Unrelated parallel machine energy-efficient scheduling considering sequence-dependent setup times and time-of-use electricity tariffs

Given that about half of the produced energy in the world is consumed in industries, there has been an increasing concern about optimizing energy consumption in manufacturing sectors. As one of the most effective ways, proper production scheduling to reduce energy consumption is of crucial importance among researchers and manufacturers. This paper addresses an unrelated parallel machine energy-efficient scheduling problem with sequence-dependent setup times by considering different energy consumption tariffs. The setup times are studied in two modes: disjointed from/jointed to processing time. For each one of these problems, two mixed-integer linear programming models have been formulated. The presented models for the problem with setup time disjointed from processing time can solve up to 16 machines and 45 jobs. In contrast, this capability is changed to 20 machines and 40 jobs for processing time jointed to the setup time problem. Furthermore, a fix and relax heuristic algorithm is presented for large-size instances, which can solve instances of up to 20 machines and 100 jobs for each of the two considered problems.