A simple new continuous-time formulation for short-term scheduling of multipurpose batch processes

A new continuous-time formulation for scheduling short-term multipurpose batch processes is presented. The formulation gives rise to a mixed-integer linear programming (MILP) model. The state-task network (STN) representation forms the basis of the proposed approach. A number of event points is prepostulated, which is the same for all tasks in the process. Event times are defined by the ends of task execution, and they are generally different for different tasks of the process, giving rise to a nonuniform time grid. The necessary time monotonicity for single tasks is guaranteed by means of simple duration constraints. Suitable sequencing constraints, applicable to batch tasks involving the same state, are also introduced, so that state balances are properly posed in the context of the nonuniform time grid. The expression of duration and sequencing constraints is greatly simplified by hiding all unit information within the task data. Three benchmark problems are used to illustrate the efficiency and applicability of the new formulation. Results are shown to compare favorably with existing continuous-time formulations in terms of model size and computational effort.