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.

Abstract
This work extends the energy-efficient job shop scheduling problem with transport resources by considering speed adjustable resources of two types, namely: the machines where the jobs are processed on and the vehicles that transport the jobs around the shop-floor. Therefore, the problem being considered involves determining, simultaneously, the processing speed of each production operation, the sequence of the production operations for each machine, the allocation of the transport tasks to vehicles, the travelling speed of each task for the empty and for the loaded legs, and the sequence of the transport tasks for each vehicle. Among the possible solutions, we are interested in those providing trade-offs between makespan and total energy consumption (Pareto solutions). To that end, we develop and solve a bi-objective mixed-integer linear programming model. In addition, due to problem complexity we also propose a multi-objective biased random key genetic algorithm that simultaneously evolves several populations. The computational experiments performed have show it to be effective and efficient, even in the presence of larger problem instances. Finally, we provide extensive time and energy trade-off analysis (Pareto front) to infer the advantages of considering speed adjustable machines and speed adjustable vehicles and provide general insights for the managers dealing with such a complex problem.

Abstract

Abstract
This work addresses the flexible job shop scheduling problem with transportation (FJSPT), which can be seen as an extension of both the flexible job shop scheduling problem (FJSP) and the job shop scheduling problem with transportation (JSPT). Regarding the former case, the FJSPT additionally considers that the jobs need to be transported to the machines on which they are processed on, while in the latter, the specific machine processing each operation also needs to be decided. The FJSPT is NP-hard since it extends NP-hard problems. Good-quality solutions are efficiently found by an operation-based multistart biased random key genetic algorithm (BRKGA) coupled with greedy heuristics to select the machine processing each operation and the vehicles transporting the jobs to operations. The proposed approach outperforms state-of-the-art solution approaches since it finds very good quality solutions in a short time. Such solutions are optimal for most problem instances. In addition, the approach is robust, which is a very important characteristic in practical applications. Finally, due to its modular structure, the multistart BRKGA can be easily adapted to solve other similar scheduling problems, as shown in the computational experiments reported in this paper.

Abstract
Energy-efficient scheduling has become a new trend in industry and academia, mainly due to extreme weather conditions, stricter environmental regulations, and volatile energy prices. This work addresses the energy-efficient Job shop Scheduling Problem with speed adjustable machines. Thus, in addition to determining the sequence of the operations for each machine, one also needs to decide on the processing speed of each operation. We propose a multi-population biased random key genetic algorithm that finds effective solutions to the problem efficiently and outperforms the state-of-the-art solution approaches.