Optimality of an (s, S) Policy with Compound Poisson and Diffusion Demands: A Quasi-Variational Inequalities Approach

摘要: We prove that an (s, S)policy is optimal in a continuous-review stochastic inventory model with fixed ordering cost when the demand mixture of (i) diffusion process and compound Poisson exponentially distributed jump sizes, (ii) constant process. The proof uses theory impulse control. Bellman equation dynamic programming for such problem reduces to set quasi-variational inequalities (QVI). An analytical study QVI leads showing existence policy as well optimality S) policy. Finally, combination general not completely solved. explain difficulties what remains open. also provide numerical example case.