Makespan Minimization with Sequence-dependent Non-overlapping Setups

This paper deals with a scheduling problem that emerges in the production of water tubes of different sizes that require reconfiguration of the machines. The reconfiguration of the machines leads to the notion of sequence-dependent setup times between tasks. These setups are often performed by a single person who cannot serve more than one machine at the same moment, i.e., the setups must not overlap. Surprisingly, the problem with non-overlapping setups has received only a little attention so far. To solve this problem, we propose an Integer Linear Programming formulation, Constraint Programming models and a hybrid heuristic that leverages the strength of Integer Linear Programming in the shortest Hamiltonian path problem and the efficiency of Constraint Programming at sequencing problems with makespan minimization. The experimental evaluation shows that among the proposed exact approaches, the Constraint Programming is a superior method being able to solve instances with 3 machines and up to 11 tasks on each machine to optimality within a few seconds. The proposed hybrid heuristic attains high-quality solutions for instances with 50 machines and up to 116 tasks on each machine.