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