Mean–Variance Analysis for the Newsvendor Problem

The newsvendor problem is a fundamental building block for inventory management with a stochastic demand. The classical newsvendor problem focuses on a sole objective of either minimizing the expected cost or maximizing the expected profit. However, the performance measure with expected value alone is insufficient, and it ignores the risk preferences of the decision makers. As a result, we carry out a mean-variance analysis of the newsvendor problem. We construct analytical models and reveal the problem's structural properties. We propose the solution schemes which help to identify the optimal solutions. Interesting findings regarding the efficient frontier, the case with a stockout penalty cost, and the safety-first objective are discussed.

[1]  M. Anvari,et al.  Optimality Criteria and Risk in Inventory Models: The Case of the Newsboy Problem , 1987 .

[2]  Jan A. Van Mieghem,et al.  Commissioned Paper: Capacity Management, Investment, and Hedging: Review and Recent Developments , 2003, Manuf. Serv. Oper. Manag..

[3]  A. Atkinson.  INCENTIVES, UNCERTAINTY, AND RISK IN THE NEWSBOY PROBLEM , 1979 .

[4]  Mahmut Parlar,et al.  Balancing desirable but conflicting objectives in the newsvendor problem , 2003 .

[5]  Gérard P. Cachon,et al.  Decision Bias in the Newsvendor Problem with a Known Demand Distribution: Experimental Evidence.: Experimental Evidence. , 2000 .

[6]  J. Dickinson,et al.  COST-VOLUME-PROFIT ANALYSIS UNDER UNCERTAINTY , 1974 .

[7]  R. Norland.  REFINEMENTS IN THE ISMAIL‐LOUDERBACK STOCHASTIC CVP MODEL* , 1980 .

[8]  L. Eeckhoudt,et al.  The Risk-Averse and Prudent Newsboy , 1995 .

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

[10]  Kee H. Chung,et al.  Risk in Inventory Models: The Case of the Newsboy Problem — Optimality Conditions , 1990 .

[11]  Tsan-Ming Choi,et al.  Mean-variance analysis of a single supplier and retailer supply chain under a returns policy , 2008, Eur. J. Oper. Res..

[12]  A. Roy.  SAFETY-FIRST AND HOLDING OF ASSETS , 1952 .

[13]  Stephen A. Ross,et al.  Equilibrium and Agency--Inadmissible Agents in the Public Agency Problem , 1979 .

[14]  H. Markowitz,et al.  Mean-Variance versus Direct Utility Maximization , 1984 .

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

[16]  Henk Grootveld,et al.  Variance vs downside risk: Is there really that much difference? , 1999, Eur. J. Oper. Res..

[17]  Houmin Yan,et al.  Channel coordination in supply chains with agents having mean-variance objectives , 2008 .

[18]  M. Khouja.  The single-period (news-vendor) problem: literature review and suggestions for future research , 1999 .

[19]  Elisa Luciano,et al.  VaR as a risk measure for multiperiod static inventory models , 2003 .

[20]  Steven Nahmias,et al.  Production and operations analysis , 1992 .

[21]  Woody M. Liao,et al.  A Stochastic demand CVP model with return on investment criterion , 1984 .

[22]  A. Roy.  Safety first and the holding of assetts , 1952 .

[23]  Sifeng Liu,et al.  Supply-Chain Coordination With Combined Contract for a Short-Life-Cycle Product , 2006, IEEE Trans. Syst. Man Cybern. Part A.

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

[25]  Tsan-Ming Choi,et al.  Optimal two-stage ordering policy with Bayesian information updating , 2003, J. Oper. Res. Soc..

[26]  B. Ismail,et al.  OPTIMIZING AND SATISFICING IN STOCHASTIC COST‐VOLUME‐PROFIT ANALYSIS , 1979 .

[27]  E. Sankarasubramanian,et al.  Note-Note on Optimal Ordering Quantity to Realize a Pre-Determined Level of Profit , 1983 .

[28]  Charles S. Tapiero,et al.  Value at risk and inventory control , 2005, Eur. J. Oper. Res..

[29]  Maqbool Dada,et al.  Pricing and the Newsvendor Problem: A Review with Extensions , 1999, Oper. Res..