On optimal and approximate policies for a multistage production/inventory problem

A stochastic multistage production/inventory problem can be solved by an approximate procedure developed by Clark and Scarf. Previous researchers have made comparisons of the solutions obtained by this procedure with optimal solutions obtained by a Markov Decision Process solution procedure and found that the Clark-Scarf procedure gives close to optimal solutions. Their experimentation was restricted to two-stage problems. In this paper the authors extend the comparison to three-stage problems. It is found that the differences in average costs per period grow noticeably as the number of stages of the problem increases. Observations that may facilitate the development of a heuristic procedure to improve the Clark-Scarf solution are given.