Exact and metaheuristic approaches for identical parallel machine scheduling with a common server and sequence-dependent setup times

We consider the problem of scheduling parallel machines with a common server and sequence-dependent setup times, whose objective is to minimize the makespan. In this case, the common server, which can be a machine, individual or a team, is responsible for performing the setup operations. Therefore, there must be no conflicts while conducting them. An arc-time-indexed formulation is proposed for the problem, as well as an algorithm based on the metaheuristic iterated local search that makes use of an improved decoding algorithm. Computational experiments were carried out on 150 instances involving up to 100 jobs ranging from 2 to 10 machines. The results obtained suggest that the methods developed were capable of finding highly competitive solutions when compared to those achieved by existing approaches.