An energy-efficient permutation flowshop scheduling problem

Abstract The permutation flowshop scheduling problem (PFSP) has been extensively explored in scheduling literature because it has many real-world industrial implementations. In some studies, multiple objectives related to production efficiency have been considered simultaneously. However, studies that consider energy consumption and environmental impacts are very rare in a multi-objective setting. In this work, we studied two contradictory objectives, namely, total flowtime and total energy consumption (TEC) in a green permutation flowshop environment, in which the machines can be operated at varying speed levels corresponding to different energy consumption values. A bi-objective mixed-integer programming model formulation was developed for the problem using a speed-scaling framework. To address the conflicting objectives of minimizing TEC and total flowtime, the augmented epsilon-constraint approach was employed to obtain Pareto-optimal solutions. We obtained near approximations for the Pareto-optimal frontiers of small-scale problems using a very small epsilon level. Furthermore, the mathematical model was run with a time limit to find sets of non-dominated solutions for large instances. As the problem was NP-hard, two effective multi-objective iterated greedy algorithms and a multi-objective variable block insertion heuristic were also proposed for the problem as well as a novel construction heuristic for initial solution generation. The performance of the developed heuristic algorithms was assessed on well-known benchmark problems in terms of various quality measures. Initially, the performance of the algorithms was evaluated on small-scale instances using Pareto-optimal solutions. Then, it was shown that the developed algorithms are tremendously effective for solving large instances in comparison to time-limited model.