Unrelated parallel machine scheduling with processing constraints and sequence dependent setup times

In real-world problems, machines are often not available for some periods of time due to events such as breakdowns, maintenance activities, and already planned operations. In this research, an unrelated parallel machine scheduling problem is considered where each machine is not available for some times during the planning horizon and also may not be capable of processing some jobs; these constraints are referred to as the processing constraints. On the other hand, the setup times are assumed to be job sequence-dependent as well as machine-dependent. The objective function of the problem considered is to minimize the total earliness and tardiness. First, the problem is formulated as a mixed integer linear programming model and then, in view of its NP-hardness, an imperialist competitive algorithm utilizing a new decoding procedure is proposed to solve large-sized problem instances. To assess the performance of the proposed algorithm, a number of instances are generated and solved.