Multiperiod blending has a number of important applications in a range of industrial sectors. It is typically formulated as a nonconvex mixed integer nonlinear program (MINLP), which involves binary variables and bilinear terms. In this study, we first propose a reformulation of the constraints involving bilinear terms using lifting. We introduce a method for calculating tight bounds on the lifted variables calculated by aggregating multiple constraints. We propose valid constraints derived from the reformulation-linearization technique (RLT) that use the bounds on the lifted variables to further tighten the formulation. Computational results indicate our method can substantially reduce the solution time and optimality gap. Summary of Contribution: In this paper, we study the multiperiod blending problem, which has a number of important applications in a range of industrial sectors, such as refining, chemical production, mining, and wastewater management. Solving this problem efficiently leads to significant economic and environmental benefits. However, solving even medium-scale instances to global optimality remains challenging. To address this challenge, we propose a variable bound tightening algorithm and tightening constraints for multiperiod blending. Computational results show that our methods can substantially reduce the solution time and optimality gap.

We propose mixed-integer programming models for fitting univariate discrete data points with continuous piecewise linear (PWL) functions. The number of approximating function segments and the locations of break points are optimized simultaneously. The proposed models include linear constraints and convex objective function and, thus, are computationally more efficient than previously proposed mixed-integer nonlinear programming models. We also show how the proposed models can be extended to approximate univariate functions with PWL functions with the minimum number of segments subject to bounds on the pointwise error.

Scheduling problems arise in many applications in process industries. However, despite various efforts to develop efficient scheduling methods, current approaches cannot be used to solve instances of industrial importance in reasonable time frames. The goal of this paper is the development of a dynamic decomposition framework that exploits the structure of the problem and is well suited for grid computing. The problem we study is the simultaneous batching and scheduling of multistage batch processes for which the binary decision variables are batch selection, batch-unit assignment, and batch sequencing on units. We present methods to decompose the original problem into a number of subproblems in a dynamic fashion. First, we discuss the generation of subproblems based on fixing the batch-selection variables. Second, we generate subproblems by fixing the batch-unit assignment variables in a bottlenecking stage. Third, we generate subproblems by fixing the last batch in the sequence on each unit of the bottlenecking stage. Furthermore, the second and third methods can be carried out in various combinations. Alternatively, a problem can be decomposed into a number of promising subproblems using an automatic strong branching scheme. Our results show that the proposed method can be used on a grid computer to solve large problems to optimality in a reasonable computational time.