A three-stage decomposition approach for energy-aware scheduling with processing-time-dependent product quality

Due to increasing concerns about energy and environmental demands, decision-makers in industrial companies have developed awareness about energy use and energy efficiency when engaging in short-term production scheduling and planning. This paper studied a flow-shop scheduling problem consisting of a series of processing stages and one final quality check stage with the aim of minimising energy consumption. In particular, the product quality in the problem depends on its processing time at each stage, and the energy consumption is related to the processing speed, equipment state and product quality. A novel three-stage decomposition approach is presented to solve the proposed energy-aware scheduling (EAS) problem. The decomposition approach can drastically reduce the search space and provide reliable solutions for the EAS problem. The numerical experiments show that the computational results can achieve an optimality gap of less than 4% when compared to the global optimal solutions. The parameter analysis demonstrates the managerial implications of the proposed problem. For example, increasing the number of alternative processing speeds or relaxing the delivery date will increase energy efficiency. The energy-saving potential is illustrated by comparing the scheduling results using the proposed approach and human experience.