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Constraint programming models for serial batch scheduling with minimum batch size
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DOI：10.1016/j.orp.2025.100352.png)
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Abstract
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• We fully embraced the recommendations of Reviewer 3 about ensuring the minimum batch sizes using a constraint that sums the presences of the variables inside a batch. This allowed us to reduce the complexity of the model by removing extra variables and constraints. The resulting Interval Assignment (IA) model is named after its central modeling approach: defining interval variables for the sequencing of jobs on machines and handling the job assignment to batches using additional interval variables. • Although the IA model proved to be useful for the IPF s-batch variation, the suggested constraint by Reviewer 3 in it does not provide a global view of the problem structure to the CP engine. For this reason, we proposed a Global (G) model that exclusively uses the removed global constraints that do provide this global perspective. Nonetheless, it uses cumulative functions to keep track of the size of the batches at every point in time, even though it is only necessary to keep it at the assignment level. For this reason, we included an additional Hybrid (H) model that combines the extra global constraints that provide the global perspective but replaces the cumulative functions with the sum-of-presences constraints, which boost efficiency. This approach proved to be the best one for the BC variation. • We significantly improved the explanation of these models by including detailed illustrative examples and also reran all the experiments comparing them against the existing mixed-integer programming models in the literature.
Keywords:
Scheduling
Serial batch
Setup times
Minimum batch size
Constraint programming
Mixed-integer programming
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