Production , Manufacturing and Logistics A benchmark solution for the risk-averse newsvendor problem

In this paper, we derive the first order conditions for optimality for the problem of a risk-averse expected-utility maximizer newsvendor. We use these conditions to solve a special case where the utility function is any increasing differentiable function, and the random demand is uniformly distributed. This special case has a simple closed form solution and therefore it provides an insightful and practical interpretation to the optimal point. We show some properties of the solution and also demonstrate how it can be used for assessing the newsvendor utility function parameters.

[1]  J. Pratt.  RISK AVERSION IN THE SMALL AND IN THE LARGE11This research was supported by the National Science Foundation (grant NSF-G24035). Reproduction in whole or in part is permitted for any purpose of the United States Government. , 1964 .

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

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

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

[5]  T. M. Whitin.  Inventory Control and Price Theory , 1955 .

[6]  Peter Kischka,et al.  Risk-averse and risk-taking newsvendors: a conditional expected value approach , 2007 .

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

[8]  J. Neumann,et al.  The Theory of Games and Economic Behaviour , 1944 .

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

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

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

[12]  J. Pratt.  RISK AVERSION IN THE SMALL AND IN THE LARGE11This research was supported by the National Science Foundation (grant NSF-G24035). Reproduction in whole or in part is permitted for any purpose of the United States Government. , 1964 .

[13]  Arthur F. Veinott,et al.  Analysis of Inventory Systems , 1963 .

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

[15]  S. Karlin,et al.  Studies in the Mathematical Theory of Inventory and Production, by K.J. Arrow, S. Karlin, H. Scarf with contributions by M.J. Beckmann, J. Gessford, R.F. Muth. Stanford, California, Stanford University Press, 1958, X p.340p., $ 8.75. , 1959, Bulletin de l'Institut de recherches économiques et sociales.

[16]  Haim Levy,et al.  Portfolio and Investment Selection: Theory and Practice , 1984 .