Financial management in inventory problems: Risk averse vs risk neutral policies

In this work, we discuss the effect of risk measure selection in the determination of inventory policies. We consider an inventory system characterized by the loss function of Luciano et al. [2003. VaR as a risk measure for multi-period static inventory models. International Journal of Production Economics 81-82, 375-384]. We derive the optimization problems faced by risk neutral, quadratic utility, mean-absolute and CVaR decision makers. Results show that while the global nature of the optimal policy is assured for risk coherent and risk neutral decision makers, the convexity of the quadratic utility problem depends on the stochastic properties of demand. We investigate the economic and stochastic determinants of the different policies. This allows us to establish the conditions under which each type of decision maker is indifferent to imprecision in the distribution families. Finally, we discuss the numerical impact of the choice of the risk measure by means of a multi-item inventory. The introduction of an approach based on Savage Scores allows us to offer a quantitative measurement of the similarity/discrepancy of policies reflecting different risk attitudes.