A Periodic Review Inventory System with S-Shaped Utility Function

Prospect theory shows that human behavior in decision making can often be characterized by an S-shaped utility function. In this paper, we consider a periodic review inventory system with an exponential-type S-shaped utility function. The objective is to maximize the total expected utility over the planning horizon. We show that, for the single-period case without setup cost, a state-dependent order-up-to policy is optimal, to which it is not difficult to obtain the optimal order-up-to level. For the multi-period case without setup costs, we partially characterize the optimal policy when the demand distributions are log-concave, and present an iterative algorithm for computing the optimal policy. Numerical studies are conducted to illustrate the impact of parameters on the system performance and optimal policies. The results show that the ordering behavior of the inventory manager can be significantly different from those derived from the classical models. It is also shown that the approaches in this paper can be applied to both single-period and multi-period systems with setup costs for obtaining optimal policies.