Computational complexity of convoy movement planning problems

Convoy movement planning problems arise in a number of important logistical contexts, including military planning, railroad optimization and automated guided vehicle routing. In the convoy movement problem (CMP), a set of convoys, with specified origins and destinations, are to be routed with the objective of minimizing either makespan or total flow time, while observing a number of side constraints. This paper characterizes the computational complexity of several restricted classes of CMPs. The principal objective is to identify the most parsimonious set of problem features that make the CMP intractable. A polynomial-time algorithm is provided for the single criterion two-convoy movement problem. The performance of a simple prioritization-idling approximation algorithm is also analyzed for the K-convoy movement problem. Error bounds are developed for the makespan and flow time objectives.