On time-indexed formulations for the parallel machine scheduling problem with a common server

This article studies the problem of scheduling independent jobs on parallel machines with a common server, the objective of which is to minimize the makespan. In this case, the common server is responsible for performing the setup operations and, therefore, there must be no conflicts while conducting them. Four alternative time-indexed formulations for the problem are considered and evaluated computationally. Moreover, two algorithms are presented that can significantly improve the performance of the best time-indexed formulation. The results obtained on two benchmark datasets involving up to 100 jobs suggest that the proposed improved algorithms are substantially better than existing approaches.