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Practical Python AI Projects Mathematical Models of Optimization Problems with Google OR-Tools Serge Kruk Practical Python AI Projects: Mathematical Models of Optimization Problems with Google OR-Tools Serge Kruk Rochester, Michigan, USA ISBN-13 (pbk): 978-1-4842-3422-8 ISBN-13 (electronic): 978-1-4842-3423-5 https://doi.org/10.1007/978-1-4842-3423-5 Library of Congress Control Number: 2018934677 Copyright © 2018 by Serge Kruk Any source code or other supplementary material referenced by the author in this book is available to readers on GitHub via the book's product page, located at www.apress.com/9781484234228. For more detailed information, please visit www.apress.com/source-code. Contents Chapter 1: Introduction�������������������������������������������������������������������������1 1.1 What Is This Book About? ................................................................................1 1.2 Features of the Text ........................................................................................3 1.2.1 Running the Models ................................................................................5 1.2.2 A Note on Notation ..................................................................................6 1.3 Getting Our Feet Wet: Amphibian Coexistence ................................................6 Chapter 2: Linear Continuous Models �������������������������������������������������19 2.1 Mixing ...........................................................................................................20 2.1.1 Constructing a Model ...........................................................................22 2.1.2 Variations ..............................................................................................26 2.1.3 Structure of the Problems Under Consideration ...................................28 2.2 Blending ........................................................................................................30 2.2.1 Constructing a Model ...........................................................................32 2.2.2 Variations ..............................................................................................36 2.3 Project Management .....................................................................................38 2.3.1 Constructing a Model ...........................................................................40 2.3.2 Variations ..............................................................................................43 2.4 Multi-Stage Models .......................................................................................45 2.4.1 Problem Instance ..................................................................................46 2.4.2 Constructing a Model ...........................................................................48 2.4.3 Variations ..............................................................................................54 2.5 Pattern Classification ....................................................................................57 2.5.1 Constructing a Model ...........................................................................58 2.5.2 Executable Model .................................................................................60 Chapter 3: Hidden Linear Continuous Models �������������������������������������63 3.1 Piecewise Linear ...........................................................................................65 3.1.1 Constructing a Model ...........................................................................66 3.1.2 Variations ..............................................................................................70 3.2 Curve Fitting ..................................................................................................76 3.2.1 Constructing a Model ...........................................................................78 3.2.2 Variations ..............................................................................................84 3.3 Pattern Classification Revisited ....................................................................85 3.3.1 Executable Model .................................................................................87 Chapter 4: Linear Network Models �����������������������������������������������������89 4.1 Maximum Flow..............................................................................................90 4.1.1 Constructing a Model ...........................................................................91 4.1.2 Decision Variables ................................................................................92 4.1.3 Variations ..............................................................................................98 4.2 Minimum Cost Flow ......................................................................................99 4.2.1 Constructing a Model .........................................................................100 4.2.2 Variations ............................................................................................105 4.3 Transshipment .............................................................................................106 4.3.1 Constructing a Model .........................................................................107 4.3.2 Variations ............................................................................................112
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