Bi-objective unrelated parallel machine joint scheduling of jobs and preventive maintenance with a dynamic speed-scaling technique

Abstract

Nowadays, industries contribute to a substantial consumption of energy. This consumption leads to significant greenhouse gas emissions, energy dependence and ever-increasing costs for manufacturers. Controlling consumption and improving energy efficiency in industry are therefore major challenges in terms of environmental issues. In this context, this article examines an energy-efficient bi-objective unrelated parallel machine joint scheduling of jobs and preventive maintenance activities problem to minimize both makespan and total energy consumption. The parallel machines are speed-scaling. To solve the problem, we propose a bi-objective mixed integer linear programming (MILP) model. Since the problem involves assigning jobs to machines and selecting an appropriate processing speed level for each job, we characterize each individual by two vectors: a job-machine assignment vector and a speed vector. To the best of our knowledge, no papers considering both production scheduling and Preventive Maintenance periods with minimizing the bi-objective makespan and the total of energy consumption. The gap between theory and practice prevents the satisfying performance of the schedules in industry. The purpose of this paper is to establish a joint model for integrating the production and PM scheduling to optimize the bi-objective of the total of energy consumption (TEC) and makespan (Cmax) simultaneously; and to make the theory applied in practice more efficaciously. The performance of the proposed mixed binary integer programming model is evaluated based on the exact method of Branch and Bound integrated on the CPLEX solver plus analyses using MATLAB software. A study of the results proved the performance of the model developed.