A time-bucket MILP formulation for optimal lot-sizing and scheduling of real-world chemical batch plants
Roderich Wallrath, Florian Seeanner, Matthias Lampe, Meik B. Franke
Abstract
We propose a new time-bucket MILP model for lot-sizing and scheduling problems arising in chemical batch plants. The main idea behind time-bucket models is to partition time into fixed-length macroperiods and flexible length microperiods, that lie within the macroperiods. We show that the time-bucket model benefits from advantages of both continuous and discrete time representations. It allows to include important real-world constraints, can be solved with moderate computational effort, and thus promotes MILP for large-scale, industrial problems. We investigate the scalability of the model and apply it to a formulation and filling process from an industrial agrochemical production with 7 formulation lines, intermediate buffer tanks, and 7 filling lines. We optimize a one month period with 50 intermediates, and 83 finished products. A comparison of the MILP solution to a discrete event simulation solution shows that 17% of production capacity can be freed up and significant improvement in on-time delivery.