Bounds, Heuristics, and Approximations for Distribution Systems

This paper develops simple approximate methods to analyze a two-stage stochastic distribution system consisting of one warehouse and multiple retailers. We consider local and central control schemes. The main ideas are based on relaxing and or decomposing the system into more manageable newsvendor type subsystems. We provide bounds on optimal echelon base-stock levels and on the optimal expected cost. We show that one of the heuristics is asymptotically optimal in the number of retailers. The results of this paper provide practicaly useful techniques as well as insights into stock-positioning issues and the drivers of system performance.