Scheduling uniform parallel dedicated machines with job splitting, sequence-dependent setup times, and multiple servers

Abstract

We address a uniform parallel machine scheduling problem with machine eligibility, job splitting, sequence-dependent setup times, and limited setup servers, which has been defined from a real application of piston manufacturing in Korea. The objective is to minimize the makespan. We first propose a mathematical programming model and derive four lower bounds. We then develop an efficient heuristic algorithm that assigns jobs to machines by considering processing times, setup times, and machine eligibility constraints, and then balances machine workloads by splitting jobs. We analyze a worst-case bound of the algorithm and perform extensive experiments with various scenarios. The gap from a lower bound is not significant for practical cases.