Format:
1 Online-Ressource (291 Seiten)
ISBN:
9783030572501
Series Statement:
International Series in Operations Research and Management Science Ser. v.298
Note:
Description based on publisher supplied metadata and other sources
,
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) -- 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 -- 6.3 Quantitative Specifications of Selection -- 6.4 Capacity Specifications -- 6.4.1 Case 1: Variable Capacity Consumption and Fixed Contribution -- 6.4.2 Case 2: Variable Consumption with Fixed and Variable Capacity Contribution -- 6.4.3 Case 3: Fixed Capacity Demand and Variable Capacity Contribution -- 6.5 Supply of a Demand -- 6.6 Bound Imposition Specifications -- 6.7 Allocation, Balance, or Equilibrium Specifications -- 6.7.1 Explicit Case -- 6.7.2 Implicit Case -- 6.8 Modelling of Propositional Logic Specifications -- 6.8.1 Simple Propositions and Logical Operators -- 6.8.2 Reduction of Signs -- 6.8.3 Modelling Operators Individually -- 6.8.3.1 Negation Operator (NOT -- ) -- 6.8.3.2 Conditional Operator (IF THEN -- ) -- 6.8.3.3 Biconditional Operator (IF AND ONLY IF -- ) -- 6.8.3.4 Disjunction Operator (OR.
,
) -- 6.8.3.5 Conjunction Operator (AND -- ) -- 6.8.3.6 Exclusive Disjunction Operator (EITHER OR -- ) -- 6.8.4 Modelling Compound Propositions with Various Operators -- 6.8.4.1 Negation Operator (NOT -- ): -- 6.8.4.2 Disjunction Operator (OR -- ) and Exclusive Disjunction (EITHER OR -- ): -- 6.8.4.3 Conjunction Operator (AND -- ) -- 6.8.4.4 Conditional and Biconditional Operators -- 6.8.5 Data as Propositions -- 6.8.6 Logical Propositions That Express Possibility -- 6.9 Objective Criterion -- 6.9.1 Cost According to Interval of Values -- 6.9.2 Cost According to the Value of Another Variable -- 6.9.3 Costs Depending on the Deviation of the Variable -- 6.9.3.1 Penalty by Excess -- 6.9.3.2 Bonus by Excess -- 6.9.3.3 Penalty by Default -- 6.9.3.4 Bonus by Default -- 6.10 Identification of Specifications -- References -- Chapter 7: The Quantitative Nature of the Elements -- 7.1 Introduction -- 7.2 Individual Element Not Measurable Defined as Measurable -- 7.3 Measurable Element with Both Measurable and Logical Decisions -- 7.4 Individual Elements with Capacity to be Grouped in Collective Elements: Redefining the System with Simple Changes -- 7.5 Individual Elements with Capacity to Be Grouped in Collective Elements: Redefining the System Description with Complex Cha... -- 7.6 Individual Elements with Capacity to be Grouped in Collective Elements: Through Grouping into Subsets -- 7.7 Individual Elements with Capacity to Be Grouped in Collective Elements: Through Small Changes in the Data Values -- 7.8 Items of Indeterminate Collective Elements that Need to Be Defined Individually -- References -- Chapter 8: Practical Examples -- 8.1 Production with Fixed Costs -- 8.2 Graph Coloring Problem [Jensen and Toft (1995)] -- 8.3 Configuration of Work Centers -- 8.4 Production and Delivery of Solar Panels -- 8.5 Selection of a Tree in a Graph
,
8.6 Programming of Pilots for an Airline's Flights -- References -- Correction to: Modelling in Mathematical Programming
Additional Edition:
Erscheint auch als Druck-Ausgabe García Sánchez, José Manuel Modelling in Mathematical Programming Cham : Springer International Publishing AG,c2020 ISBN 9783030572495
Language:
English
Subjects:
Computer Science
,
Economics
,
Mathematics
Keywords:
Optimierung
;
Mathematische Modellierung
