Minimizing the makespan on two identical parallel machines with mold constraints

Abstract

This paper deals with the scheduling problem of minimizing the makespan on two identical parallel machines with molds as resource constraints. Two or more jobs with the same mold requirement cannot be processed on the same or different machines at the same time. While quite common in practice, like in wafer fabrication, such problems have not received much attention in the literature. Since this problem is NP-hard, a mathematical model for solving it is derived and tested. Moreover, three simple, fast, and effective heuristics are proposed with a worst-case performance ratio of 3/2. Computational results show that the proposed heuristics can efficiently obtain good solutions for problem instances containing a large number of jobs. In addition, the use of these proposed algorithms as initial solution can improve the performance of metaheuristics. Furthermore, the solutions obtained by these proposed heuristics can be improved by metaheuristics.