Optimal and Near-Optimal ( s, S) Inventory Policies for Levy Demand Processes

A is a continuous-time, real-valued stochastic process which has independent and Levy jump process stationary increments, with no Brownian component. We study some of the fundamental properties of Levy jump processes and develop inventory models for them. Of particular interest to us is the gamma-distributed Levy process, in which the demand that occurs in a fixed period of time has a gamma distribution. We study the relevant properties of these processes, and we develop a quadratically convergent algorithm for finding optimal policies. We develop a simpler heuristic policy and derive a bound