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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.

Keywords

Batch processing machines, flow shop, waiting time constraints, makespan, maximum tardiness.

(ProQuest: ... denotes formulae omitted.)

1. Introduction

This research was based on an application observed at an electronics manufacturer. Printed Circuit Boards (PCBs) used in different applications (e.g. notebooks, handheld devices, servers, etc.) are manufactured at this facility. After the PCBs are assembled, they are subjected to a couple of accelerated tests to identify any failures. The testing machines can test several PCBs simultaneously. Hence, these machines are referred to as Batch Processing Machines (BPMs). The job of a scheduler is to group the PCBs into batches and schedule them on the BPMs. The two BPMs are arranged in a flow shop environment and each PCB must be tested on these machines sequentially. The minimum testing times of the PCBs are predefined by the customer. When the PCBs are batched, the testing (or processing) time of the batch is determined by the longest testing time of the PCB in that batch. The due date of the batch is determined the earliest due date of all the jobs in that batch. Testing each PCB sequentially is time consuming and less efficient. Although a customer may not pay for the additional time required to test a PCB, from an operational...

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