Novel Continuous Time MILP Formulation for Multipurpose Batch Plants. 2. Integrated Planning and Scheduling X. X. Zhu* and T. Majozi Department of Process Integration, University of Manchester Institute of Science and Technology, P.O. Box 88, Manchester M60 1QD, United Kingdom While the first part of this series focuses on the application of the proposed formulation to scheduling, this paper focuses mainly on the integration of planning and scheduling in multipurpose batch plants. In dealing with this problem, the method presented in this paper exploits the mathematical structure of the overall plant model. It is discovered that the overall model exhibits a block angular structure that is decomposed by raw material allocation. If raw materials can be allocated optimally to individual plants, solving individual models for each plant can produce the same results as solving an overall model for the site. This discovery leads to a decomposition strategy that consists of two levels. In the first level, only planning decisions are made, and the objective function is the maximization of the overall profit. The results from solving the planning model give optimal raw material allocation to different plants. In the second level, the raw material targets from the first (planning) level are incorporated into the scheduling submodels for each plant, which are solved independently without compromising global optimality. The objective function for each scheduling submodel is the maximization of product throughput. The scheduling level uses the concept of the state sequence network presented in part 1. Solving scheduling submodels for individual plants rather than the overall site model leads to problems with much a smaller number of binary variables and, hence, shorter CPU times. If conflicts arise, i.e., the planning targets are too optimistic to be realized at the scheduling level, the planning model is revisited with more realistic targets. This eventually becomes an iterative procedure that terminates once the planning and scheduling solutions converge within a specified tolerance. In this way, the planning model acts as coordination for scheduling models for individual plants. An industrial case study with three chemical processes is presented to demonstrate the effectiveness of this approach. Introduction Conflicts usually exist between planning and schedul- ing targets. Most chemical sites with distinct planning and scheduling departments experience this problem on a daily basis. This occurs due to the inconsistency between planning and scheduling in terms of time horizons and the focus of decision making. While scheduling focuses on short-term operational issues, planning is aimed at long-term economic issues and tends to overlook operational aspects and disturbances occurring on a daily basis. However, these aspects affect the selection and allocation of raw materials to indi- vidual plants. Whenever these disturbances occur, the predetermined schedules may not be valid anymore, and the production throughput may be affected. This causes the incoherence between planning and scheduling. Therefore, there is a need to develop methods that can reconcile planning and scheduling targets to guarantee the coherence between them. Most of the work done on batch processes has focused on developing better models for scheduling alone with- out involving planning. A significant amount of work has also been dedicated to developing planning models for chemical processes, with more emphasis on multi- period models. 3,4,7-10 Until recently, very limited atten- tion has been paid on integrating planning and sched- uling decisions. Furthermore, multiplant models have received very limited attention whereas they are fre- quently encountered in practice. In addressing the problem of integrated planning and scheduling, Subrahmanyam et al. 11 and Bassett et al. 1 attempted to tackle the problem of applying distributed computing to batch plant design and scheduling. Their approach is based on the decomposition of the problem into design and scheduling levels, yielding a Design Super Problem (DSP) and Scheduling Sub Problem (SSP), respectively. The DSP entails aggregation of plant life span time horizon into nonuniform time periods. The boundaries of the time periods define aggregate production deadlines. The SSP addresses scheduling within short-term time horizons, i.e., time periods from the DSP, to cater for the day-to-day plant operations. Uniform time discretization is applied within each short-term time horizon. The scenario concept is adopted to yield an MILP formulation for DSP problem. The scenario is a collection of predicted demand levels associated with their probabilities. Once the schedules are optimized within a given time period, they are then spliced/linked together to yield an overall solution to the original problem. It was acknowledged, however, that the complexity behind solving problems of this nature has prevented the application of this methodology to large-scale problems. The problem formulation results in a colossal model that cannot be solved easily by the existing computational techniques, even for very simple problems. A similar integration strategy that also includes large-scale model predictive control has been * Corresponding author e-mail: F.Zhu@umist.ac.uk. 5621 Ind. Eng. Chem. Res. 2001, 40, 5621-5634 10.1021/ie000597r CCC: $20.00 © 2001 American Chemical Society Published on Web 10/18/2001