A novel approach to lot-sizing and scheduling of multistage batch

MARCHETTI, PABLO A.; MÉNDEZ, CARLOS A.; CERDÁ, JAIME

Proceedings of XVIII Congreso Brasileño de Ingeniería Química

Asociación Ingenieros Químicos - Brasil

Año: 2010; p. 1029 - 1038

This work presents a pair of MILP continuous-time formulations to address the combined lot-sizing and scheduling of multi-product batch plants with multiple processing stages. The proposed mathematical models can handle multiple orders per product with different due dates as well as variable processing times. A predefined set of batches for each order with enough elements to guarantee optimality is initially proposed. Batch integrity is preserved throughout the entire processing sequence, but a lot of final product can be split to satisfy two or more orders. Both MILP formulations use a precedence-based continuous-time representation, but deal with batch allocation and sequencing decisions in a different manner. The first model rigorously arranges individual batches assigned to the same unit, while the second sequences clusters of batches featuring the same product, due-date, and processing route. In the latter formulation, final contents of clusters are model decisions. Effective symmetry breaking constraints based on allocation variables to avoid redundant solutions were also developed. The proposed formulations were applied to several examples, yielding very good results at quite competitive CPU times.