MILP models for energy-aware flexible job shop scheduling problem

With energy shortage and environmental pollution becoming increasingly severe problems, energy-efficient scheduling is attracting much more attention than before. This paper addresses the flexible job shop scheduling problem (FJSP) with the objective of minimizing total energy consumption. Firstly, the total energy consumption of the workshop is discussed and modelled. Then, based on two different modeling ideas namely idle time variable and idle energy variable, six new mixed integer linear programming (MILP) models with turning Off/On strategy are proposed. The original objective function of the model based on idle time variable is nonlinear and linearization is needed. For the linearization, additional decision variables and constraints are added. The objective function of the model based on idle energy variable is originally linear and concise. Lastly, those six proposed models and the existing one are detailedly compared and evaluated under both the size and computational complexities. The correctness and effectiveness of all MILP models are verified by using CPLEX SLOVER to carry out numerical experiments. The results show that the MILP models based on different modeling ideas vary remarkably in both size and computational complexities, and all the six models proposed in this paper outperform the existing model significantly. The proposed models will help the enterprises rationalize production so as to reduce energy consumption and costs.