Effective Continuous-Time Formulation for Short-Term Scheduling. 1. Multipurpose Batch Processes

TLDR

Production scheduling is a critical issue in industrial plant operations, particularly for multipurpose batch processes. This study introduces a new mathematical formulation for short‑term scheduling of batch plants. The formulation uses a continuous‑time representation to produce a mixed‑integer linear program, featuring decoupled task and unit events, time‑sequencing constraints, and overall linearity. Compared with prior continuous‑time models, the new approach yields smaller, simpler MILPs with fewer variables and constraints, tighter integrality gaps, and markedly reduced CPU time, as demonstrated by illustrative examples.

Abstract

During the last decade, the problem of production scheduling has been realized to be one of the most important problems in industrial plant operations especially when multipurpose/multiproduct batch processes are involved. This paper presents a novel mathematical formulation for the short-term scheduling of batch plants. The proposed formulation is based on a continuous time representation and results in a mixed integer linear programming (MILP) problem. The novel elements of the proposed formulation are (i) the decoupling of the task events from the unit events, (ii) the time sequencing constraints, and (iii) its linearity. In contrast to the previously presented continuous-time scheduling formulations, the proposed approach leads to smaller and simpler mathematical models which exhibit fewer binary and continuous variables, have smaller integrality gaps, require fewer constraints, need fewer linear programming relaxations, and can be solved in significantly less CPU time. Several examples are presented that illustrate the effectiveness of the proposed formulation, and comparisons with other approaches are provided.