A Variable Block Insertion Heuristic for the Energy-Efficient Permutation Flowshop Scheduling with Makespan Criterion

Abstract

Permutation flow shop scheduling problem is a well-known problem in the scheduling literature. Even though various multi-objective permutation flowshop scheduling problems have been studied in the literature energy consumption consideration in scheduling is still very seldom. In this paper we consider a bi-objective permutation flowshop scheduling problem with the objectives of minimizing the total energy consumption and the makespan. We present a bi-objective mixed integer programming model for the problem applying a speed-scaling approach. Then we employ the augmented ε -constraint method to generate the Pareto-optimal solution sets for small-sized instances. For larger instances we use the augmented ε -constraint method with a time limit on CPLEX solver to approximate the Pareto frontiers. We also propose a heuristic approach which employs a very recent variable block insertion heuristic algorithm. In order to evaluate performance of the proposed algorithm we have carried out detailed computational experiments using well-known benchmarks from the literature. First we present the performance of the proposed algorithm on small-sized problems, then we show that the proposed algorithm is very effective to solve larger problems as compared with the time-limited CPLEX. © 2020 Elsevier B.V. All rights reserved.