A new and simple general mathematical formulation for scheduling multipurpose plants involving batch and/or continuous processes, based on the resource-task network (RTN) representation, is presented. The formulation uses a uniform-time-grid continuous-time representation and results in a very efficient mixed integer linear programming model that can be solved to optimality for a given number of event points. The performance of the formulation is illustrated through the solution of two case studies that have been thoroughly examined in the literature: the first involves a continuous plant and is solved for three different storage policies, and the second concerns a batch plant. The formulation is shown to compare favorably to existing continuous-time formulations. More specifically, a new optimal solution is obtained for the finite intermediate storage scenario of the first case that is also a global optimal solution.

This paper presents an improved general mathematical programming formulation for optimal scheduling of batch processes based on the resource−task network (RTN) representation. The formulation uses a continuous-time representation and results in a mixed integer linear programming problem. It is a relaxation of the problem presented by Schilling (Schilling, G. Optimal Scheduling of Multipurpose Plants. Ph.D. Thesis, University of London, London, U., K., 1997). By allowing, if possible, finite storage within the processing tasks resource equipments of the involved raw materials and/or products, the proposed approach leads to simpler and less degenerate mathematical models. These models can be solved in significantly less CPU time, when compared to other RTN continuous-time formulations. Three published example problems are presented to illustrate the effectiveness of the proposed formulation. Finally, we show that the STN-based continuous-time scheduling formulation of Ierapetritou and Floudas (Ierapetritou, M. G.; Floudas, C. A. Effective Continuous-Time Formulation for Short-Term Scheduling. 1. Multipurpose Batch Processes. Ind. Eng. Chem. Res. 1998, 37, 4341) is less accurate, as it violates time horizon constraints in two of the examples solved.

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