A genetic algorithm to minimize maximum lateness on a batch processing machine

Abstract

We consider the problem of minimizing maximum lateness on a batch processing machine in the presence of dynamic job arrivals. The batch processing machine can process up to B jobs simultaneously, and the processing time of a batch is given by that of the job with the longest processing time in the batch. We adapt a dynamic programming algorithm from the literature to determine whether a due-date feasible batching exists for a given job sequence. We then combine this algorithm with a random keys encoding scheme to develop a genetic algorithm for this problem. Computational experiments indicate that this algorithm has excellent average performance with reasonable computational burden. Scope and purpose In this paper we address the problem of scheduling a single batch processing machine subject to dynamic job arrivals, which generalizes a number of classical single-machine models from scheduling theory (Pinedo. Scheduling theory, algorithms, and systems. Englewood Cliffs, NJ: Prentice-Hall, 1995.) Batch processing machines, where a number of jobs are processed simultaneously as a batch, are quite common in the metalworking and microelectronics industries. Although an extensive literature on several scheduling models for this type of machine has developed in the last decade, there has been relatively little work on models that consider jobs arriving at the machine dynamically over time. However, such dynamic models are an essential component of decomposition heuristics (Ovacik, Uzsoy. Decomposition methods for complex factory scheduling problems. Massachusetts: Kluwer Academic Publishers, 1997.) used to schedule the factories within which the batch processing machines form an individual workcenter. This paper builds on results developed in prior work (Lee et al. Operations Research 1992;40:764–75.) and (Uzsoy. International Journal of Production Research 1995;33:2605–708.) to develop an effective genetic algorithm (Goldberg. Genetic algorithms in search, optimization and machine learning. Reading, MA: Addison-Wesley, 1989.) for solving this provably intractable scheduling problem. Our procedure combines an optimization algorithm to evaluate job sequences with a random key representation that guarantees feasible solutions after crossover operations. Extensive computational experiments show that it consistently obtains high-quality solutions in modest CPU times.