Unrelated parallel-machine scheduling problem with machines risk time and workload-dependent maintenance activities

Parallel machine scheduling problem is one of the practical scheduling problems that has been investigated by many researchers in the last two decades. In this paper, unrelated parallel machine scheduling problem is studied in which each machine is unavailable in a time interval due to maintenance activity. Start time and duration of each unavailable interval in a machine is related to risk time and jobs processed on the machine. On the other hand, processing time of a job depends on its start time. Also, sequence-dependent setup times and release dates are some other constraints which are considered. The goal is to minimize total completion time of jobs. A mixed integer programming (MIP) model is presented for this problem. Since the problem is NP-hard, an Imperialist Competitive Algorithm (ICA) with greedy based method is developed to solve large size instances. In order to evaluate the performance of the proposed algorithm, a number of instances are generated and solved. The computational results show the efficiency of the proposed algorithm.