Optimal periodic scheduling of multipurpose batch plants

A rigorous mathematical programming framework for the scheduling of multipurpose batch plants operated in a cyclic mode is presented. The proposed formulation can deal with batch operations described by complex processing networks, involving shared intermediates, material recycles, and multiple processing routes to the same end-product or intermediate. Batch aggregation and splitting are also allowed. The formulation permits considerable flexibility in the utilisation of processing equipment and storage capacity, and accommodates problems with limited availability of utilities. The scheduling problem is formulated as a large mixed integer linear program (MILP). For a given cycle time, it is shown that it is sufficient for the formulation to characterize a single cycle of the periodic schedule despite the existence of tasks that span two successive cycles. The optimal cycle time is determined by solving a sequence of fixed cycle time problems. The MILP is solved by a branch-and-bound algorithm modified so as to avoid exploring branches that are cyclic permutations of others already fathomed. The resulting implementation permits the solution of problems of realistic size within reasonable computational effort. Several examples are used to illustrate the applicability of the algorithm.