Review, extensions and computational comparison of MILP formulations for scheduling of batch processes

In this paper we investigate mixed-integer linear programs for minimizing the makespan of batch processes. Thereby it turns out that some additional valid constraints which were originally given for event driven model (EDM) also accelerate the running time for uniform discretization of time model (UDM) considerably. With help of an example for EDM we show that we can store some products in the batches if we prolong the processing times. For this reason EDM differs from the standard model. To achieve the same results as for UDM we introduce the ending times of the batches as additional variables. Moreover we extend the model by considering flexible proportions of output as well. However, computational tests indicate a rise of CPU time for the modified problem although the number of binary variables is smaller compared to UDM. Furthermore we point out that an upper bound on the total number of batchstarts is only possible for some production processes. Extensive computational tests on five benchmark problems proposed in the literature are reported. Thereby new optimal solutions could be found.