| Description |
1 online resource |
| Series |
International Series in Operations Research & Management Science, 0884-8289 ; v. 298 |
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International series in operations research & management science ; 298. 0884-8289
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| 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 |
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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 |
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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 |
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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) |
| Summary |
This book provides basic tools for learning how to model in mathematical programming, from models without much complexity to complex system models. It presents a unique methodology for the building of an integral mathematical model, as well as new techniques that help build under own criteria. It allows readers to structure models from the elements and variables to the constraints, a basic modelling guide for any system with a new scheme of variables, a classification of constraints and also a set of rules to model specifications stated as logical propositions, helping to better understand models already existing in the literature. It also presents the modelling of all possible objectives that may arise in optimization problems regarding the variables values. The book is structured to guide the reader in an orderly manner, learning of the components that the methodology establishes in an optimization problem. The system includes the elements, which are all the actors that participate in the system, decision activities that occur in the system, calculations based on the decision activities, specifications such as regulations, impositions or actions of defined value and objective criterion, which guides the resolution of the system |
| Bibliography |
References-Chapter 5: Calculations in a System-5.1 Introduction-5.2 Auxiliary Calculations-5.2.1 Auxiliary Calculation of Value Selection-5.3 Logical Calculations-5.3.1 Logical Propositions and Logical Operators-5.3.2 Identification and Definition of a Logical Calculation-5.3.3 Reduction of the Definition of a Logical Calculation-5.4 Lower/Upper Bound Calculations-5.4.1 Bounds on Undetermined Variables-References-Chapter 6: Modelling and Types of Specifications-6.1 Introduction-6.2 Elements on Which the Specification Falls on |
| Notes |
Online resource; title from PDF title page (SpringerLink, viewed January 20, 2021) |
| Subject |
Mathematical models.
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Programming (Mathematics)
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Models, Theoretical
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mathematical models.
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Mathematical models
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Programming (Mathematics)
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| Form |
Electronic book
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| ISBN |
9783030572501 |
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3030572501 |
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