Vehicle routing and scheduling with time windows

Abstract

Consider a set of trips where each trip is specified a priori by a place of origin, a destination, a duration, a cost and a time interval within which the trip must begin. The problem is to minimize fleet size and total travel costs. This is a generalization of the m-travelling salesman problem. We compare results for three algorithms. The first one is an adaptation of the Carpaneto-Toth algorithm for the asymmetric travelling salesman problem: solution of nework problems by relaxing scheduling constraints, and branch-and-bound on flow variables. The second one consists in solution of network problems by relaxing scheduling constraints and branch-and-bound based on dividing the time windows. In the third algorithm, we use column generation on a set partitioning problem solved by simplex and branch-and-bound; columns are generated by a shortest path algorithm with time windows on the nodes.