Route Constrained Fleet Scheduling

This paper attempts to provide some insight into the structure of a large class of fleet scheduling problems. Scheduling under fixed due date constraints is shown to be easily solved using a new formulation of the problem. Scheduling under flexible due date constraints is shown to be inherently complex, and strong evidence is given for asserting that no efficient (polynomial bounded) algorithm exists for solving this problem exactly. A fast heuristic approach is described which has worked well in some school bus scheduling applications.