Postoptimal analyses, parametric programming, and related topics: degeneracy, multicriteria decision making, redundancy
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German English |
| Published: |
Berlin [u.a.]
<<de>> Gruyter
1995
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | XXV, 437 S. graph. Darst. |
| ISBN: | 3110140608 |
Staff View
MARC
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| 245 | 1 | 0 | |a Postoptimal analyses, parametric programming, and related topics |b degeneracy, multicriteria decision making, redundancy |c Tomas Gal |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b <<de>> Gruyter |c 1995 | |
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Record in the Search Index
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|---|---|
| adam_text | Tomas Gal
Postoptimal Analyses,
Parametric Programming,
and Related Topics
Degeneracy, Multicriteria Decision Making,
Redundancy
Second Edition
W
DE
G
Walter de Gruyter • Berlin • New York 1995
Contents
Foreword VII
Preface to the (second) English edition IX
Preface to the (first) English edition XI
Preface to the German edition XIII
List of symbols XVII
Chapter one
Basic concepts and notation in linear programming 1
1-1 The simplex tableau 4
1-2 Geometric meaning 11
1-3 Types of solution vectors 11
1-4 The simplex method 14
1-5 The dual problem 19
1-6 The dual simplex method 22
1-7 Degenerate solutions 23
I Abridged mathematical presentation 27
References 35
Chapter two
Suboptimality, redundancy and degeneracy graphs 37
2-1 Suboptimal solutions 39
2-1-1 Influence of a single nonbasic variable 40
2-1-2 Influence of several nonbasic variables 43
2-1-3 Influence of certain values of nonbasic variables 45
2-1-4 Some remarks on the geometric meaning of slack variables 49
2-2 Redundant constraints 50
2-3 Degenerate convex polyhedrons and degeneracy graphs 54
II Abridged mathematical presentation 65
II-l Suboptimality 65
II-2 Redundancy 68
II-2-1 Theoretical part ; 68
II-2-2 An algorithm for determining redundant constraints 71
II-3 Degenerate polytopes and degeneracy graphs 73
References 79
XXII Contents
Chapter three
Sensitivity analysis with respect to b
Changing the right hand side without basis-exchange 81
3-1 Sensitivity analysis with respect to a single component b; of the
right hand side b 83
3-1-1 Geometric meaning of a single parameter 88
3-2 Sensitivity analysis with respect to several components of the
right-hand side depending on a scalar parameter 91
3-3 Multiparametric sensitivity analysis: Changing several
components of the right-hand side depending on several
parameters (on a vector parameter) 93
III Abridged mathematical presentation 99
III-l General considerations 99
III-2 Special cases 101
III-3 Approximation region 105
References 107
Chapter four
Linear parametric programming with respect to b
Changing the right-hand side with basis exchange 109
4-1 Linear scalar parametric programming
Changing a single component of the right-hand side with basis
exchange I l l
4-2 Vector parametric linear programming with respect to the
right-hand side
Changing several components of the right-hand side with basis
exchange 120
4-2-1 Dependence on a scalar parameter 120
4-2-2 Description of systematic parametrization for a scalar parameter 129
4-2-3 Dependence on several parameters (on a vector parameter) 131
4-2-4 Degeneracy 147
4-3 Homogeneous multiparametric linear programming 155
4-3-1 Problem (F) 156
4-3-2 Problem (FD) 163
4-4 Sensitivity analysis and shadow prices Under (primal)
degeneracy 167
4-4-1 Sensitivity analysis 167
4-4-2 Shadow prices 171
IV Abridged mathematical presentation 177
IV-1 Basic definitions and theorems 178
Contents XXIII
IV-2 The task 185
IV-3 A solution procedure 185
IV-3-1 The application of the algorithm to the given multiparametric
linear programming problem 186
IV-4 Some modifications of the simplex algorithm 189
IV-4-1 Linear programs with sign-unrestricted variables 189
IV-4-2 A special form of the additional restrictions 190
IV-4-3 Determination of the feasible bases in the auxiliary problems 192
IV-5 Special cases 193
IV-5-1 Linear parametric programming with a scalar parameter 193
IV-6 Homogeneous multiparametric linear programming 194
IV-6-1 Problem (F) 194
IV-6-2 Problem (FD) 199
IV-7 Sensitivity analysis and shadow prices under degeneracy 201
IV-7-1 Sensitivity analysis 201
IV-7-2 Shadow prices 203
References 207
Chapter five
Sensitivity analysis with respect to c
Changing cost coefficients without basis exchange 209
5-1 Changing single cost coefficients 212
5-2 Changing several cost coefficients 216
5-2-1 Dependence on a scalar parameter 216
5-2-2 Dependence on several parameters (on a vector parameter) 219
V Abridged mathematical presentation 223
V-l Special cases 226
V-2 Approximation region 230
References 231
Chapter six
Linear parametric programming with respect to c
Changing cost coefficents with basis exchange 233
6-1 Changing several cost coefficients depending on a scalar
parameter with basis exchange 235
6-2 Geometric meaning 243
6-3 Dependence on several parameters (on a vector parameter) 245
6-4 Homogeneous multiparametric linear programming 252
VI Abridged mathematical presentation 261
XXIV Contents
VI-1 A solution procedure 262
VI-2 Description of systematic parametrization with a scalar
parameter 263
VI-3 Homogeneous multiparametric linear programming 266
VI-3-1 Problem (H) 266
VI-3-2 Problem (HD) 269
References 271
Chapter seven
RIM parametric linear programming
Simultaneous changing of the right-hand side and of the cost
coefficients 273
7-1 Dependence on a scalar parameter 275
7-2 Dependence on several parameters (on a vector parameter)
RIM-multiparametric linear programming with dependent
parameters 285
VII Abridged mathematical presentation , 299
VIM A solution procedure 302
VII-2 A special case 303
References 307
Chapter eight
Sensitivity analysis with respect to the elements of the
technological matrix A 309
VIII Abridged mathematical presentation 319
VIII-1 Changing a column of matrix A 320
VIII-2 Definition of a critical region 322
VIII-3 Basis exchange 325
VIII-4 Changing a row of matrix A 327
References 333
Chapter nine
Multicriteria linear programming 335
9-1 A method for determining the set of all efficient solutions 340
9-2 Nonessential objective functions 349
9-3 Postefficient analysis 352
IX Abridged mathematical presentation 353
Contents XXV
DC-1 Introduction 353
IX-2 Theoretical part 353
IX-3 A solution procedure 359
IX-4 Special cases 361
IX-4-1 Dual degeneracy 361
K-4-2 Set E is not compact 361
References 363
Chapter ten
Possible applications of sensitivity analysis and linear
parametric programming 365
10-1 Changing the values of basic variables 367
10-1-1 Changing the values of the basic slack variables 367
10-1-2 Changing the values of basic real variables 368
10-1-3 Nonbasic variables and the right-hand side 368
10-2 Inconsistency of the constraint set 369
10-3 Some remarks on redundancy and parametrization 373
References 379
Annotated bibliography 381
Bibliography 385
Index 433
|
| any_adam_object | 1 |
| author | Gál, Tomáš 1926-2013 |
| author_GND | (DE-588)119016117 |
| author_facet | Gál, Tomáš 1926-2013 |
| author_role | aut |
| author_sort | Gál, Tomáš 1926-2013 |
| author_variant | t g tg |
| building | Verbundindex |
| bvnumber | BV009884854 |
| callnumber-first | T - Technology |
| callnumber-label | T57 |
| callnumber-raw | T57.95.G3413 1995 |
| callnumber-search | T57.95.G3413 1995 |
| callnumber-sort | T 257.95 G3413 41995 |
| callnumber-subject | T - General Technology |
| classification_rvk | QH 425 SK 870 |
| ctrlnum | (OCoLC)30437345 (DE-599)BVBBV009884854 |
| dewey-full | 658.4/033 658.4/03320 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 658 - General management |
| dewey-raw | 658.4/033 658.4/033 20 |
| dewey-search | 658.4/033 658.4/033 20 |
| dewey-sort | 3658.4 233 |
| dewey-tens | 650 - Management and auxiliary services |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV009884854 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:42:34Z |
| institution | BVB |
| isbn | 3110140608 |
| language | German English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006545619 |
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| physical | XXV, 437 S. graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
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| publisher | <<de>> Gruyter |
| record_format | marc |
| spelling | Gál, Tomáš 1926-2013 Verfasser (DE-588)119016117 aut Betriebliche Entscheidungsprobleme, Sensitivitätsanalysen und pa rametrische Programmierung Postoptimal analyses, parametric programming, and related topics degeneracy, multicriteria decision making, redundancy Tomas Gal 2. ed. Berlin [u.a.] <<de>> Gruyter 1995 XXV, 437 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturangaben Prise de décision ram Programmation linéaire ram Decision making Linear programming Sensitivitätsanalyse (DE-588)4129730-1 gnd rswk-swf Lineare parametrische Optimierung (DE-588)4167707-9 gnd rswk-swf Operations Research (DE-588)4043586-6 gnd rswk-swf Unternehmen (DE-588)4061963-1 gnd rswk-swf Entscheidung (DE-588)4014904-3 gnd rswk-swf Lineare Optimierung (DE-588)4035816-1 gnd rswk-swf Parametrische Optimierung (DE-588)4044615-3 gnd rswk-swf Lineare parametrische Optimierung (DE-588)4167707-9 s Sensitivitätsanalyse (DE-588)4129730-1 s DE-604 Unternehmen (DE-588)4061963-1 s Entscheidung (DE-588)4014904-3 s Parametrische Optimierung (DE-588)4044615-3 s 1\p DE-604 Lineare Optimierung (DE-588)4035816-1 s Operations Research (DE-588)4043586-6 s 2\p DE-604 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006545619&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Gál, Tomáš 1926-2013 Postoptimal analyses, parametric programming, and related topics degeneracy, multicriteria decision making, redundancy Prise de décision ram Programmation linéaire ram Decision making Linear programming Sensitivitätsanalyse (DE-588)4129730-1 gnd Lineare parametrische Optimierung (DE-588)4167707-9 gnd Operations Research (DE-588)4043586-6 gnd Unternehmen (DE-588)4061963-1 gnd Entscheidung (DE-588)4014904-3 gnd Lineare Optimierung (DE-588)4035816-1 gnd Parametrische Optimierung (DE-588)4044615-3 gnd |
| subject_GND | (DE-588)4129730-1 (DE-588)4167707-9 (DE-588)4043586-6 (DE-588)4061963-1 (DE-588)4014904-3 (DE-588)4035816-1 (DE-588)4044615-3 |
| title | Postoptimal analyses, parametric programming, and related topics degeneracy, multicriteria decision making, redundancy |
| title_alt | Betriebliche Entscheidungsprobleme, Sensitivitätsanalysen und pa rametrische Programmierung |
| title_auth | Postoptimal analyses, parametric programming, and related topics degeneracy, multicriteria decision making, redundancy |
| title_exact_search | Postoptimal analyses, parametric programming, and related topics degeneracy, multicriteria decision making, redundancy |
| title_full | Postoptimal analyses, parametric programming, and related topics degeneracy, multicriteria decision making, redundancy Tomas Gal |
| title_fullStr | Postoptimal analyses, parametric programming, and related topics degeneracy, multicriteria decision making, redundancy Tomas Gal |
| title_full_unstemmed | Postoptimal analyses, parametric programming, and related topics degeneracy, multicriteria decision making, redundancy Tomas Gal |
| title_short | Postoptimal analyses, parametric programming, and related topics |
| title_sort | postoptimal analyses parametric programming and related topics degeneracy multicriteria decision making redundancy |
| title_sub | degeneracy, multicriteria decision making, redundancy |
| topic | Prise de décision ram Programmation linéaire ram Decision making Linear programming Sensitivitätsanalyse (DE-588)4129730-1 gnd Lineare parametrische Optimierung (DE-588)4167707-9 gnd Operations Research (DE-588)4043586-6 gnd Unternehmen (DE-588)4061963-1 gnd Entscheidung (DE-588)4014904-3 gnd Lineare Optimierung (DE-588)4035816-1 gnd Parametrische Optimierung (DE-588)4044615-3 gnd |
| topic_facet | Prise de décision Programmation linéaire Decision making Linear programming Sensitivitätsanalyse Lineare parametrische Optimierung Operations Research Unternehmen Entscheidung Lineare Optimierung Parametrische Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006545619&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT galtomas betrieblicheentscheidungsproblemesensitivitatsanalysenundparametrischeprogrammierung AT galtomas postoptimalanalysesparametricprogrammingandrelatedtopicsdegeneracymulticriteriadecisionmakingredundancy |