Energy-efficient distributed heterogeneous re-entrant hybrid flow shop scheduling problem with sequence dependent setup times considering factory eligibility constraints

In the face of energy crisis, manufacturers pay more and more attention to energy-saving scheduling. In the paper, we consider the distributed heterogeneous re-entrant hybrid flow shop scheduling problem (DHRHFSP) with sequence dependent setup times (DHRHFSP-SDST) considering factory eligibility constraints under time of use (TOU) price, which means that each job can only be assigned to its available set of factories and all factories have different number of machines and processing capacity, and so on. To deal with DHRHFSP-SDST, a multi-objective Artificial Bee Colony Algorithm (MOABC) is proposed to optimize both the makespan and total energy consumption. For the MOABC, firstly, a hybrid initialization method is presented to initialize the population; then, due to the electricity price shows significant differences vary from periods under TOU price, the energy saving operator based on right-shift strategy is proposed to avoid processing jobs with the high electricity price without affecting the productivity; thirdly, based on the full consideration of distributed heterogeneous and factory eligibility, crossover and mutation operators, three neighborhood search operators and new food sources generation strategy are designed; lastly, extensive experiments demonstrate the effectiveness of the proposed algorithm on solving the DHRHFSP-SDST.