Unrelated Parallel Machines Scheduling with Sequence-Dependent Setup Times to Minimize Makespan and Tariff Charged Energy Consumption

Abstract

An appropriate trade-off between total electricity costs and makespan can lead to good production planning and reduce unnecessary energy consumption. Time-of-use (TOU) electricity pricing policy has been executed in many countries which enabled industrial consumers with high energy consumption to reduce their energy costs. In this study, an unrelated parallel machines scheduling problem is considered for minimizing makespan and also energy consumption costs. Due to the importance of sequence-dependent setup times in production environments, they are considered according to the restricted duration of time periods under TOU policy. These considerations are added to the current literature. A mixed-integer bi-objective mathematical model is presented and the e-constraint method is applied to solve small and also medium-sized instances. Because the problem is shown to be NP-hard, several large-sized instances are approximately solved using Multiple Objective Particle Swarm Optimization algorithm, and Multiple Objective Simulated Annealing algorithm. Computational experiments are conducted on randomly generated data. The results show the efficiency and appropriate performance of the proposed methods.