Batching to minimize weighted mean flow time on a single machine with batch size restrictions

This paper considers a single machine job batching problem with multiple job types involved where each given type of job is allowed to split into several batches whose individual sizes are varied in integral number and restricted between lower and upper bounds. Major and minor setup times are also involved in batch sequencing. The objective is to find the optimal job batching and sequencing for minimizing weighted mean flow time which is measured in the “batch-flow” concept. In the analysis, a feasibility condition is derived to take care of the batch size restrictions, and some solution properties are characterized. These are used to exploit a dynamic programming algorithm, and also to suggest an effective heuristic algorithm.