Simultaneous lot sizing and scheduling of multistage batch processes handling multiple orders per product - Marchetti, Pablo Andres (2012)
A pair of precedence-based continuous-time formulations addressing the combined lot sizing and scheduling of order-driven multistage batch facilities is presented. The proposed mixed-integer linear programming (MILP) models can handle multiple orders per product with different delivery dates, variable processing times, and sequence-dependent changeovers. As each order may be filled by one or more batches, enough batches for each order ensuring optimality are initially defined. The two monolithic formulations are intended for sequential batch processes where batch integrity is preserved throughout the entire production system. However, lots of final products can be split to satisfy two or more orders. One of the approaches is based on a detailed MILP formulation allocating individual batches to units and ordering them in every unit. In contrast, the second methodology is specially designed for large scheduling problems. It first gathers batches for the same order into clusters, and then assigns clusters to units and sequences groups of batches in every unit. The larger the number of groups, the more rigorous is the cluster-based formulation. Alternative sequencing constraints based on reliable assumptions were also tested. Several examples involving up to 92 batches have been successfully solved using one or both formulations.