(356f) On Computational Performance of Big-M Formulations in Scheduling of Multipurpose Batch Plants

A large amount of research has gone in to the development of optimization techniques for scheduling of batch plants. Scheduling of these batch plants has become a challenging task which has led to several formulations in literature. The formulations that are based on continuous time representation of time have gained significant attention for their advantage of requiring less number of time points, smaller problem size and less binary variables. The formulations that use unit specific time points where tasks are allowed to start processing at different time with the same time point generally lead to big-M constraints. As the time horizon increases, the big-M constraints increase drastically thereby necessitating large computational time. This tends to limit their practical application in scheduling over a long time horizon. Due to this, cyclic scheduling is adopted for long time horizon with a compromise in objective value. If the formulation is beautiful both in structure and performance, there is no need to resort to cyclic scheduling as a way of approximating long term scheduling. In this paper a novel scheduling model based on state sequence network (SSN) representation that has no big-M constraints is presented. The formulation uses a continuous time representation that results in mixed integer linear programming (MILP) problem. The model was tested for a number of case studies taken from published literature. The results obtained showed that the model is computationally superior to existing models and capable of modelling and solving over a long time horizon without resorting to cyclic scheduling. This consequently sustains accuracy of the model.

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