A multi-objective differential evolution algorithm for parallel batch processing machine scheduling considering electricity consumption cost

The manufacturing industry consumes massive amounts of energy and produces great numbers of greenhouse gases every year. Recently, an increasing attention has been paid to the energy efficiency of the manufacturing industry. This paper considers a parallel batch processing machine (BPM) scheduling problem in the presence of dynamic job arrivals and a time-of-use pricing scheme. The objective is to simultaneously minimize makespan, a measure of production efficiency and minimize total electricity cost (TEC), an indicator for environmental sustainability. A BPM is capable of processing multiple jobs at a time, which has wide applications in many manufacturing industries such as electronics manufacturing facilities and steel-making plants. We formulate this problem as a mixed integer programming model. Considering the problem is strongly NP-hard, a multi-objective differential evolution algorithm is proposed for effectively solving the problem at large scale. The performance of the proposed algorithm is evaluated by comparing it to the well-known NSGA-II algorithm and another multi-objective optimization algorithm AMGA. Experimental results show that the proposed algorithm performs better than NSGA-II and AMGA in terms of solution quality and distribution.