Mixed Integer Optimization in the Chemical Process Industry

Abstract

Proper organization, planning and design of production, storage locations, transportation and scheduling are vital to retain the competitive edge of companies in the global economy. Typical additional problems in the chemical industry suitable for optimization are process design, process synthesis and multi-component blended-¯ow problems leading to nonlinear or even mixed integer nonlinear models. Mixed integer optimization (MIP) determines optimal solutions of such complex problems; the development of new algorithms, software and hardware allow the solution of larger problems in acceptable times.This tutorial paper addresses two groups. The focus towards the ®rst group (managers and senior executives) and readers who are not very familiar with mathematical programming is to create some awareness regarding the potential bene®ts of MIP, to transmit a sense of what kind of problems can be tackled, and to increase the acceptance of MIP. The second group (a more technical audience with some background in mathematical optimization), might rather appreciate the state-of-the-art view on good-modelling practice, algorithms and an outlook into global optimization.Some real-world MIP problems solved by BASF's mathematical consultants are brie¯y described, among them discrete blending and multi-stage production planning and distribution with several sites, products and periods. Finally, there is a focus on future perspectives and sources of MIP support are indicated from academia, software providers and consulting ®rms.

Conceptual Design of Azeotropic Distillation Processes

“…Discrete decisions accounting for the position of the feed tray and the number of trays in each column section can be encoded by binary decision variables as introduced and worked out by Grossmann and coworkers (see [117] for the original contribution and the Chapter 12 "Optimization of Distillation Processes" for a detailed overview on problem formulations and solution strategies). The resulting superstructure models are generally of large scale and present strongly non-convex MINLP problems that are particularly hard to solve [118]. This is especially true for the numerical optimization of azeotropic distillation processes, which has only been addressed more recently [119e121].…”

Logic-Based Modeling and Solution of Nonlinear Discrete/Continuous Optimization Problems

“…Mixed-integer linear programming (MILP) models and solution algorithms have been developed and applied to many industrial problems successfully (Nemhauser and Wolsey, 1988;Kallrath, 2000).…”

Planning and scheduling in the process industry

“…Only if the pooling problem occurs, e.g., in the refinery industry or the food industry, we are really facing a MINLP problem. For a review on algorithms used in LP, MILP, NLP, and MINLP the reader is referred to [39].…”

“…In the case of MINLP, the solution efficiency depends strongly on the individual problem and the model formulation. However, as stressed in [39] for both problem types, MILP and MINLP, it is recommended that the full mathematical structure of a problem is exploited, that appropriate reformulations of models are made and that problem specific valid inequalities or cuts are used. Software packages may also differ with respect to the ability of pre-solving techniques, default-strategies for the Branch&Bound algorithm, cut generation within the Branch&Cut algorithm, and last but not least diagnosing and tracing infeasibilities which is an important issue in practice.…”

“…For the topics of valid inequalities and cutting plane algorithms the reader is referred to the well written book by Wolsey [70]. Using these techniques, for some BASF planning problems including up to 100,000 constraints and up to 150,000 variables with several thousand binary variables, good solution with integrality gaps below 2% have been achieved within 30 minutes on standard Pentium machines [39].…”