(475g) Computational Performance of Big-M Formulations In Scheduling of Multipurpose Batch Plants

                               ¹E. Reshid and ^1,2T. Majozi

¹ Department of Chemical Engineering, University of Pretoria, Lynnwood Road, Pretoria, 0002, South Africa

² Modeling and Digital Science, CSIR, Pretoria, South Africa

Abstract

A large amount of research has gone into the development of optimization techniques for scheduling of batch plants. Scheduling of these batch plants becomes a challenging task which leads to several mathematical formulations to exist in the literature. The formulations that are based on continuous-time have gained significant attention for their advantage of requiring less number of time points, smaller problem size and less binary variables. The continuous-time formulations that use unit specific time points where tasks are allowed to start processing at different time with the same time point lead to big-M constraints. As the time horizon increases, the big M formulations require large computational time and difficult to close the relative gap. Due to this, cyclic scheduling is adopted for long time horizon by compromising 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 presentation a novel scheduling model based on state sequence network (SSN) representation is presented. The formulation uses a continuous-time representation and a two index binary variable that result into mixed integer linear programming (MILP) problem. The model was tasted for a number of case studies taken from published literature. The results obtained showed that the model is computationally superior to existing model and capable of modelling and solving for long time horizon. The model is therefore advantageous over cyclic scheduling where the objective value is compromised by computational performance.

Key words: Scheduling; Multipurpose Batch Plant; Optimization; MILP; Big-M, continuous-time