A new time-bucket MILP formulation for optimal lot-sizing and scheduling of an industrial make-and-fill process

We propose a new time-bucket MILP model for lot-sizing and scheduling problems arising in multistage production processes. The time-bucket model benefits from advantages of both continuous and discrete time representations while overcoming their shortcomings. In particular, we show how the time-bucket model allows to easily include a variety of typical, important real-world constraints, can be solved with moderate computer effort, and thus promotes MILP for large-scale, industrial problems. To illustrate that, we apply the time-bucket approach to the flow shop problem of a batch formulation and filling process from an industrial pesticide production. We reconcile the MILP solution with a validated discrete event simulation (DES) model of the process to obtain optimal and real-world feasible results. A comparison of the MILP-DES solution to a manually optimized solution for a one-month production data set shows that more than 17% of production capacity can be freed up and significant improvement in on-time delivery.