Building and Solving Mathematical Programming Models in Engineering and Science

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.

"...plenty of examples are given...suitable for mathematical programming undergraduate courses..." (Zentralblatt Math, Vol. 1029, 2004) "I think this textbook is worth having in the college library…” (Interfaces, July-August 2003)"...can be quite valuable because of its documentation of the GAMS software product...a means to learn and utilize a sophisticated linear and nonlinear programming tool." (Journal of Mathematical Psychology, 2002)"...a welcome addition to the series of publications on mathematical programming applications to engineering problems..." Note: Review features an image of wiley.com. (IEEE Computer Applications in Power)"...intention is to discuss the subject from an angle different from the standard, emphasizing conditions leading to well-defined problems, compatibility and uniqueness of solutions." (Mathematical Reviews, 2002i)"...a useful and welcome addition to existing books on mathematical programming…I recommend this book..." (IIE Transactions)"...very well suited as a professional reference or as a text for advanced mathematics or engineering courses." (Journal of Applied Mathematics and Stochastic Analysis, Vol. 15, No. 4)

• Preface xiii I Models 11 Linear Programming 31.1 Introduction 31.2 The Transportation Problem 41.3 The Production Scheduling Problem 61.4 The Diet Problem 91.5 The Network Flow Problem 111.6 The Portfolio Problem 131.7 Scaffolding System 151.8 Electric Power Economic Dispatch 182 Mixed-Integer Linear Programming 252.1 Introduction 252.2 The 0-1 Knapsack Problem 252.3 Identifying Relevant Symptoms 272.4 The Academy Problem 292.5 School Timetable Problem 322.6 Models of Discrete Location 352.7 Unit Commitment of Thermal Power Units 383 Nonlinear Programming 473.1 Introduction 473.2 Some Geometrically Motivated Examples 473.3 Some Mechanically Motivated Examples 513.4 Some Electrically Motivated Examples 553.5 The Matrix Balancing Problem 623.6 The Traffic Assignment Problem 64II Methods 714 An Introduction to Linear Programming 734.1 Introduction 734.2 Problem Statement and Basic Definitions 734.3 Linear Programming Problem in Standard Form 784.4 Basic Solutions 814.5 Sensitivities 834.6 Duality 845 Understanding the Set of All Feasible Solutions 975.1 Introduction and Motivation 975.2 Convex Sets 1015.3 Linear Spaces 1055.4 Polyhedral Convex Cones 1075.5 Polytopes 1095.6 Polyhedra 1105.7 Bounded and Unbounded LPP 1136 Solving the Linear Programming Problem 1176.1 Introduction 1176.2 The Simplex Method 1186.3 The Exterior Point Method 1407 Mixed-Integer Linear Programming 1617.1 Introduction 1617.2 The Branch-Bound Method 1627.3 The Gomory Cuts Method 1728 Optimality and Duality in Nonlinear Programming 1838.1 Introduction 1838.2 Necessary Optimality Conditions 1888.2.1 Differentiability 1888.3 Optimality Conditions: Sufficiency and Convexity 2078.4 Duality Theory 2168.5 Practical Illustration of Duality and Separability 2218.6 Constraint Qualifications 2269 Computational Methods for Nonlinear Programming 2359.1 Unconstrained Optimization Algorithms 2369.2 Constrained Optimization Algorithms 2549.2.1 Dual Methods 254III Software 28310 The GAMS Package 28510.1 Introduction 28510.2 Illustrative Example 28610.3 Language Features 29011 Some Examples Using GAMS 31111.1 Introduction 31111.2 Linear Programming Examples 31111.3 Mixed-Integer LPP Examples 33011.4 Nonlinear Programming Examples 344IV Applications 36912 Applications 37112.1 Applications to Artificial Intelligence 37112.2 Applications to CAD 37812.3 Applications to Probability 38712.4 Regression Models 39512.5 Applications to Optimization Problems 40112.6 Transportation Systems 41712.7 Short-Term Hydrothermal Coordination 44213 Some Useful Modeling Tricks 45113.1 Introduction 45113.2 Some General Tricks 45113.3 Some GAMS Tricks 466A Compatibility and Set of All Feasible Solutions 477A.l The Dual Cone 478A.2 Cone Associated with a Polyhedron 480A.3 The Γ Procedure 483A.4 Compatibility of Linear Systems 488A.5 Solving Linear Systems 491A.6 Applications to Several Examples 494B Notation 517Bibliography 533Index 541