Effective heuristics for makespan minimization in parallel batch machines with non-identical capacities and job release times

Abstract

We consider the problem of scheduling a set of \begin{document} $n$ \end{document} jobs with arbitrary job sizes, processing times and release times on a set of \begin{document} $m$ \end{document} parallel batch machines with non-identical capacities; the objective is to minimize the makespan. We first present an algorithm to compute a lower bound for the optimal makespan. Based on different rules of batching the jobs and assigning the batches to the machines, several heuristics are proposed to solve the problem. The performance of the proposed heuristics is evaluated by computational experiments. The proposed heuristics are compared against the lower bound and against each other. Our results show that the one of the proposed algorithms outperforms all the other heuristics.