Abstract

This paper considers the scheduling of n jobs on m parallel machines to minimize the weighted number of early and tardy jobs. The single machine case of this problem has been shown to be NP- complete in the strong sense. This problem on m parallel machineis also NP complete in the strong sense and finding an optimal solution appears unlikely. The problem is formulated as an integer linear programming model. In this paper, we propose some meta-heuristics for solving this problem. Extensive computational experiments were performed which gave promising results.

Key words: Scheduling, parallel machine, heuristics, metaheuristics, particle swarm optimization, genetic algorithm, simulated annealing, hybrid.