Bounds, heuristics, and approximations for distribution systems

This paper develops simple approximate methods to analyze a two-stage distribution system consisting of one warehouse and multiple retailers with stochastic demand. 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 also provide bounds on the optimal policy and the optimal expected cost. We show that one of the heuristics is asymptotically optimal in the number of retailers. These results provide practically useful techniques as well as insights into stock-positioning issues and the drivers of system performance.