Exact and heuristic dynamic programming algorithms for the traveling salesman problem with flexible time windows

Abstract

This article proposes extensions of exact and heuristic dynamic programming algorithms for the traveling salesman problem with flexible time windows, which are a limited enlargement of the generally referred to as hard time windows. The service of a customer can be started before or after the hard time window at a penalty cost. The addressed problem thus requires the determination of a sequence of customers and their respective service start times in order to minimize the sum of traveling cost with earliness and lateness cost. Computational tests are conducted on a variety of symmetric and asymmetric instances proposed in the literature, and the advantages of flexible windows are stressed.