Hierarchical Planning for Probabilistic Distribution Systems in Euclidean Spaces

We develop an analytical model to assist the design and control of probabilistic distribution systems. These distribution systems are characterized by the explicit inclusion of probabilistic elements. The probabilistic aspect considered is that only a subset of all potential customers needs service on any given working day. This subset of customers and their demand are determined according to some probability distribution. The cost of operating such systems is significantly affected by decisions on the number and locations of the distribution centers, the allocation of customers to each center, and the routing strategy. We propose a three-stage hierarchical approach in which decisions about the number of centers and their locations (first stage), customers allocations (second stage) and routing strategies (third stage) are combined to reduce total system cost.