Spatial decomposition for a multi-facility production and distribution problem

Many firms are trying to optimize their production systems by only concentrating on the production stage, but possible savings by this approach are limited. Nowadays, it is more important to analyze the entire production/distribution system. The drawback of such an approach is the large number of elements one has to consider. Therefore, we present here a hierarchical scheme which decomposes a global industrial problem into several subproblems. A model for these subproblems is developed, based on an analogy to the vehicle routing problem (VRP). Comparisons between this approach and a global method are done in terms of the number of variables and constraints of the underlying linear programs. A branch and bound method is developed to obtain the exact solutions of the subproblems. Experiments compare the solution of problems with a central procedure using a heuristic and the solution with the spatial decomposition using the branch and bound method.