On the comparison of risk-neutral and risk-averse newsvendor problems Abhilasha Prakash Katariya 1 , Sıla C ¸etinkaya 1 and Eylem Tekin 2 1 Texas A&M University, College Station, TX, USA; and 2 University of Houston, Houston, TX, USA The objective of this paper is to investigate and compare the relationship between risk-neutral and risk-averse newsvendor problems under three different decision criteria: expected utility (EU) maximization, mean-variance (MV) analysis, and conditional value-at-risk (CVaR) minimization. Several models in the literature have shown that for special cases of the newsvendor problem (eg, no salvage value, no shortage penalty, and with recourse option), a risk-averse newsvendor orders less than a risk-neutral newsvendor. First, we present an observation about the EU maximization models with such special cases where a risk-averse newsvendor orders less than a risk-neutral one. We note that this observation does not extend to the newsvendor problem with positive shortage penalty. Using several counterexamples, we demonstrate that the common wisdom that a risk-averse newsvendor orders less than a risk-neutral newsvendor is not true in general. Second, we demonstrate, analytically where possible and numerically if not, that the comparison of the optimal order quantities of risk- neutral and risk-averse newsvendors depends on the key assumptions regarding the model inputs, namely, the decision criterion, the demand distribution and the cost parameters such as shortage penalty and unit ordering cost. Third, we show that EU and the MV criteria yield consistent results while EU and CVaR criteria may yield consistent or conflicting results depending on the loss function used for the CVaR criterion. Journal of the Operational Research Society (2014) 65(7), 1090–1107. doi:10.1057/jors.2013.48 Published online 22 May 2013 Keywords: conditional value-at-risk; expected utility theory; risk-aversion; newsvendor model 1. Introduction and literature review The newsvendor problem is one of the fundamental problems in the context of production and inventory management. The classical newsvendor problem is a single- period problem where the decision maker places an order at the beginning of the period before the stochastic demand is realized. If the order quantity is greater than the realized demand, excess units can be salvaged at a value lower than the unit ordering cost. On the other hand, if the order quantity is less than the realized demand, the newsvendor loses an opportunity to make additional profit. Owing to its wide applicability, the newsvendor problem and its extensions have been extensively studied. Traditional models assume that the newsvendor’s objec- tive is to maximize the expected profit or to minimize the expected cost, which is appropriate for risk-neutral decision makers. However, not all decision makers are risk neutral. On the contrary, risk-averse nature of decision makers is well established in decision theory. This is also supported by the experimental results, which suggest that the order quantity decisions made by the managers in real life systematically deviate from those that maximize the expected profit (Schweitzer and Cachon, 2000). Conse- quently, in recent years, several inventory management models have been developed to incorporate the risk-averse nature of the decision maker (Qin et al, 2011). Naturally, one interesting question that arises is: For the classical newsvendor problem, how do the optimal order quantity decisions made by a risk-neutral newsvendor compare with those made by a risk-averse one? The objective of this paper is to investigate this relationship between the risk- neutral and risk-averse newsvendor problems. The risk-averse nature of a newsvendor can be modelled by using three different approaches: mean-variance (MV) analysis (Lau, 1980; Wu et al, 2009), conditional value- at-risk (CVaR) minimization (Gotoh and Takano, 2007), and expected utility (EU) maximization (Horowitz, 1970; Baron, 1973; Eeckhoudt et al, 1995; Keren and Pliskin, 2006). Under the MV analysis, the newsvendor’s objective is to maximize the difference between the expected profit and the variance of the profit multiplied by a constant, aX0. The constant a characterizes the decision maker’s risk aversion and represents a quantitative trade-off between Journal of the Operational Research Society (2014) 65, 1090–1107 © 2014 Operational Research Society Ltd. All rights reserved. 0160-5682/14 www.palgrave-journals.com/jors/  Correspondence: Sıla C¸etinkaya, Department of Industrial and Systems Engineering, Texas A&M University, 4044 ETB, College Station, TX 77843-3131, USA. E-mail: sila@tamu.edu