A heuristic approach to the multi-period multi-commodity transportation problem

This paper describes an approach to solving a real-world problem which involves the transportation of multiple types of commodities from a number of sources to a number of destinations in discrete time periods, using a capacitated heterogeneous fleet of vehicles. The preliminary objective is to minimize the total number of discrete periods needed to complete the entire operation. The problem is first formulated as a mixed integer program and its tractability is then greatly improved by reformulating it through backward decomposition into two separate models and solved iteratively. A heuristic approach harnessing specific features of the second approach is developed for solving large size problems to obtain near-optimal solutions within reasonable time. The design of the heuristic also takes into consideration the secondary objectives of minimizing the total vehicle capacity used and minimizing the total capacity of sources needed to satisfy the demands at the destinations. Computational results are provided for a variety of randomly generated problems as well as problems from the literature. The approach described here may be applied to the multi-period transportation of personnel and goods from multiple starting points to multiple destinations in both military and civilian applications.