Iterative job splitting algorithms for parallel machine scheduling with job splitting and setup resource constraints

Abstract

This paper examines a parallel machine scheduling problem with job splitting and setup resource constraints for makespan minimization. Jobs can be split into multiple sections, and such sections can be processed simultaneously on different machines. It is necessary to change setups between the processes of different jobs on a machine, and the number of setups that can be performed simultaneously is restricted due to limited setup operators. To solve this problem, we propose a mathematical programming model and develop iterative job splitting algorithms that improve a feasible initial solution step by step, taking into account job splitting, setup times, and setup resources. We derive a worst-case performance ratio of the algorithms and evaluate the performance of the proposed heuristics on a large number of randomly generated instances. We finally provide a case study of piston manufacturing in Korea.