A Cont inuous -Time Formulat ion for S imultaneous Considerat ion of Planning and Scheduling Decis ions

Planning and scheduling of batch and semi-continuous plants involving problem formulation, information flow and solution methodologies are the subject of numerous publications during the last two decades. A typical planning problem includes hundreds of different products produced utilizing a variety of process unit operations over a time horizon of several weeks to few months. The mathematical formulation of such planning problem, involving detailed scheduling decisions, results in models with thousands of variables that cannot be directly addressed due to their computational complexity. In this work a new formulation is presented to address the simultaneous consideration of planning and scheduling problems based on the continuous time representation and the idea of periodic scheduling. In this paper, demand and prices are assumed fixed along the time horizon under consideration. The proposed formulation corresponds to a MINLP problem and results in the determination of the optimal cycle length and detailed schedule. Although the approach does not guarantee to provide the optimal solution to the planning problem, it results in excellent near optimal solution in reasonable computation time. Case study is presented to illustrate the efficiency of the proposed model.