Batching to Minimize Flow Times on One Machine

Machine sequencing formulations typically assume that the characteristics of the job set to be processed are given. However, in many applications, jobs can be batched in different ways. Two types of minimum flow-time sequencing problems with lot sizing are formulated. The "item-flow" formulation is solved giving an index rule for ordering items. The "batch-flow" formulation is solved for the single product case showing that processing is done in unequal batches ordered in decreasing size. Heuristics and bounds are provided for the multiproduct case.