An optimal solution algorithm for a batch-processing machine scheduling problem with a product-mix ratio constraint

Abstract

This paper focuses on the scheduling problem of minimizing makespan for a given set of jobs on a batch-processing machine subject to a product-mix ratio constraint. A given product-mix ratio of job types should be kept in each batch and the processing time for each batch is determined by the longest processing time of jobs included in the batch. We identify several optimal solution properties of the problem and present a polynomial-time algorithm that solves the problem to the optimality. The algorithm developed in this research can be used at a plating workstation in a real printed circuit board (PCB) manufacturing system, and may help to improve the overall performance of the system since the plating workstation is a bottleneck of the system.