An analytical theory of multi-echelon production/distribution systems

In this paper, we study inventory control problems arising in multi-echelon production/distribution chains. In these chains, material is delivered by outside suppliers, proceeds through a number of manufacturing stages, and is distributed finally among a number of local warehouses in order to meet market demand. Each stage requires a fixed leadtime; furthermore, we assume a stochastic, stationary end-item demand process. The problem to balance inventory levels and service degrees can be modelled and analyzed by defining appropriate cost functions. Under an average cost criterion, we study the three most important structures arising in multi-echelon systems: assembly systems, serial systems and distribution systems. For all three systems, it is possible to prove exact decomposition results which reduce complex multi-dimensional control problems to simple one-dimensional problems. In addition, we establish the optimality of base-stock control policies.