Solving a Production Scheduling Problem as a Time-Dependent Traveling Salesman Problem

This paper introduces and compares several formulations of a production scheduling problem with sequence-dependent and time-dependent setup times on a single machine. The setup time is divided into two parts: one that can be performed at any time and another one that is restricted to be made outside of a given time interval. As a result, the setup time between two jobs is a function of the completion time of the first job. The problem can be formulated as a time-dependent traveling salesman problem, where the travel time between two nodes is a function of the departure time from the first node. We show that the resulting formulation can be strengthened to provide stronger linear programming relaxation lower bounds. We also introduce several families of valid inequalities which are used within a branch-and-cut algorithm. Computational experiments show that this algorithm can solve instances with up to 20 jobs within reasonable computing times.