An integer programming approach for the time-dependent TSP

The Time-Dependent Travelling Salesman Problem (TDTSP) is a generalization of the traditional TSP where the travel cost between two cities depends on the moment of the day the arc is travelled. In this paper, we focus on the case where the travel time between two cities depends not only on the distance between them, but also on the position of the arc in the tour. We consider the formulations proposed in Picard and Queryanne [J.C. Picard and M. Queyranne. The time-dependent traveling salesman problem and its application to the tardiness problem in one-machine scheduling. Operations Res., 26(1):86–110, 1978] and Vander Wiel and Sahinidis [R.J. Vander Wiel and N.V. Sahinidis. An exact solution approach for the time-dependent traveling-salesman problem. Naval Res. Logist., 43(6):797–820, 1996], analyze the relationship between them and derive some valid inequalities and facets. Computational results are also presented for a Branch and Cut algorithm (B&C) that uses these inequalities, which showed to be very effective.