Scheduling two interfering job sets on parallel machines under peak power constraint

This study considers the problem of scheduling two interfering job sets A and B that comprise \({n_A}\) and \({n_B}\) jobs, respectively, on m parallel machines. For the jobs in the set A, we are interested in minimizing the total weighted tardiness (TWT) and for the jobs in the set B, we are interested in minimizing the total completion time (TCT). Although these job sets are evaluated using different criteria, they must be processed using the same resources (machines, workers, and tools), causing interference. In this study, not only is interference considered, but also the operating speed of machine is treated as an independent variable, which affects the peak power. Peak power is considered here since electricity costs for production facilities rise sharply if instantaneous power demand exceeds contract capacity, so production schedules that reduce peak power reduce the cost of energy. Therefore, this paper uses a constraint on peak power consumption while TWT and TCT are simultaneously minimized. This study proposes the domination number-based genetic algorithm (DNGA) to generate a set of non-dominated solutions to the problem, so the decision-maker can evaluate the trade-offs and select the schedule to be implemented. The DNGA is compared with NSGA-II, which has been demonstrated to be the most efficient algorithm for multi-objective optimization, in terms of quality, diversity and computation time. Experimental results reveal that DNGA can find better solutions more quickly than can NSGA-II.