New General Continuous-Time State−Task Network Formulation for Short-Term Scheduling of Multipurpose Batch Plants

TLDR

The authors present a new continuous‑time MILP model for short‑term scheduling of multipurpose batch plants. The model uses a state‑task network approach with a continuous‑time representation, binary assignment variables defined only for tasks, eliminates start‑time variables in favor of finish‑time matching constraints, incorporates a new class of valid inequalities to tighten the LP relaxation, and handles resource constraints, variable batch sizes and times, multiple storage policies, batch mixing/splitting, and sequence‑dependent changeovers, as demonstrated on four example problems. Compared with other general continuous‑time STN formulations, the model is faster, and relative to event‑driven formulations it is more general—accounting for additional resources beyond equipment—while achieving comparable computational times.

Abstract

A new continuous-time MILP model for the short-term scheduling of multipurpose batch plants is presented. The proposed model relies on the state−task network (STN) approach and addresses the general problem of batch scheduling, accounting for resource (utility) constraints, variable batch sizes and processing times, various storage policies (UIS, FIS, NIS, ZW), batch mixing/splitting, and sequence-dependent changeover times. The key features of the proposed model are the following: (a) a continuous-time representation is used, common for all units; (b) assignment constraints are expressed using binary variables that are defined only for tasks, not for units; (c) start times of tasks are eliminated, so that time-matching constraints are used only for the finish times of tasks; and (d) a new class of valid inequalities that improves the LP relaxation is added to the MILP formulation. Compared to other general continuous time STN formulations, the proposed model is faster. Compared to event-driven formulations, it is more general, as it accounts for resources other than equipment and gives solutions in comparable computational times. The application of the model is illustrated through four example problems.