| It is usually assumed that decision makers are risk-neutral in the traditional inventory models, i.e., characterizing replenishment strategies that maximize ex-pected total profits during the planning horizon. However, facing uncertain and complex market environment,retailers have appetite for risk. There are a lot of literatures that focus on the risk aversion of inventory management up to now, but usually considering the backorder case. In practice, lost sales are more common. In this paper, we study the risk aversion in inventory management with lost sales from two aspects of the constant procurement cost and the Markov chain procurement cost change.This paper is organized as follows. Section 1 discusses the background and progress. Section 2 introduces K-convex function and modular function, and their properties. When the procurement cost is constant, Section 3 discusses the optimal order strategies under generally increasing concave utility function and exponen-tial utility function by introducing consumer decision model. We conclude that a wealth dependent bask-stock inventory policy is optimal under the generally in-creasing concave utility function without fixed ordering cost; and an (s, S) inventory policy is optimal under. exponential utility function with fixed ordering cost. In ad-dition, by using the properties of modular function, we discuss the influence of the shortage cost, inventory holding cost and retailing price on the base-stock level, re-order point and order-up-to level. Furthermore, Section 4 discusses a risk averse lost sales inventory model with Markovian procurement costs under generally in-creasing concave utility function and exponential utility functions. We obtain the results similar to those of Section 3, but the optimal strategies are dependent on the state in each period. |
