On the open-shop problem with preemption and minimizing the average completion time

We consider an open-shop problem: n jobs have to be processed on m machines where each machine can process at most one job at a time and each job can be processed on at most one machine at a time. The processing times for all operations are given. Preemptions are allowed, that means each operation can be stopped and continued later on. The order of machines for job J(i) is called machine order of job J(i), the order of jobs on machine M-j is called job order on machine M-j In the case of an open-shop problem all machine orders and job orders have to be determined in such a way, that the average completion time is minimized. New models of scheduling problems with preemption are presented which base on models for problems without preemption. Because the considered problem is NP-hard, lower bounds and heuristics are developed. Computational experiments demonstrate the quality of the algorithms. For small numbers of jobs and machines the obtained results are also compared with the optimal solutions determined by an exact algorithm. (C) 2003 Elsevier B.V. All rights reserved.