Parallel machine scheduling with preference of machines

This paper considers a scheduling problem in the manufacturing of anodic electro-etching aluminium foil. To reduce cost and increase efficiency, the manufacturer of aluminium foil usually designs the equipment for electro-etching of aluminium foil into specialised equipment that is dedicated to produce high voltage or medium voltage aluminium foil based on the range the aluminium foil can bear. Nevertheless, high voltage equipment can be used to produce medium voltage aluminium foil with longer processing time, and vice versa. The problem is to schedule jobs on the high and medium voltage equipment, each having several pieces in parallel, with setup times to minimise to the total completion time. In this paper, we propose a three-stage heuristic for this problem and computationally evaluate the performance of the heuristic in comparison to a heuristic for unrelated parallel machines and a branch-and-bound algorithm.