Linear Programming-Based Preprocessing Algorithm and Tightening Constraints for Multiperiod Blend Scheduling Problems

Abstract

The multiperiod blend scheduling problem has a wide variety of engineering applications and is typically formulated as a nonconvex mixed-integer nonlinear program (MINLP). Such an MINLP is challenging to solve due to a large number of bilinear terms and binary variables. One prevalent solution method is branch and bound, whose efficiency heavily relies on the tightness of the convex relaxation of the MINLP. In this article, we propose new constraints that can be used for tightening such convex relaxation. These constraints are derived from the physical information lost due to relaxation and require solving linear programs during preprocessing. Extensive numerical tests are executed to examine the effectiveness of the proposed methods. The results show that even though hundreds of linear programs may be solved during preprocessing, our new methods can significantly reduce the overall computational time, including both the preprocessing and MINLP solver solution time. Further implications are discussed.