(190b) A New Continuous-Time Model for Short-Term Scheduling of Multipurpose Batch Plants Using Non-Uniform Time Grid

Production scheduling has received a lot of attention from the academic and industrial community for last 30 years. A lot of papers have been published highlighting different aspects as to the kind of problems addressed, the different ways on how the problem is represented (STN and RTN) and on which kind of time grid a formulation is built on (Uniform Time Grid and Non-Uniform Time Grid). Although, a lot of important contributions have been proposed in the literature and much progress has been achieved, production scheduling of industrial-size problems is still challenging and poses as an open problem so that new ideas are still welcome. The present work presents a new STN formulation for the short-term scheduling of multipurpose batch plants, which uses the continuous time representation based on a non-uniform time grid. The time grid for each unit is created by positioning event points on the basis of the duration of the tasks that the unit is able to perform. No starting or ending time variables associated with tasks are involved. The formulation is able to deal with different storage policies (ZW, FIS, NIS and UIS). A collection of benchmark problems have been used to test the model performance in terms of both problem size and relaxation quality as well as in terms of computational resources. Our formulation is compared with that proposed by Ierapetritou and Floudas and revised in Shaik, Janak and Floudas (Ind. Eng. Chem. Res. 2006, 45, 6190-6209). The proposed formulation is able to always produce the optimal solution although it does not outperform the formulation by Ierapetritou and Floudas.