Parallel machine scheduling problem with preemptive jobs and transportation delay

In this research the parallel machine scheduling problem with preemption by considering a constant transportation delay for migrated jobs and minimization of makespan as the criterion i.e., Pm|pmtn(delay)|Cmax is investigated. It is assumed that when a preempted job resumes on another machine, it is required a delay between the processing time of the job on these two machines. This delay is called transportation delay. We criticize an existing mathematical model for the research problem in the literature [Boudhar M, Haned A. Preemptive scheduling in the presence of transportation times. Computers & Operations Research 2009; 36(8):2387-93]. Then, we prove that there exists an optimal schedule with at most (m−1) preemptions with transportation among machines for the problem. We also propose a linear programming formulation and an exact algorithm for the research problem in case of equal transportation delay. The experiments show that the proposed exact algorithm performs better than the proposed mathematical model.