Novel continuous time MILP formulation for multipurpose batch plants. 2. Integrated planning and scheduling

While the first part of this series focuses on the application of the propo sed formulation to scheduling, this paper focuses mainly on the integration of planning and scheduling in multipurpose batch plants. In dealing with t his problem, the method presented in this paper exploits the mathematical s tructure of the overall plant model. It is discovered that the overall mode l exhibits a block angular structure that is decomposed by raw material all ocation. If raw materials can be allocated optimally to individual plants, solving individual models for each plant can produce the same results as so lving an overall model for the site. This discovery leads to a decompositio n strategy that consists of two levels. In the first level, only planning d ecisions are made, and the objective function is the maximization of the ov erall profit. The results from solving the planning model give optimal raw material allocation to different plants. In the second level, the raw mater ial targets from the first (planning) level are incorporated into the sched uling submodels for each plant, which are solved independently without comp romising global optimality. The objective function for each scheduling subm odel is the maximization of product throughput. The scheduling level uses t he concept of the state sequence network presented in part 1. Solving sched uling submodels for individual plants rather than the overall, site model l eads 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 re visited with more realistic targets. This eventually becomes an iterative p rocedure that terminates once the planning and scheduling solutions converg e within a specified tolerance. In this way, the planning model acts as coo rdination for scheduling models for individual plants. An industrial case s tudy with three chemical processes is presented to demonstrate the effectiv eness of this approach.