Arc-flow approach for single batch-processing machine scheduling

We address the problem of scheduling jobs with non-identical sizes and distinct processing times on a single batch-processing machine, aiming at minimizing makespan. The extensive literature this NP-hard mostly focuses heuristics. Using an arc-flow based optimization approach, we construct novel formulation that represents it as determining flows in graphs. size increases machine capacity number among jobs, but does not increase which makes very effective to solve large instances optimality, especially when multiple have equal time. compare our model other models from literature, showing its clear superiority benchmark proving optimality random up 100 million jobs.