A Formal Description of the Transportation Problem

In this paper we provide a compact, formal description for an important class of problems involving the deployment of diverse equipment (e.g., planes, ships, trucks) to transport cargo (e.g., personnel and material) throughout large geographical areas for private, government, and military purposes. The problem is particularly interesting for its combination of static and dynamic sources of complexity, and the fact that it allows and in some cases strongly encourages distributed solutions. The merit of this formalization is shown by its application to both understanding the complexities in existing restricted transportation problems and creating new natural restrictions on the general problem. Starting from the general formulation we are able to isolate the static and dynamic sources of complexity in transportation problems and relate them to existing research in computer science and operations research. In addition, we describe techniques for constructing algorithms for the transportation problem with provable performance guarantees.