Identical Parallel Machines Scheduling Considering Common Operations to Minimize Total Energy Consumption and Total Tardiness

Managing energy consumption at the same time as scheduling production operations has particular importance because optimal scheduling can also help reduce energy consumption. This paper considers an identical parallel machines scheduling problem considering common operations to minimize simultaneously total energy consumption and total tardiness. For this purpose, the bi-objectives Mixed Integer Linear Programming model is presented and for small scale instances, an augmented ε – constraint method is applied to obtain an optimal Pareto front. To tackle strongly NP-hard problem, NSGA-II Algorithm and NRGA Algorithm are developed to solve medium and large-scale instances. The efficiency and performance of the proposed algorithms are evaluated by performing computational experiments on the sample instances. The results show that the NSGA-II Algorithm can generate approximate Pareto fronts with better convergency, so that the performance of this algorithm in comparison with NRGA algorithm in terms of relative percentage deviation (RPD) in the indicators (Q) and (MID) 30% and 22% is better, respectively. On the other hand, the NRGA Algorithm is faster and can obtain more non-dominated solutions with better diversity, so that the performance of this algorithm compared to the NSGA-II algorithm in terms of relative percentage deviation (RPD) in the indicators (D) and (NPS) 12% and 8% is better, respectively