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Table of Contents
Intro
Preface
Contents
Chapter 1: Introduction to Modelling in Mathematical Programming
1.1 Model
1.2 Classical Components of a Mathematical Programming Model
1.3 Classification of Mathematical Programming Models
1.4 First Example
1.5 Considerations on the Format of a Mathematical Model
1.6 Justification of the Use of Mathematical Programming Models
References
Chapter 2: Structure of a Mathematical Programming Model
2.1 Environment of an Optimization Problem
2.2 Components of an Optimization Problem
2.3 Examples
References
Chapter 3: The Elements of a System
3.1 Introduction
3.2 Data of Elements
3.2.1 Belonging of the Data
3.2.2 Primary Element in a Shared Attribute
3.2.3 Type of Value of the Data
3.2.4 Representation
3.2.5 Inclusion of Calculated Data
3.3 The Quantitative Nature of the Elements
3.3.1 Collective Element vs Individual Items
3.4 Association of Elements in Sets
3.4.1 Assigning or Removing Data to Create Sets
3.4.2 Shared Data Between Elements of the Same Set
3.4.3 Hierarchical Definition of Sets
3.5 Data Generating Elements
3.6 Identification of Data in Graphic Environments. Elements in Graphs
3.6.1 Representation of Graphs
3.7 The Time Element
3.8 Element Duplication
3.9 Examples
3.9.1 Fire Stations (Source: Larrañeta et al. 2003)
3.9.2 Food Service (Source: Larrañeta et al. 2003)
3.9.3 Location of TV Cameras (Source: Larrañeta et al. 2003)
3.9.4 Trip Planning
3.9.5 Fixed Job Scheduling Problem (Kroon et al. 1995)
3.9.6 Health Centers
References
Chapter 4: Decision Activities
4.1 Introduction
4.2 Actions of a System
4.2.1 Actions with Calculated Value
4.2.2 Actions with Undetermined Value
4.3 Participating Elements in a Decision Activity
4.3.1 Rules of Participation
4.4 Quantification of the Activity
4.5 Union of Activities
4.6 Examples
4.6.1 Fire Stations (Example 3.9.1
Source: Larrañeta et al. 2003)
4.6.2 Food Service (Example 3.9.2
Source: Larrañeta et al. 2003)
4.6.3 Location of TV Cameras (Example 3.9.3
Source: Larrañeta et al. 2003)
4.6.4 Trip Planning (Example 3.9.4)
4.6.5 Fixed Job Scheduling Problem (Example 3.9.5
Kroon et al. 1995
Kolen et al. 2007)
4.6.6 Health Centers (Example 3.9.6)
Preface
Contents
Chapter 1: Introduction to Modelling in Mathematical Programming
1.1 Model
1.2 Classical Components of a Mathematical Programming Model
1.3 Classification of Mathematical Programming Models
1.4 First Example
1.5 Considerations on the Format of a Mathematical Model
1.6 Justification of the Use of Mathematical Programming Models
References
Chapter 2: Structure of a Mathematical Programming Model
2.1 Environment of an Optimization Problem
2.2 Components of an Optimization Problem
2.3 Examples
References
Chapter 3: The Elements of a System
3.1 Introduction
3.2 Data of Elements
3.2.1 Belonging of the Data
3.2.2 Primary Element in a Shared Attribute
3.2.3 Type of Value of the Data
3.2.4 Representation
3.2.5 Inclusion of Calculated Data
3.3 The Quantitative Nature of the Elements
3.3.1 Collective Element vs Individual Items
3.4 Association of Elements in Sets
3.4.1 Assigning or Removing Data to Create Sets
3.4.2 Shared Data Between Elements of the Same Set
3.4.3 Hierarchical Definition of Sets
3.5 Data Generating Elements
3.6 Identification of Data in Graphic Environments. Elements in Graphs
3.6.1 Representation of Graphs
3.7 The Time Element
3.8 Element Duplication
3.9 Examples
3.9.1 Fire Stations (Source: Larrañeta et al. 2003)
3.9.2 Food Service (Source: Larrañeta et al. 2003)
3.9.3 Location of TV Cameras (Source: Larrañeta et al. 2003)
3.9.4 Trip Planning
3.9.5 Fixed Job Scheduling Problem (Kroon et al. 1995)
3.9.6 Health Centers
References
Chapter 4: Decision Activities
4.1 Introduction
4.2 Actions of a System
4.2.1 Actions with Calculated Value
4.2.2 Actions with Undetermined Value
4.3 Participating Elements in a Decision Activity
4.3.1 Rules of Participation
4.4 Quantification of the Activity
4.5 Union of Activities
4.6 Examples
4.6.1 Fire Stations (Example 3.9.1
Source: Larrañeta et al. 2003)
4.6.2 Food Service (Example 3.9.2
Source: Larrañeta et al. 2003)
4.6.3 Location of TV Cameras (Example 3.9.3
Source: Larrañeta et al. 2003)
4.6.4 Trip Planning (Example 3.9.4)
4.6.5 Fixed Job Scheduling Problem (Example 3.9.5
Kroon et al. 1995
Kolen et al. 2007)
4.6.6 Health Centers (Example 3.9.6)