Scheduling of incompatible families of jobs on a single batch processing machine to minimize the weighted number of tardy jobs and consumption of electrical energy

This paper considers the optimization problem of scheduling jobs with identical sizes on a single batch processing machine. The jobs are divided into some incompatible families where each family contains the jobs with the same processing times and the jobs from different families could not proceed in the same batch. Our optimization problem has two objectives. The first objective is minimizing the weighted number of tardy jobs regarding the due dates of jobs given by customers. The second one aims to minimize operations costs by finding the schedules with the minimum electrical cost consummation under the Time-of-Use tariff policy. A two-objective mixed integer programming mathematical programming is proposed to find optimal solutions for small-size instances of the problem. To solve the medium and large-scale size of the problem, two meta-heuristic algorithms NSGA-II and MOPSO are proposed. The Computational experiments results show that two solution algorithms are capable to find near-optimal solutions at a reasonable computational time. The MOPSO algorithm generate more diverse solutions in less computational time comparing with NSGA II algorithm. But the quality of the solutions obtained by NSGA II algorithm are superior to the ones obtained by MOPSO.