Strengthening a Mixed-Integer Program for Scheduling an Industrial Formulation Plant : Using Facet-Defining Inequalities and a Separation Algorithm

The problem of solving a scheduling problem for a two-level industrial formulation plants is discussed. An improved version of the mixed-integer program (MIP) introduced by Yfantis (Computer Aided Chemical Engineering, Vol. 46, (2019)) is given. However, the integrality gap in existing MIPs is too large. Hence, the goal is to strengthen the MIP formulation to reduce the integrality gap. The entire model is too large and intricate to immediately improve. So a subproblem is set up that only includes the filling part of the formulation plant. The linking of the indicator variable for the makespan plays a big role in the integrality gap, that is why the focus is on the filling part that includes this indicator variable. For this subproblem, facet-defining inequalities are found, as well as a separation algorithm to implement these specific inequalities. The found inequalities strengthen the MIP formulation.