This book presents a structured approach to formulate, model, and solve mathematical optimization problems for a wide range of real world situations. Among the problems covered are production, distribution and supply chain planning, scheduling, vehicle routing, as well as cutting stock, packing, and nesting. The optimization techniques used to solve the problems are primarily linear, mixed-integer linear, nonlinear, and mixed integer nonlinear programming. The book also covers important considerations for solving real-world optimization problems, such as dealing with valid inequalities and symmetry during the modeling phase, but also data interfacing and visualization of results in a more and more digitized world. The broad range of ideas and approaches presented helps the reader to learn how to model a variety of problems from process industry, paper and metals industry, the energy sector, and logistics using mathematical optimization techniques.

Autorentext

Prof. Dr. Josef Kallrath has studied mathematics, physics and astronomy in Bonn, where he received his doctorate in 1989 with an astrophysical dissertation on the dynamics of colliding binary stellar winds. He is working in practice (BASF SE, Ludwigshafen; 1989-2019), freelances since 1998 as a scientific consultant and solves practical problems in industry with scientific computing and operations research techniques. His work focuses on mathematical optimization to support decision processes in chemical industry, paper industry, metal industry, energy industry, transport infrastructure and the modeling of physical systems. He has taught at the University of Heidelberg (1991-2001) and, since 1997, at the University of Florida in Gainesville/USA. Since 2002, he has headed the Mathematical Optimization Practice Group of the Gesellschaft für Operations Research (GOR).

Inhalt

Optimization: Using Models, Validating Models, Solutions, Answers.- From the Problem to its Mathematical Formulation.- Mathematical Solution Techniques.- Problems Solvable Using Linear Programming.- How Optimization is Used in Practice: Case Studies in Linear Programming.- Modeling Structures Using Mixed Integer Programming.- Types of Mixed Integer Linear Programming Problems.- Case Studies and Problem Formulations.- User Control of the Optimization Process and Improving Efficiency.- How Optimization is Used in Practice: Case Studies in Integer Programming.- Beyond LP and MILP Problems.- Mathematical Solution Techniques - The Nonlinear World.- Global Optimization in Practice.- Polylithic Modeling and Solution Approaches.- Cutting & Packing beyond and within Mathematical Programming.- The Impact and Implications of Optimization.- Concluding Remarks and Outlook.