The infinite horizon non-stationary stochastic inventory problem: Near myopic policies and weak ergodicity

In this paper we consider a periodic review dynamic inventory problem with non-stationary demands. The purpose of this paper is to show that near myopic policies are sufficiently close to optimal decisions for the infinite horizon inventory problem. In order to show this we pay attention to the fact that inventory processes with base-stock policies are weakly ergodic, and we discuss how the weak ergodicity is related to near myopic policies. Then we derive the error bounds of near myopic policies for the optimal decisions and evaluate them with a number of numerical experiments.

[1]  Dean Isaacson,et al.  Markov Chains: Theory and Applications , 1976 .

[2]  T. Morton.  The Nonstationary Infinite Horizon Inventory Problem , 1978 .

[3]  T. Morton,et al.  The finite horizon nonstationary stochastic inventory problem: near-myopic bounds, heuristics, testing , 1995 .

[4]  A. F. Veinott.  Optimal Policy for a Multi-product, Dynamic Non-Stationary Inventory Problem , 1965 .

[5]  Robert L. Smith,et al.  Conditions for the Existence of Planning Horizons , 1984, Math. Oper. Res..

[6]  W. Lovejoy.  Stopped Myopic Policies in Some Inventory Models with Generalized Demand Processes , 1992 .

[7]  Samuel Karlin,et al.  Optimal Policy for Dynamic Inventory Process with Stochastic Demands Subject to Seasonal Variations , 1960 .

[8]  W. Lovejoy.  Myopic policies for some inventory models with uncertain demand distributions , 1990 .

[9]  Robert L. Smith,et al.  A New Optimality Criterion for Nonhomogeneous Markov Decision Processes , 1987, Oper. Res..

[10]  Wallace J. Hopp,et al.  Technical Note - Identifying Forecast Horizons in Nonhomogeneous Markov Decision Processes , 1989, Oper. Res..

[11]  T. Morton,et al.  Discounting, Ergodicity and Convergence for Markov Decision Processes , 1977 .

[12]  S. Karlin.  Dynamic Inventory Policy with Varying Stochastic Demands , 1960 .

[13]  J. C. Bean,et al.  Denumerable state nonhomogeneous Markov decision processes , 1990 .

[14]  Paul H. Zipkin,et al.  Critical Number Policies for Inventory Models with Periodic Data , 1989 .

[15]  C. Bes,et al.  Concepts of Forecast and Decision Horizons: Applications to Dynamic Stochastic Optimization Problems , 1986, Math. Oper. Res..

[16]  Thomas E. Morton,et al.  The Nonstationary Stochastic Lead-Time Inventory Problem: Near-Myopic Bounds, Heuristics, and Testing , 1996 .

[17]  Raymond L. Smith,et al.  Rolling Horizon Procedures in Nonhomogeneous Markov Decision Processes , 1992, Oper. Res..