The planning of chemical production often involves the optimization of the size of the tasks to be performed subject to unit capacity constraints, as well as inventory constraints for intermediate materials. While several mixed-integer programming (MIP) models have been proposed that account for these features, the development of tightening methods for these formulations has received limited attention. In this paper, we develop a constraint propagation algorithm for the calculation of lower bounds on the number and size of tasks necessary to satisfy given demand. These bounds are then used to express three types of tightening constraints which greatly enhance the computational performance of the MIP scheduling model. Importantly, the proposed methods are applicable to a wide range of problem classes and time-indexed MIP models for chemical production scheduling.
Department of Chemical and Biological Engineering University of Wisconsin – Madison 1415 Engineering Dr., Madison, WI, 53706 October 2012