Heuristic methods for the identical parallel machine flowtime problem with set-up times

We consider the scheduling of N jobs divided into G families for processing on M identical parallel machines. No set-up is necessary between jobs belonging to the same family. A set-up must be scheduled when switching from the processing of family i jobs to those of another family j, i≠j, the duration of this set-up being the sequence-independent set-up time sj for family j. We propose heuristics for this problem and computationally evaluate the performance of the heuristics relative to lower bounds and solutions obtained using an exact algorithm.Scope and purposeWe study a machine-scheduling problem within which we have identical parallel machines, jobs arranged into families, and sequence-independent set-up times between jobs of different families on these machines. Our purpose is to develop simple, effective and efficient heuristics for this problem, and we seek to maximise the use of ideas and algorithms that have appeared previously in the literature for related problems. In our computational experiments, we seek to study the behaviour of these heuristics and uncover relevant properties of the scheduling problem. Within this experiment, we compare the observed performance of the heuristics relative to lower bounds and optimal solutions.