Introduction to stochastic programming:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY [u.a.]
Springer
2011
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Springer series in operations research and financial engineering
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | Literaturverz. S.: 451 - 469 |
| Beschreibung: | XXV, 485 S. graph. Darst. |
| ISBN: | 9781461402367 9781461402374 |
Internformat
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| 100 | 1 | |a Birge, John R. |d 1956- |e Verfasser |0 (DE-588)170238830 |4 aut | |
| 245 | 1 | 0 | |a Introduction to stochastic programming |c John R. Birge ; François Louveaux |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York, NY [u.a.] |b Springer |c 2011 | |
| 300 | |a XXV, 485 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 and financial engineering | |
| 500 | |a Literaturverz. S.: 451 - 469 | ||
| 650 | 0 | 7 | |a Stochastische Optimierung |0 (DE-588)4057625-5 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4123623-3 |a Lehrbuch |2 gnd-content | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-022650543 | ||
Datensatz im Suchindex
| _version_ | 1804145818550140928 |
|---|---|
| adam_text | Contents
Parti
Models
1
Introduction
and Examples
..................................... 3
1.1
A Farming Example and the News Vendor Problem
.............. 4
a. The farmer s problem
................................. 4
b. A scenario representation
............................. 6
с
General model formulation
............................ 10
d. Continuous random variables
.......................... 11
e. The news vendor problem
............................. 15
1.2
Financial Planning and Control
............................... 20
1.3
Capacity Expansion
......................................... 28
1.4
Design for Manufacturing Quality
............................. 35
1.5
A Routing Example
......................................... 40
a. Presentation
......................................... 40
b. Wait-and-see solutions
................................ 42
с
Expected value solution
............................... 43
d. Recourse solution
.................................... 44
e. Other random variables
............................... 46
f. Chance-constraints
................................... 47
1.6
Other Applications
......................................... 48
2
Uncertainty and Modeling Issues
................................ 55
2.1
Probability Spaces and Random Variables
...................... 55
2.2
Deterministic Linear Programs
............................... 57
2.3
Decisions and Stages
........................................ 57
2.4
Two-Stage Program with Fixed Recourse
....................... 59
a. Fixed distribution pattern, fixed demand,
r,·,Vj,tij stochastic
................................... 62
b. Fixed distribution pattern, uncertain demand
............. 63
с
Uncertain demand, variable distribution pattern
........... 64
d. Stages versus periods; Two-stage versus multistage
....... 65
xvi
CoMents
2.5
Random Variables and Risk Aversion
.......................... 66
2.6
Implicit Representation of the Second Stage
.................... 68
a. A closed form expression is available for ¿2(x)
.......... 69
b. For a given
χ
,
£¿(x)
is computable
.................... 70
2.7
Probabilistic Programming
................................... 71
a. Deterministic linear equivalent: a direct case
............. 71
b. Deterministic linear equivalent: an indirect case
........... 72
с
Deterministic nonlinear equivalent: the case of random
constraint coefficients
................................ 73
2.8
Modeling Exercise
......................................... 74
a. Presentation
......................................... 74
b. Discussion of solutions
............................... 76
2.9
Alternative Characterizations and Robust Formulations
........... 84
2.10
Relationship to Other Decision-Making Models
................. 87
a. Statistical decision theory and decision analysis
.......... 87
b. Dynamic programming and Markov decision processes
.... 89
с
Machine learning and online optimization
................ 90
d. Optimal stochastic control
............................. 91
e. Summary
........................................... 93
2.11
Short Reviews
............................................. 94
a. Linear programming
................................. 94
b. Duality for linear programs
............................ 96
с
Nonlinear programming and convex analysis
............. 97
Part II Basic Properties
3
Basic Properties and Theory
....................................103
3.1
Two-Stage Stochastic Linear Programs with Fixed Recourse
......103
a. Formulation
.........................................103
b. Discrete random variables
.............................105
с
General cases
.......................................109
d. Special cases: relatively complete, complete,
and simple recourse
..................................113
e. Optimality conditions and duality
.......................115
f. Stability and nonanticipativity
.........................118
3.2
Probabilistic or Chance Constraints
...........................124
a. General case
........................................124
b. Probabilistic constraints with discrete random variables
___130
3.3
Stochastic Integer Programs
..................................135
a. Recourse problems
...................................135
b. Simple integer recourse
...............................140
с
Probabilistic constraints
...............................146
3.4
Multistage Stochastic Programs with Recourse
..................149
3.5
Stochastic Nonlinear Programs with Recourse
..................156
Contents
xv¡¡
4
The Value of Information and the Stochastic Solution
..............163
4.1
The Expected Value of Perfect Information
.....................163
4.2
The Value of the Stochastic Solution
...........................165
4.3
Basic Inequalities
..........................................166
4.4
The Relationship between EVPI and
VSS
.....................167
a. EVPI
= 0
and
VSS
φ
0..............................168
b. VSS = 0 and EVPI
φ
0..............................169
4.5
Examples.................................................
170
4.6
Bounds on EVPI and
VSS
..................................171
Partili
Solution Methods
5
Two-Stage Recourse Problems
...................................181
5.1
The
L
-Shaped Method
......................................182
a. Optimality cuts
......................................184
b. Feasibility cuts
......................................191
с
Proof of convergence
.................................196
d. The multicut version
.................................198
5.2
Regularized Decomposition
..................................202
5.3
The Piecewise Quadratic Form of the
L
-shaped Methods
.........210
5.4
Bunching and Other Efficiencies
..............................217
a. Full decomposability
.................................218
b. Bunching
...........................................219
5.5
Basis Factorization and Interior Point Methods
..................222
5.6
Inner Linearization Methods and Special Structures
..............237
5.7
Simple and Network Recourse Problems
.......................242
5.8
Methods Based on the Stochastic Program Lagrangian
...........253
5.9
Additional Methods and Complexity Results
....................262
6
Multistage Stochastic Programs
.................................265
6.1
Nested Decomposition Procedures
............................266
6.2
Quadratic Nested Decomposition
.............................276
6.3
Block Separability and Special Structure
.......................282
6.4
Lagrangian-Based Methods for Multiple Stages
.................284
7
Stochastic Integer Programs
.....................................289
7.1
Stochastic Integer Programs and LP-Relaxation
.................289
7.2
First-stage Binary Variables
..................................291
a. Improved optimality cuts
..............................294
b. Example with continuous random variables
..............299
7.3
Second-stage Integer Variables
...............................302
a. Looking in the space of tenders
........................303
b. Discontinuity points
..................................305
с
Algorithm
..........................................306
7.4
Reformulation
.............................................312
a. Difficulties of reformulation in stochastic integer programs
.312
Contents
XVIII
b.
Disjunctive
cuts
.....................................314
c.
First-stage dependence
................................316
d.
An algorithm
........................................317
7.5
Simple Integer Recourse
.....................................319
a.
χ
restricted to be integer
.............................322
b. The case where
5 = 1, %
not integral
..................325
7.6
Cuts Based on Branching in the Second Stage
...................326
a. Feasibility cuts
......................................326
b. Optimality cuts
......................................329
7.7
Extensive Forms and Decomposition
..........................331
7.8
Short Reviews
.............................................334
a. Branch-and-bound
...................................334
b. A
simple example of valid inequalities
..................335
c. Disjunctive cuts
.....................................336
Part IV Approximation and Sampling Methods
8
Evaluating and Approximating Expectations
......................341
8.1
Direct Solutions with Multiple Integration
......................342
8.2
Discrete Bounding Approximations
...........................346
8.3
Using Bounds in Algorithms
.................................352
8.4
Bounds in Chance-Constrained Problems
.......................357
8.5
Generalized Bounds
........................................363
a. Extensions of basic bounds
............................363
b. Bounds based on separable functions
....................367
c. General-moment bounds
..............................372
8.6
General Convergence Properties
..............................381
9
Monte Carlo Methods
..........................................389
9.1
Sample Average Approximation and Importance Sampling
in the
L
-Shaped Method
....................................390
9.2
Stochastic Decomposition
...................................395
9.3
Stochastic
Quasi-Gradient
Methods
...........................399
9.4
Sampling Methods for Probabilistic Constraints and
Quantités
.....404
9.5
General Results for Sample Average Approximation and
Sequential Sampling
........................................409
10
Multistage Approximations
.....................................417
10.1
Extensions of the Jensen and Edmundson-Madansky Inequalities
.. 418
10.2
Bounds Based on Aggregation
................................422
10.3
Scenario Generation and Distribution Fitting
....................426
10.4
Multistage Sampling and Decomposition Methods
...............432
10.5
Approximate Dynamic Programming and Special Cases
..........436
a. Network revenue management
.........................438
b. Vehicle allocation problems
...........................439
с
Piecewise-linear separable bounds
......................441
Contents xix
d.
Nonlinear bounds and a production planning example
......444
e. Extensions
..........................................446
Sample Distribution Functions
.......................................449
A.I Discrete Random Variables
..................................449
A.2 Continuous Random Variables
................................450
References
.........................................................451
Author Index
......................................................471
Subject Index
......................................................477
John R.
Birge
·
François Louveaux
Introduction to Stochastic Programming
Second Edition
The aim of stochastic programming is to find optimal decisions in problems which
involve uncertain data. This field is currently developing rapidly with contributions from
many disciplines including operations research, mathematics, and probability. At the
same time, it is now being applied in a wide variety of subjects ranging from agriculture
to financial planning and from industrial engineering to computer networks. This
textbook provides a first course in stochastic programming suitable for students with
a basic knowledge of linear programming, elementary analysis, and probability. The
authors aim to present a broad overview of the main themes and methods of the subject.
Its prime goal is to help students develop an intuition on how to model uncertainty into
mathematical problems, what uncertainty changes bring to the decision process, and
what techniques help to manage uncertainty in solving the problems.
In this extensively updated new edition there is more material on methods and examples
including several new approaches for discrete variables, new results on risk measures
in modeling and Monte Carlo sampling methods, a new chapter on relationships to
other methods including approximate dynamic programming, robust optimization
and online methods.The book is highly illustrated with chapter summaries and many
examples and exercises. Students, researchers and practitioners in operations research
and the optimization area will find it particularly of interest.
Review of Rrst
Edition.· ^
discussion on modeling issues, the hrge number ofexamples used
to
illustrate
the material, and the breadth of the coverage make Introduction to Stochastic
Programming an ideal textbook for the
àrea.
(Interfaces,
1998)
About the Author
John R. Birge, is a Jerry W. and Carol Lee Levin Professor of Operations Management
at the University of Chicago Booth School of Business.
François
Louveaux is a Professor at the University of Namur(FUNDP) in the Department
of Business Administration.
|
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| author_GND | (DE-588)170238830 (DE-588)170060810 |
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| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 2. ed. |
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| indexdate | 2024-07-09T23:25:30Z |
| institution | BVB |
| isbn | 9781461402367 9781461402374 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-022650543 |
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| spelling | Birge, John R. 1956- Verfasser (DE-588)170238830 aut Introduction to stochastic programming John R. Birge ; François Louveaux 2. ed. New York, NY [u.a.] Springer 2011 XXV, 485 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer series in operations research and financial engineering Literaturverz. S.: 451 - 469 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 1949- Verfasser (DE-588)170060810 aut Erscheint auch als Online-Ausgabe 10.1007/978-1-4614-0237-4 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022650543&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022650543&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Birge, John R. 1956- Louveaux, François 1949- Introduction to 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 | Stochastische Optimierung (DE-588)4057625-5 gnd |
| topic_facet | Stochastische Optimierung Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022650543&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022650543&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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