Two-agent scheduling on a single batch processing machine with non-identical job sizes

A new scheduling model in which both two-agent and a batch processing machine with non-identical job sizes exist is considered in this paper. Two agents compete to process their respective job sets on a common single batch processing machine. The objectives of the two agents are both to minimize the makespan. It is proved in the literature[7] that the complexity of minimizing makespan of one agent on a single batch processing machine with non-identical job sizes is NP-hard in the strong sense. We developed an improved ant colony optimal algorithm to search for the Pareto optimal solutions. The experimental results showed that the proposed algorithm could get better non-dominated solutions compared with the non-dominated sorting genetic algorithm (NSGA-II) which was widely used in solving the multi-objective optimization problem.