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Informationen zum Autor ENRIQUE CASTILLO , PhD, is Full Professor of Applied Mathematics at the University of Cantabria in Santander, Spain. ANTONIO J. CONEJO , PhD, is Full Professor of Electrical Engineering at the Universidad de Castilla La Mancha, Ciudad Real, Spain. PABLO PEDREGAL , PhD, is Full Professor of Applied Mathematics at the University of Cantabria. RICARDO GARCIA is a mathematician in the fields of optimization and operation research. NATALIA ALGUACIL , PhD, researches optimization by decomposition techniques. Klappentext Fundamental concepts of mathematical modeling Modeling is one of the most effective, commonly used tools in engineering and the applied sciences. In this book, the authors deal with mathematical programming models both linear and nonlinear and across a wide range of practical applications. Whereas other books concentrate on standard methods of analysis, the authors focus on the power of modeling methods for solving practical problems-clearly showing the connection between physical and mathematical realities-while also describing and exploring the main concepts and tools at work. This highly computational coverage includes: Discussion and implementation of the GAMS programming system Unique coverage of compatibility Illustrative examples that showcase the connection between model and reality Practical problems covering a wide range of scientific disciplines, as well as hundreds of examples and end-of-chapter exercises Real-world applications to probability and statistics, electrical engineering, transportation systems, and more Building and Solving Mathematical Programming Models in Engineering and Science is practically suited for use as a professional reference for mathematicians, engineers, and applied or industrial scientists, while also tutorial and illustrative enough for advanced students in mathematics or engineering. Zusammenfassung Modeling is one of the most appealing areas in engineering and applied sciences. Engineers need to build models to solve real life problems. The aim of a model consists of reproducing the reality as faithfully as possible! trying to understand how the real world behaves! and obtaining the expected responses to given actions or inputs. Inhaltsverzeichnis Preface xiii I Models 1 1 Linear Programming 3 1.1 Introduction 3 1.2 The Transportation Problem 4 1.3 The Production Scheduling Problem 6 1.4 The Diet Problem 9 1.5 The Network Flow Problem 11 1.6 The Portfolio Problem 13 1.7 Scaffolding System 15 1.8 Electric Power Economic Dispatch 18 2 Mixed-Integer Linear Programming 25 2.1 Introduction 25 2.2 The 0-1 Knapsack Problem 25 2.3 Identifying Relevant Symptoms 27 2.4 The Academy Problem 29 2.5 School Timetable Problem 32 2.6 Models of Discrete Location 35 2.7 Unit Commitment of Thermal Power Units 38 3 Nonlinear Programming 47 3.1 Introduction 47 3.2 Some Geometrically Motivated Examples 47 3.3 Some Mechanically Motivated Examples 51 3.4 Some Electrically Motivated Examples 55 3.5 The Matrix Balancing Problem 62 3.6 The Traffic Assignment Problem 64 II Methods 71 4 An Introduction to Linear Programming 73 4.1 Introduction 73 4.2 Problem Statement and Basic Definitions 73 4.3 Linear Programming Problem in Standard Form 78 4.4 Basic Solutions 81 4.5 Sensitivities 83 4.6 Duality 84 5 Understanding the Set of All Feasible Solutions 97 5.1 Introduction and Motivation 97 5.2 Convex Sets 101 5.3 Linear Spaces 105 5.4 Polyhedral Convex Cones 107 5.5 Polytopes 109 5.6 Polyhedra 110 5.7 Bounded and Un...
