Batch scheduling on a two-machine jobshop with machine-dependent setup times

Abstract

The problem of minimum makespan on an m machine jobshop with unit execution time (UET) jobs (m ≥ 3) is known to be strongly NP-hard even with no setup times. We focus in this article on the two-machine case. We assume UET jobs and consider batching with batch availability and machine-dependent setup times. We introduce an efficient \documentclass{article}\usepackage{mathrsfs}\usepackage{amsmath}\pagestyle{empty}\begin{document} \begin{align*}(O(\sqrt{n}))\end{align*} \end{document} algorithm, where n is the number of jobs. We then introduce a heuristic for the multimachine case and demonstrate its efficiency for two interesting instances. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011