A new heuristic for m-machine flowshop scheduling problem with bicriteria of makespan and maximum tardiness

Abstract

This paper addresses the m-machine flowshop problem with the objective of minimizing a weighted sum of makespan and maximum tardiness. Two types of the problem are addressed. The first type is to minimize the objective function subject to the constraint that the maximum tardiness should be less than a given value. The second type is to minimize the objective without the constraint. A new heuristic is proposed and compared to two existing heuristics. Computational experiments indicate that the proposed heuristic is much better than the existing ones. Moreover, a dominance relation and a lower bound are developed for a three-machine problem. The dominance relation is shown to be quite efficient. Scope and purpose The majority of research on scheduling problems addresses only a single criterion while the majority of real-life problems require the decision maker to consider more than a single criterion before arriving at a decision. The scheduling literature reveals that the research on multi-criteria is mainly focused on the single-machine problem as a result of the difficulty of the multiple machines problem. This paper addresses an m-machine flowshop scheduling problem with a multi-criteria objective function.