Available online at www.sciencedirect.com ScienceDirect EUROPEAN JOURNAL OF OPERATIONAL RESEARCH ELSEVIER European Journal of Operational Research 174(2006)1643-1650 www.elsevier.com/locate/ejor Production,Manufacturing and Logistics A benchmark solution for the risk-averse newsvendor problem Baruch Keren a.",Joseph S.Pliskin b Sami Shamoon College of Engineering.The Department of Industrial Engineering and Management. Ben-Gurion University of the Negev.Bialik/Basel Streets,P.O.Box 45.Beer Sheva 84100,Israel Department of Industrial Engineering and Management.Ben-Gurion University of the Negev.Israel Received 19 January 2004:accepted 31 March 2005 Available online 19 July 2005 Abstract 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 2005 Elsevier B.V.All rights reserved. Keywords:Utility theory:Newsvendor problem:Risk-aversion:Uniform distribution 1.Introduction The interest in the newsvendor problem and its extensions has remained high since it was first intro- duced by Within (1955).A variety of extensions to the single period inventory problems,newsvendor problem and other newsvendor type problems have been presented and researched since then.Khouja's (1999)survey includes more than 10 types of extensions to the newsvendor problems.Kabak and Schiff (1978)dealt with the objective of maximizing the probability of achieving a target profit.Ismail and Loudberback (1979)examined the penalties for output not equaling demand for a firm facing an uncer- tain demand with a known probability function and under several alternatives for the objective function. Lau(1980)analyzes the newsvendor model under two different objective functions.In the first objective, Corresponding author.Tel.:+972 8 647 5641/42/46:fax:+972 8 647 5643. E-mail addresses:baruchke@sce.ac.il,baruchke@bgu.ac.il (B.Keren). 0377-2217/S-see front matter 2005 Elsevier B.V.All rights reserved doi:l0.1016/.ejor.2005.03.047Production, Manufacturing and Logistics A benchmark solution for the risk-averse newsvendor problem Baruch Keren a,*, Joseph S. Pliskin b a Sami Shamoon College of Engineering, The Department of Industrial Engineering and Management, Ben-Gurion University of the Negev, Bialik/Basel Streets, P.O. Box 45, Beer Sheva 84100, Israel b Department of Industrial Engineering and Management, Ben-Gurion University of the Negev, Israel Received 19 January 2004; accepted 31 March 2005 Available online 19 July 2005 Abstract 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. 2005 Elsevier B.V. All rights reserved. Keywords: Utility theory; Newsvendor problem; Risk-aversion; Uniform distribution 1. Introduction The interest in the newsvendor problem and its extensions has remained high since it was first intro￾duced by Within (1955). A variety of extensions to the single period inventory problems, newsvendor problem and other newsvendor type problems have been presented and researched since then. Khoujas (1999) survey includes more than 10 types of extensions to the newsvendor problems. Kabak and Schiff (1978) dealt with the objective of maximizing the probability of achieving a target profit. Ismail and Loudberback (1979) examined the penalties for output not equaling demand for a firm facing an uncer￾tain demand with a known probability function and under several alternatives for the objective function. Lau (1980) analyzes the newsvendor model under two different objective functions. In the first objective, 0377-2217/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.ejor.2005.03.047 * Corresponding author. Tel.: +972 8 647 5641/42/46; fax: +972 8 647 5643. E-mail addresses: baruchke@sce.ac.il, baruchke@bgu.ac.il (B. Keren). European Journal of Operational Research 174 (2006) 1643–1650 www.elsevier.com/locate/ejor