Infinite-Horizon Dynamic Programming Models—A Planning-Horizon Formulation

Two major areas of research in dynamic programming are optimality criteria for infinite-horizon models with divergent total costs and forward algorithm planning-horizon procedures. A fundamental observation for both problems is that the relative cost of two possible initial actions for a given initial state may be quite insensitive to structural information in all but the first few periods of a multiperiod model. Recently Lundin and Morton have developed a unified machinery for the dynamic lot size model that provides a general optimality criterion for the infinite horizon problem and complete planning-horizon procedures. Here those ideas are extended to provide a formal infinite-horizon/planning-horizon framework for a reasonably general form of the dynamic programming problem. Several examples and illustrations are provided. The approach provides a good vehicle for investigating the non-stationary stochastic inventory problem; this work will appear elsewhere.