Efficient heuristics for the weighted tardiness distributed permutation flowshop scheduling problem

Abstract

In this paper, we consider the distributed permutation flowshop scheduling problem with a total weighted tardiness objective. Our focus is on dispatching rules, which are widely used in practical settings and can quickly provide solutions for even quite large instances. We consider a total of 23 dispatching rules. Twelve are adaptations to the distributed flowshop setting of existing heuristics, two are simple distributed flowshop rules, four are modified versions of two procedures developed for the distributed flowshop with a blocking constraint and five are newly developed procedures. These dispatching rules are combined with three factory assignment rules, as well as with two different approaches (one newly proposed) for dealing with the last few jobs. Therefore, a total of 138 procedures are considered and evaluated. Extensive preliminary tests were performed to determine appropriate values for the parameters required by some of the procedures. The heuristics were then evaluated on a dataset that is both quite large, and diverse in terms of due dates. Multiple performance measures, as well as statistical tests, were used to evaluate the procedures, the factory assignment rules and the two ways of dealing with the last few jobs. The computational results show that a new approach for dealing with the last few jobs outperforms its traditional counterpart. The top positions in terms of solution quality were consistently occupied by the newly developed rules. In particular, the WIT_WCT_3 procedure achieved, with a single exception, the best performance across all solution quality performance measures and factory assignment rules.