Production, manufacturing and Logistics Value at risk and inventory control Charles S. Tapiero * Groupe ESSEC, B.P. 105, Ave. Bernard Hirsch, 95021 Cergy Pontoise, France Received 23 May 2001; accepted 9 May 2003 Available online 31 December 2003 Abstract The purposes of this paper are two-fold. On the one hand, we shall provide a decision analysis justification for the Value at Risk (VaR) approach based on ex-post, disappointment decision making arguments. We shall show that the VaR approach is justified by a disappointment criterion. In other words, the asymmetric valuation between ex-ante expected returns above an appropriate target return and the expected returns below that same target level, provide an explanation for the VaR criterion when it is used as a tool for VaR efficiency design. Second, this paper provides applications to inventory management based on VaR risk exposure. Although the mathematical problems arising from an application of the VaR approach, tuned to current practice in financial risk management, are difficult to solve analytically, solutions can be found by application of standard computational and simulation techniques. A number of cases are solved and formulated to demonstrate the paperÕs applicability. Ó 2003 Elsevier B.V. All rights reserved. Keywords: VaR; Inventory; Risk 1. Introduction Traditionally, inventory control has empha- sized an ex-ante rather than an ex-post approach. In practice, however, time phasing of information and the inventory decision-making process com- bine to render most theoretical models of limited usefulness. For example, supply flexibility, supply delays management and related issues may often be the determinant factors in adopting an appro- priate policy that is sensitive to demand and other uncertainties. These problems recur in many forms. In the economic literature it appears under the irreversibility effect and option value (Kreps, 1979; Freixas, 1987), although they are rarely ap- plied in inventory control (for an exception see Ritchken and Tapiero, 1986 for the use of options in inventory control with price and demand uncertainty). Further, the traditional approach to measuring costs in inventory management has been oblivious to revenues generated by main- taining inventories on the one hand and to the difficulties encountered when shortage costs must be assessed. Costs such as, ‘‘goodwill’’, managerial attitudes towards losses and regrets (compared to ‘‘reaching the right decision’’) and so on, are hardly quantifiable and therefore mostly neglected. Further, traditional inventory models have been based essentially on the minimization of expected * Tel.: +33-13-443-3041; fax: +33-13-443-3001. E-mail address: tapiero@essec.fr (C.S. Tapiero). 0377-2217/$ - see front matter Ó 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.ejor.2003.05.005 European Journal of Operational Research 163 (2005) 769–775 www.elsevier.com/locate/dsw