Green Scheduling of Identical Parallel Machines with Release Date, Delivery Time and No-Idle Machine Constraints

Global warming and climate change are threatening life on earth. These changes are due to human activities resulting in the emission of greenhouse gases. This is caused by intensive industrial activities and excessive fuel energy consumption. Recently, the scheduling of production systems has been judged to be an effective way to reduce energy consumption. This is the field of green scheduling, which aims to allocate jobs to machines in order to minimize total costs, with a focus on the sustainable use of energy. Several studies have investigated parallel-machine shops, with a special focus on reducing and minimizing the total consumed energy. Few studies explicitly include the idle energy of parallel machines, which is the energy consumed when the machines are idle. In addition, very few studies have considered the elimination of idle machine times as an efficient way to reduce the total consumed energy. This is the no-idle machine constraint, which is the green aspect of the research. In this context, this paper addresses the green parallel-machine scheduling problem, including release dates, delivery times, and no-idle machines, with the objective of minimizing the maximum completion time. This problem is of practical interest since it is encountered in several industry processes, such as the steel and automobile industries. A mixed-integer linear programming (MILP) model is proposed for use in obtaining exact solutions for small-sized instances. Due to the NP-hardness of the studied problem, and encouraged by the successful adaptation of metaheuristics for green scheduling problems, three genetic algorithms (GAs) using three different crossover operators and a simulated annealing algorithm (SA) were developed for large-sized problems. A new family of lower bounds is proposed. This was intended for the evaluation of the performance of the proposed algorithms over the average percent of relative deviation (ARPD). In addition, the green aspect was evaluated over the percentage of saved energy, while eliminating the idle-machine times. An extensive experimental study was carried out on a benchmark of test problems with up to 200 jobs and eight machines. This experimental study showed that one GA variant dominated the other proposed procedures. Furthermore, the obtained numerical results provide strong evidence that the proposed GA variant outperformed the existing procedures from the literature. The experimental study also showed that the adoption of the no-idle machine time constraints made it possible to reduce the total consumed energy by 29.57%, while the makespan (cost) increased by only 0.12%.