Scheduling Batch Processing Machines in a Flow Shop with Two Objectives and Limited Waiting Time Constraints

Abstract

This paper presents mathematical formulations to an application observed at an electronics manufacturer. After assembly, the electronic products are subjected to different accelerated tests using Batch Processing Machines (BPMs) arranged in a flow shop. A BPM can process several jobs simultaneously. When forming batches, the total size of all the jobs contained in a batch cannot exceed the machine capacity. The configuration of the batch affects the batch processing time and its due date. Due to the nature of the test conducted, the jobs cannot wait for more than a certain amount of time between two machines. The objective is to minimize the makespan and the maximum tardiness. The processing times, due dates, and sizes of the jobs are given. The capacity of the BPMs is known. This paper presents a weighted sum and a goal programming formulations of the problem under study. Heuristics were also developed. An experimental study compares the different formulations, and the heuristics based on solution quality and run time.