Introduction to stochastic programming:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
New York [u.a.]
Springer
1997
|
| Series: | Springer series in operations research
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Item Description: | Literaturverz. S. 387 - 410 |
| Physical Description: | XIX, 421 S. graph. Darst. |
| ISBN: | 0387982175 |
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MARC
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| 100 | 1 | |a Birge, John R. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Introduction to stochastic programming |c John R. Birge ; François Louveaux |
| 264 | 1 | |a New York [u.a.] |b Springer |c 1997 | |
| 300 | |a XIX, 421 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Springer series in operations research | |
| 500 | |a Literaturverz. S. 387 - 410 | ||
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| 650 | 7 | |a Programmazione (matematica) |2 sbt | |
| 650 | 4 | |a Stochastic programming | |
| 650 | 0 | 7 | |a Stochastische Optimierung |0 (DE-588)4057625-5 |2 gnd |9 rswk-swf |
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Record in the Search Index
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| adam_text | Contents
Preface
vii
Notation xv
I Models
1
1
Introduction and Examples
3
1.1
A Farming Example and the News Vendor Problem
.... 4
1.2
Financial Planning and Control
............... 20
1.3
Capacity Expansion
...................... 28
1.4
Design for Manufacturing Quality
.............. 37
1.5
Other Applications
....................... 42
2
Uncertainty and Modeling Issues
49
2.1
Probability Spaces and Random Variables
......... 49
2.2
Deterministic Linear Programs
................ 51
2.3
Decisions and Stages
...................... 52
2.4
Two-Stage Program with Fixed Recourse
.......... 54
2.5
Random Variables and Risk Aversion
............ 61
2.6
Implicit Representation of the Second Stage
........ 63
2.7
Probabilistic Programming
.................. 64
2.8
Relationship to Other Decision-Making Models
...... 67
2.9
Short Reviews
......................... 73
xii Contents
II
Basic
Properties
81
3 Basic
Properties and Theory
83
3.1
Two-Stage Stochastic Linear Programs with Fixed
Recourse
............................. 84
3.2
Probabilistic or Chance Constraints
............. 103
3.3
Stochastic Integer Programs
................. 109
3.4
Two-Stage Stochastic Nonlinear Programs with Recourse
. 122
3.5
Multistage Stochastic Programs with Recourse
...... 128
4
The Value of Information and the Stochastic Solution
137
4.1
The Expected Value of Perfect Information
........ 137
4.2
The Value of the Stochastic Solution
............ 139
4.3
Basic Inequalities
........................ 140
4.4
The Relationship between EVPI and
VSS
......... 141
4.5
Examples
............................ 144
4.6
Bounds on EVPI and
VSS
.
r
................ 145
III Solution Methods
153
5
Two-Stage Linear Recourse Problems
155
5.1
The L-Shaped Method
..................... 156
5.2
Feasibility
............................ 163
5.3
The Multicut Version
..................... 166
5.4
Bunching and Other Efficiencies
............... 169
5.5
Inner Linearization Methods
................. 174
5.6
Basis Factorization Methods
................. 179
5.7
Special Cases
—
Simple Recourse and Network Problems
. 192
6
Nonlinear
Programming
Approaches to Two-Stage Recourse
Problems
199
6.1
Regularized Decomposition
.................. 199
6.2
The Piecewise Quadratic Form of the L-Shaped Method
. 206
6.3
Methods Based on the Stochastic Program Lagrangian
. . 215
6.4
Nonlinear Programming in Simple Recourse Problems
. . 225
6.5
Other Nonlinear Programming-Based Methods
...... 231
7
Multistage Stochastic Programs
233
7.1
Nested Decomposition Procedures
.............. 234
7.2
Quadratic Nested Decomposition
.............. 244
7.3
Other Approaches to Multiple Stages
............ 251
8
Stochastic Integer Programs
253
8.1
Integer L-Shaped Method
................... 253
8.2
Simple Integer Recourse
.................... 262
Contents xiii
8.3
Binary First-Stage
Variables................. 268
8.4
Other Approaches
....................... 276
IV Approximation and Sampling Methods
283
9
Evaluating and Approximating Expectations
285
9.1
Direct Solutions with Multiple Integration
......... 286
9.2
Discrete Bounding Approximations
............. 288
9.3
Using Bounds in Algorithms
................. 296
9.4
Bounds in Chance-Constrained Problems
.......... 301
9.5
Generalized Bounds
...................... 305
9.6
General Convergence Properties
............... 323
10
Monte Carlo Methods
331
10.1
General Results for Sampled Problems
........... 332
10.2
Using Sampling in the L-Shaped Method
.......... 335
10.3
Stochastic
Quasi-Gradient
Methods
............. 343
10.4
Sampling Extensions: Uses with Analytical and Empirical
Observations
.......................... 349
11
Multistage Approximations
353
11.1
Bounds Based on the Jensen and Edmundson-Madansky
Inequalities
........................... 354
11.2
Bounds Based on Aggregation
................ 359
11.3
Bounds Based on Separable Responses
........... 362
11.4
Bounds for Specific Problem Structures
........... 366
V A Case Study
373
12
Capacity Expansion
375
12.1
Model Development
...................... 376
12.2
Demand Distribution Modeling
............... 382
12.3
Computational Comparisons
................. 383
12.4
Results and Extensions
.................... 383
A Sample Distribution Functions
385
A.I Discrete Random Variables
.................. 385
A.2 Continuous Random Variables
................ 386
References
387
Author Index
411
Subject Index
415
The aim of stochastic programming is to find optimal decisions in
problems that involve uncertain data. This field is currently devel¬
oping rapidly with contributions from many disciplines including
operations research, mathematics, and probability. Conversely, it
Ц,
being applied in a wide variety of subjects ranging from agriculture
j
to financial planning and from industrial engineering to computer
networks.
This textbook provides a first course in stochastic programmingsijir
able for students with a basic knowledge of linear programming];
elementary analysis, and probability. The authors aim to
presénf
4
broad overview of the main themes and methods of the subject.
Й?с
prime goal is to help students develop an intuition on how to model;:
uncertainty into mathematical problems, which changes uncertainty
brings into the decision process, and what techniques help to man¬
age uncertainty in solving the problems.
The first chapters introduce some worked examples of stochastic
programming and demonstrate how a stochastic model is formally
built. Subsequent chapters develop the properties of stochastic pro¬
grams and the basic solution techniques used to solve them. Three
chapters cover approximation and sampling techniques, and the
final chapter presents a case study in depth.
A wide range of students from operations research, industrial engi¬
neering, and related disciplines will find this a well-paced and
wide-ranging introduction to this subject.
|
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| indexdate | 2024-07-09T18:12:09Z |
| institution | BVB |
| isbn | 0387982175 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007797162 |
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| spelling | Birge, John R. Verfasser aut Introduction to stochastic programming John R. Birge ; François Louveaux New York [u.a.] Springer 1997 XIX, 421 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer series in operations research Literaturverz. S. 387 - 410 Processi stocastici sbt Programmazione (matematica) sbt Stochastic programming Stochastische Optimierung (DE-588)4057625-5 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Stochastische Optimierung (DE-588)4057625-5 s DE-604 Louveaux, François Verfasser aut Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007797162&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007797162&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Birge, John R. Louveaux, François Introduction to stochastic programming Processi stocastici sbt Programmazione (matematica) sbt Stochastic programming Stochastische Optimierung (DE-588)4057625-5 gnd |
| subject_GND | (DE-588)4057625-5 (DE-588)4123623-3 |
| title | Introduction to stochastic programming |
| title_auth | Introduction to stochastic programming |
| title_exact_search | Introduction to stochastic programming |
| title_full | Introduction to stochastic programming John R. Birge ; François Louveaux |
| title_fullStr | Introduction to stochastic programming John R. Birge ; François Louveaux |
| title_full_unstemmed | Introduction to stochastic programming John R. Birge ; François Louveaux |
| title_short | Introduction to stochastic programming |
| title_sort | introduction to stochastic programming |
| topic | Processi stocastici sbt Programmazione (matematica) sbt Stochastic programming Stochastische Optimierung (DE-588)4057625-5 gnd |
| topic_facet | Processi stocastici Programmazione (matematica) Stochastic programming Stochastische Optimierung Lehrbuch |
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