Optimizing job shop scheduling with speed‐adjustable machines and peak power constraints: A mathematical model and heuristic solutions

Abstract

This paper addresses a job shop scheduling problem with peak power constraints, in which jobs can be processed once or multiple times on either all or a subset of the machines. The latter characteristic provides additional flexibility, nowadays present in many manufacturing systems. The problem is complicated by the need to determine both the operation sequence and starting time as well as the speed at which machines process each operation. Due to the adherence to renewable energy production and its intermittent nature, manufacturing companies need to adopt power‐flexible production schedules. The proposed power control strategies, that is, adjusting processing speed and timing to reduce peak power requirements may impact production time (makespan) and energy consumption. Therefore, we propose a bi‐objective approach that minimizes both objectives. A linear programming model is developed to provide a formal statement of the problem, which is solved to optimality for small‐sized instances. We also proposed a multi‐objective biased random key genetic algorithm framework that evolves several populations in parallel. Computational experiments provide decision and policymakers with insights into the implications of imposing or negotiating power consumption limits. Finally, the several trade‐off solutions obtained show that as the power limit is lowered, the makespan increases at an increasing rate and a similar trend is observed in energy consumption but only for very small makespan values. Furthermore, peak power demand reductions of about 25% have a limited impact on the minimum makespan value (4–6% increase), while at the same time allowing for a small reduction in energy consumption.