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

2015/12/01 by Dacheng Yao, Xiuli Chao, Jingchen Wu · 3 citations
Business, Management and Accounting · Decision Sciences · #Advanced Queuing Theory Analysis #Supply Chain and Inventory Management #Probability and Risk Models

paper · doi:10.1239/jap/1450802743

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 ( s i , S i ). 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 ).

Cited by

• Long-Term Average Impulse Control with Mean Field Interactions
• Optimal Control of a Levy Inventory System: The Optimality of Control Band Policy
• Optimal Policy Characterization for a Class of Multi-Dimensional Ergodic Singular Stochastic Control Problems

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