A TWO-PHASE HEURISTIC APPROACH TO SOLVING THE PROBLEM OF SIZING AND SEQUENCING BATCHES WITH FRACTIONATION

This work addresses the real-world case of a large white goods manufacturer, which inspired two models proposed separately for the lot sizing and scheduling of multiple items on parallel machines with independent speeds and limits on lot splitting. To the best of our knowledge, these two models have never been used jointly for decision-making. This is what we propose in this paper. However, the mere sequential application of the models may result in a violation of the limit on working hours: the lot-sizing model considers the capacity constraint but does not account for setup times; the scheduling model, in turn, considers setup times but not capacity constraints. In view of this, we present a two-phase heuristic approach for applying the two models in an iterative process. The approach is based on the progressive reduction of capacities, forcing the lot-sizing model to account for some slack in the total number of working hours. Using this approach, we obtained solutions for six instances from the literature, with an average processing time of 19.06 minutes. Regarding solution value, the results were, on average, only 0.46% above the values obtained by applying the original lot-sizing model. However, it should be noted that no strategy was able to solve all instances within the adopted time limits. Thus, it is worth considering the search for an integrated lot-sizing and scheduling solution, with potential gains in both solution quality and processing time. This is what we intend to undertake in future research.