Makespan Minimization on Parallel Batch Processing Machines with Release Times and Job Sizes

Abstract

This paper investigates the scheduling problem of minimizing makespan on parallel batch processing machines encountered in different manufacturing environments, such as the burn-in operation in the manufacture of semiconductors and the aging test operation in the manufacture of thin film transistor-liquid crystal displays (TFT-LCDs). Each job is characterized by a processing time, a release time and a job size. Each machine can process multiple jobs simultaneously in a batch, as long as the total size of all jobs in the batch does not exceed machine capacity. The processing time of a batch is represented by the longest time among the jobs in the batch. An approximation algorithm with worst-case ratio 2+\epsilon is presented, where \epsilon > 0 can be made arbitrarily small.