISSNs: 0021-9002

Abstract

Abstract : 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 ).