Introduction to the mathematics of operations research with Mathematica:
Revised and updated to reflect recent advances, Introduction to the Mathematics of Operations Research with Mathematica, Second Edition focuses on the topics of graph theory, linear programming, stochastic processes, and dynamic programming. Integrating technology into the development, this second e...
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton, FL [u.a.]
Chapman & Hall
2006
|
| Edition: | 2nd ed. |
| Series: | Monographs and textbooks in pure and applied mathematics
|
| Subjects: | |
| Online Access: | Publisher description Inhaltsverzeichnis |
| Summary: | Revised and updated to reflect recent advances, Introduction to the Mathematics of Operations Research with Mathematica, Second Edition focuses on the topics of graph theory, linear programming, stochastic processes, and dynamic programming. Integrating technology into the development, this second edition features a CD-ROM with Mathematica, the program used throughout the text. It also offers new material in areas such as simulation, Brownian motion, and famous graph theory problems such as the traveling salesman problem. Further enhancing the interactive approach of the book, the author emphasizes problem solving with longer investigations, self-check questions, problem sets, and an appendix of solutions for selected problems. |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XIX, 567 S. Ill., graph. Darst. 1 CD-ROM (12 cm) |
| ISBN: | 1574446126 9781574446128 |
Staff View
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| 250 | |a 2nd ed. | ||
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Record in the Search Index
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| adam_text |
Contents
Chapter
1 - Graph
Theory and Network Analysis
.1
1.1
Definitions and Examples
.2
1.2
Spanning Trees
.24
Undirected Spanning Trees
.25
Directed Spanning Trees
.36
1.3
Minimal Cost Networks
.47
Undirected Graphs
.47
Directed Graphs
.56
1.4
Critical Path Algorithm
.72
1.5
Maximal Flow Problems
.91
Problem Description
.91
Main Results and Algorithm
.94
Examples
.102
1.6
Maximum Matching Problems
.1
J3
Definitions and Problem Description
.113
Matching Algorithm
.118
Examples
. 124
1.7
Other Problems of Graph Theory
.135
Graph Coloring Problem
.136
Shortest Paths Problem
.138
Traveling Salesman Problem
.139
Chapter
2 -
Linear Programming
.143
2.1
Two-Variable Problems
.145
2.2
Geometry of Linear Programming
.159
2.3
Simplex Algorithm for the Standard Maximum Problem
.170
The Simplex Algorithm
.170
Special Behavior
.176
Tableau Method
.184
2.4
Duality and the Standard Minimum Problem
.193
Chapters
-
Further Topics in Linear Programming
.211
3.1
Non-Standard Problems
.213
3.2
Transportation Problem
.227
3.3
Sensitivity Analysis
.242
Discussion of the Problem
.24?.
Matrix-Geometric View of the Simplex Method
.244
Determining Sensitivity of Parameters
.249
xviii
Contents
Chapter
4 -
Markov Chains
.261
4.1
Definitions and Examples
.263
Simulation
.268
4.2
Short-Run Distributions
.274
4.3
First Passage Times
.284
4.4
Classification of States
.292
4.5
Limiting Probabilities
.303
Main Results
.303
Long-Run Discounted Cost
.311
4.6
Absorption Probabilities
.318
Chapter
5 -
Continuous Time Processes
.327
5.1
Poisson
Processes
.327
Definitions and Main Results
.327
Examples
.332
5.2
Birth and Death Processes
.340
Preliminaries
.340
Kolmogorov Equations
.345
5.3
Renewal Processes
.355
Introduction
.355
Short-Run Distributions
.356
Long-Run Results
.360
Renewal Reward Processes
.363
5.4
Queueing Theory
.368
Preliminaries
.368
Simple Poissonian Queues
.370
M/G/l Queue
.376
G/M/l Queue
.380
5.5
Brownian Motion
.386
Relation to Random Walks
.386
Definition and Properties of Standard Brownian Motion
.389
Brownian Motion with Drift
.394
Chapter
6 -
Dynamic Programming
.403
6.1
The Markovian Decision Model
.403
Deterministic Dynamic Programming
.404
Stochastic Dynamic Programming: The Finite Horizon Problem
.406
Examples
.411
6.2
The Finite Horizon Problem
.418
Dynamic Programming Algorithm, Stochastic Case
.421
Examples
.425
6.3
The Discounted Reward Problem
.435
Method of Successive Approximations
.435
Examples
.440
6.4
Policy Improvement
.449
Main Theorem and Policy Improvement Algorithm
.449
Contents xix
Examples
.453
6.5 Optimal
Stopping of a Markov Chain
.461
Dynamic Programming Approach
.461
Linear Programming Approach
.468
6.6
Extended Applications
.476
American Option Problem
.477
Inventory Problem
.483
Conclusion
.494
Appendix A
-
Probability Review
.501
Appendix
В
-
Answers to Selected Exercises
.530
Appendix
С
-
Glossary
oí
Mathematica
Commands
.54/
References
.,.,. 558
Index
.
j
62 |
| adam_txt |
Contents
Chapter
1 - Graph
Theory and Network Analysis
.1
1.1
Definitions and Examples
.2
1.2
Spanning Trees
.24
Undirected Spanning Trees
.25
Directed Spanning Trees
.36
1.3
Minimal Cost Networks
.47
Undirected Graphs
.47
Directed Graphs
.56
1.4
Critical Path Algorithm
.72
1.5
Maximal Flow Problems
.91
Problem Description
.91
Main Results and Algorithm
.94
Examples
.102
1.6
Maximum Matching Problems
.1
J3
Definitions and Problem Description
.113
Matching Algorithm
.118
Examples
. 124
1.7
Other Problems of Graph Theory
.135
Graph Coloring Problem
.136
Shortest Paths Problem
.138
Traveling Salesman Problem
.139
Chapter
2 -
Linear Programming
.143
2.1
Two-Variable Problems
.145
2.2
Geometry of Linear Programming
.159
2.3
Simplex Algorithm for the Standard Maximum Problem
.170
The Simplex Algorithm
.170
Special Behavior
.176
Tableau Method
.184
2.4
Duality and the Standard Minimum Problem
.193
Chapters
-
Further Topics in Linear Programming
.211
3.1
Non-Standard Problems
.213
3.2
Transportation Problem
.227
3.3
Sensitivity Analysis
.242
Discussion of the Problem
.24?.
Matrix-Geometric View of the Simplex Method
.244
Determining Sensitivity of Parameters
.249
xviii
Contents
Chapter
4 -
Markov Chains
.261
4.1
Definitions and Examples
.263
Simulation
.268
4.2
Short-Run Distributions
.274
4.3
First Passage Times
.284
4.4
Classification of States
.292
4.5
Limiting Probabilities
.303
Main Results
.303
Long-Run Discounted Cost
.311
4.6
Absorption Probabilities
.318
Chapter
5 -
Continuous Time Processes
.327
5.1
Poisson
Processes
.327
Definitions and Main Results
.327
Examples
.332
5.2
Birth and Death Processes
.340
Preliminaries
.340
Kolmogorov Equations
.345
5.3
Renewal Processes
.355
Introduction
.355
Short-Run Distributions
.356
Long-Run Results
.360
Renewal Reward Processes
.363
5.4
Queueing Theory
.368
Preliminaries
.368
Simple Poissonian Queues
.370
M/G/l Queue
.376
G/M/l Queue
.380
5.5
Brownian Motion
.386
Relation to Random Walks
.386
Definition and Properties of Standard Brownian Motion
.389
Brownian Motion with Drift
.394
Chapter
6 -
Dynamic Programming
.403
6.1
The Markovian Decision Model
.403
Deterministic Dynamic Programming
.404
Stochastic Dynamic Programming: The Finite Horizon Problem
.406
Examples
.411
6.2
The Finite Horizon Problem
.418
Dynamic Programming Algorithm, Stochastic Case
.421
Examples
.425
6.3
The Discounted Reward Problem
.435
Method of Successive Approximations
.435
Examples
.440
6.4
Policy Improvement
.449
Main Theorem and Policy Improvement Algorithm
.449
Contents xix
Examples
.453
6.5 Optimal
Stopping of a Markov Chain
.461
Dynamic Programming Approach
.461
Linear Programming Approach
.468
6.6
Extended Applications
.476
American Option Problem
.477
Inventory Problem
.483
Conclusion
.494
Appendix A
-
Probability Review
.501
Appendix
В
-
Answers to Selected Exercises
.530
Appendix
С
-
Glossary
oí
Mathematica
Commands
.54/
References
.,.,. 558
Index
.
j
62 |
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| id | DE-604.BV021738903 |
| illustrated | Illustrated |
| index_date | 2024-07-02T15:28:46Z |
| indexdate | 2024-09-10T00:55:55Z |
| institution | BVB |
| isbn | 1574446126 9781574446128 |
| language | English |
| lccn | 2005056055 |
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| publisher | Chapman & Hall |
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| series2 | Monographs and textbooks in pure and applied mathematics |
| spelling | Hastings, Kevin J. 1955- Verfasser (DE-588)172128277 aut Introduction to the mathematics of operations research with Mathematica Kevin J. Hastings 2nd ed. Boca Raton, FL [u.a.] Chapman & Hall 2006 XIX, 567 S. Ill., graph. Darst. 1 CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier Monographs and textbooks in pure and applied mathematics Includes bibliographical references and index Revised and updated to reflect recent advances, Introduction to the Mathematics of Operations Research with Mathematica, Second Edition focuses on the topics of graph theory, linear programming, stochastic processes, and dynamic programming. Integrating technology into the development, this second edition features a CD-ROM with Mathematica, the program used throughout the text. It also offers new material in areas such as simulation, Brownian motion, and famous graph theory problems such as the traveling salesman problem. Further enhancing the interactive approach of the book, the author emphasizes problem solving with longer investigations, self-check questions, problem sets, and an appendix of solutions for selected problems. Mathematica (Computer file) Matemática larpcal Mathematica (Langage de programmation) Mathematica larpcal Pesquisa operacional larpcal Recherche opérationnelle - Mathématiques Mathematik Operations research Mathematics Mathematica Programm (DE-588)4268208-3 gnd rswk-swf Operations Research (DE-588)4043586-6 gnd rswk-swf Operations Research (DE-588)4043586-6 s Mathematica Programm (DE-588)4268208-3 s DE-604 http://www.loc.gov/catdir/enhancements/fy0648/2005056055-d.html Publisher description Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014952298&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hastings, Kevin J. 1955- Introduction to the mathematics of operations research with Mathematica Mathematica (Computer file) Matemática larpcal Mathematica (Langage de programmation) Mathematica larpcal Pesquisa operacional larpcal Recherche opérationnelle - Mathématiques Mathematik Operations research Mathematics Mathematica Programm (DE-588)4268208-3 gnd Operations Research (DE-588)4043586-6 gnd |
| subject_GND | (DE-588)4268208-3 (DE-588)4043586-6 |
| title | Introduction to the mathematics of operations research with Mathematica |
| title_auth | Introduction to the mathematics of operations research with Mathematica |
| title_exact_search | Introduction to the mathematics of operations research with Mathematica |
| title_exact_search_txtP | Introduction to the mathematics of operations research with Mathematica |
| title_full | Introduction to the mathematics of operations research with Mathematica Kevin J. Hastings |
| title_fullStr | Introduction to the mathematics of operations research with Mathematica Kevin J. Hastings |
| title_full_unstemmed | Introduction to the mathematics of operations research with Mathematica Kevin J. Hastings |
| title_short | Introduction to the mathematics of operations research with Mathematica |
| title_sort | introduction to the mathematics of operations research with mathematica |
| topic | Mathematica (Computer file) Matemática larpcal Mathematica (Langage de programmation) Mathematica larpcal Pesquisa operacional larpcal Recherche opérationnelle - Mathématiques Mathematik Operations research Mathematics Mathematica Programm (DE-588)4268208-3 gnd Operations Research (DE-588)4043586-6 gnd |
| topic_facet | Mathematica (Computer file) Matemática Mathematica (Langage de programmation) Mathematica Pesquisa operacional Recherche opérationnelle - Mathématiques Mathematik Operations research Mathematics Mathematica Programm Operations Research |
| url | http://www.loc.gov/catdir/enhancements/fy0648/2005056055-d.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014952298&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT hastingskevinj introductiontothemathematicsofoperationsresearchwithmathematica |