Periodic Review Multiperiod Inventory Control Under a Mean–Variance Optimization Objective

We study in this correspondence paper a solution scheme which solves a periodic review multiperiod inventory problem under a mean-variance (MV) framework. We first investigate a primal inventory problem with an MV objective function. Owing to the nonseparable nature of variance, we construct an auxiliary problem which is separable. By solving the auxiliary problem, we identify the conditions under which the solutions of the primal and auxiliary problems converge. Hence, we propose the algorithm and show that a base-stock policy is optimal.

[1]  Li Yao,et al.  A newsvendor pricing game , 2004, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[2]  Awi Federgruen,et al.  An Efficient Algorithm for Computing Optimal (s, S) Policies , 1984, Oper. Res..

[3]  A. Stuart,et al.  Portfolio Selection: Efficient Diversification of Investments , 1959 .

[4]  Ying Wei,et al.  Mean-variance analysis of supply chains under wholesale pricing and profit sharing schemes , 2010, Eur. J. Oper. Res..

[5]  Andy A. Tsay,et al.  Risk sensitivity in distribution channel partnerships: implications for manufacturer return policies , 2002 .

[6]  S. Seshadri,et al.  Risk intermediation in supply chains , 2000 .

[7]  Tsan-Ming Choi,et al.  Price Wall or War: The Pricing Strategies for Retailers , 2009, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[8]  Houmin Yan,et al.  Risk analysis of commitment–option contracts with forecast updates , 2011 .

[9]  Paul H. Zipkin,et al.  Foundations of Inventory Management , 2000 .

[10]  Youyi Feng,et al.  A new algorithm for computing optimal (s, S) policies in a stochastic single item/location inventory system , 2000 .

[11]  Tsan-Ming Choi,et al.  Mean–Variance Analysis for the Newsvendor Problem , 2008, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[12]  Kin Keung Lai,et al.  Analysis of optimal opportunistic replenishment policies for inventory systems by using a (s , 2005, Eur. J. Oper. Res..

[13]  Suresh P. Sethi,et al.  Optimality of (s, S) Policies in Inventory Models with Markovian Demand , 1995, Oper. Res..

[14]  Peilin Fu,et al.  Variance minimization approach for a class of dual control problems , 2002, IEEE Trans. Autom. Control..

[15]  K. Arrow,et al.  Optimal Inventory Policy. , 1951 .

[16]  Hon-Shiang Lau.  The Newsboy Problem under Alternative Optimization Objectives , 1980 .

[17]  Tsan-Ming Choi,et al.  Optimal Pricing and Stocking Decisions for Newsvendor Problem With Value-at-Risk Consideration , 2010, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[18]  J. Kiefer,et al.  On the Optimal Character of the (s, S) Policy in Inventory Theory , 1953 .

[19]  Hon-Shiang Lau,et al.  Manufacturer's pricing strategy and return policy for a single-period commodity , 1999, Eur. J. Oper. Res..