Mixed Integer Optimization for Cyclic Scheduling of Multiproduct Plants Under Exponential Performance Decay

The aim of this work is to propose a mathematical programming model for the economic lot scheduling problem (ELSP) in units that present performance decay. Typical examples in the chemical processing industry include catalyst deactivation and cokeification, as well as fouling in heat exchangers. The main decision related to this problem concerns processing interruption for maintenance so to restore unit performance. The dynamic behaviour of the system along time is represented by an exponential decay function. The problem is formulated as a mixed integer nonlinear programme (MINLP). Moreover, a mixed integer linear programme (MILP) that results from the discretization of cycle time is developed. The models are tested in a wide set of problems with several parameter values and the results for the models with continuous and discrete cycle times are compared. Results show that the MINLP model achieves the optimal solutions in shorter CPU times. Nevertheless, the usefulness of the MILP is shown as it provides tight bounds that provide convergence of the MINLP. Moreover, the formulations are compared to hierarchical approaches.