Optimal Scheduling of the Multigrade Parallel Distillation Column System with a Continuous-Time Formulation

In the fine chemical industry, optimal scheduling of continuous processes involving multigrade and parallel units is an important problem. The existing scheduling formulations can be classified into continuous-time (CT) and discrete-time (DT) formulations. Most previous studies adopted DT approaches that are more convenient for establishing an optimization model. However, the DT formulation has two inherent shortcomings. One is that it often requires more integer variables than the CT formulation. The other is that the solution of a DT formulation is often only suboptimal, or even infeasible, for the original scheduling problem. This work proposes a CT formulation for optimal scheduling of multigrade parallel distillation processes. This formulation simultaneously addresses continuous demand satisfaction, sequence-dependent transitions, and run-length constraints. The performance of the proposed model is demonstrated through the solution of three different delivery scenarios and is shown to be better than that of a DT formulation in terms of both model scales and solution accuracy, from which one can infer the advantages of the CT formulation in dealing with time-related issues for process scheduling.