Solving single batch-processing machine problems using an iterated heuristic

Abstract

This article considers the problem of minimising total weighted tardiness on a batch-processing machine with compatible product families, job release dates and non-identical job sizes. A batch-processing machine can process several jobs as long as the total size of jobs in the batch does not exceed the machine's capacity. All jobs in the batch are started and completed at the same time. Batch processing time is equal to the longest job processing time among jobs in the batch. This article proposes a two-phase heuristic, in which a population-based reasoning approach is developed to determine the sequence of jobs based on their intensity values at positions in the first phase, and a dynamic programming algorithm to divide the ordered jobs into batches sequentially. An iterated heuristic is also proposed to improve solution quality further. Computational results show that high-quality solutions can be obtained by the proposed heuristic algorithms in a very short time.