MIP models and hybrid algorithm for minimizing the makespan of parallel machines scheduling problem with a single server

This paper considers the identical parallel machines scheduling problem (PMSP) with a single server in charge of job setups. A job can be processed with a precedent setup by a server on one of the machines. The setup can be processed at only one machine at any time. In this paper, the problem P, S1|sj|Cmax with a general job set is formulated using mixed integer programming in two ways. The first one is developed by taking into account the characteristics of the single server problem, and the second one is developed by adding the concept of the server waiting time suggested by Abdekhodaee and Wirth (2002) [3]. Abdekhodaee and Wirth (2002) [3] define the equation of the server waiting time applied to only the special case with two machines and a regular job set. The general model for several machines is studied in this paper by developing the properties on the server waiting time. The hybrid heuristic algorithm is developed for the practical use, which can yield a near-optimal schedule in a reasonable computational time. The performance of algorithm is evaluated by comparing with the results of MIP models and heuristics appearing in the literature.