Linear programming: 1. Introduction Buch.
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
1997
|
| Schriftenreihe: | Springer series in operations research
|
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 361 - 419 |
| Beschreibung: | XXXVIII, 435 S. graph. Darst. 25 cm |
| ISBN: | 0387948333 |
Internformat
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| 100 | 1 | |a Dantzig, George Bernard |d 1914-2005 |e Verfasser |0 (DE-588)124788734 |4 aut | |
| 245 | 1 | 0 | |a Linear programming |n 1. Introduction Buch. |c George B. Dantzig ; Mukund N. Thapa |
| 264 | 1 | |a New York [u.a.] |b Springer |c 1997 | |
| 300 | |a XXXVIII, 435 S. |b graph. Darst. |c 25 cm | ||
| 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. 361 - 419 | ||
| 700 | 1 | |a Thapa, Mukund Narain |e Verfasser |0 (DE-588)124788696 |4 aut | |
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Datensatz im Suchindex
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CONTENTS
FOREWORD
XXI
PREFACE
XXXIII
DEFINITION
OF
SYMBOLS
XXXVII
1
THE
LINEAR
PROGRAMMING
PROBLEM
1
1.1
SOME
SIMPLE
EXAMPLES
.
2
1.2
MATHEMATICAL
STATEMENT
.
7
1.3
FORMULATING
LINEAR
PROGRAMS
.
8
1.3.1
THE
COLUMN
(RECIPE/ACTIVITY)
APPROACH
.
9
1.3.2
THE
ROW
(MATERIAL
BALANCE)
APPROACH
.
11
1.4
EXAMPLES
OF
MODEL
FORMULATION
.
12
1.4.1
PRODUCT
MIX
PROBLEM
(COLUMN
APPROACH)
.
12
1.4.2
PRODUCT
MIX
PROBLEM
(ROW
APPROACH)
.
15
1.4.3
A
SIMPLE
WAREHOUSE
PROBLEM
.
16
1.4.4
ON-THE-JOB
TRAINING
.
18
1.5
BOUNDS
.
21
1.6
AXIOMS
.
22
1.7
NOTES
&
SELECTED
BIBLIOGRAPHY
.
23
1.8
PROBLEMS
.
25
2
SOLVING
SIMPLE
LINEAR
PROGRAMS
35
2.1
TWO-VARIABLE
PROBLEM
.
35
2.2
TWO-EQUATION
PROBLEM
.
37
2.2.1
GRAPHICAL
SOLUTION
.
38
2.2.2
THE
DUAL
LINEAR
PROGRAM
.
41
2.3
FOURIER-MOTZKIN
ELIMINATION
.
43
2.3.1
ILLUSTRATION
OF
THE
FME
PROCESS
.
44
2.3.2
THE
FOURIER-MOTZKIN
ELIMINATION
ALGORITHM
.
46
2.3.3
FOURIER-MOTZKIN
ELIMINATION
THEORY
.
47
2.4
INFEASIBILITY
THEOREM
.
52
2.5
NOTES
&
SELECTED
BIBLIOGRAPHY
.
53
X
CONTENTS
2.6
PROBLEMS
.
54
3
THE
SIMPLEX
METHOD
63
3.1
GRAPHICAL
ILLUSTRATION
.
64
3.2
THE
SIMPLEX
ALGORITHM
.
64
3.2.1
CANONICAL
FORM
AND
BASIC
VARIABLES
.
64
3.2.2
IMPROVING
A
NONOPTIMAL
BASIC
FEASIBLE
SOLUTION
.
68
3.2.3
THE
SIMPLEX
ALGORITHM
.
71
3.2.4
THEORY
BEHIND
THE
SIMPLEX
ALGORITHM
.
73
3.3
SIMPLEX
METHOD
.
76
3.3.1
THE
METHOD
.
77
3.3.2
PHASE
I/PHASE
II
ALGORITHM
.
78
3.3.3
THEORY
BEHIND
PHASE
I
.
81
3.4
BOUNDED
VARIABLES
.
83
3.5
REVISED
SIMPLEX
METHOD
.
89
3.5.1
MOTIVATION
.
89
3.5.2
REVISED
SIMPLEX
METHOD
ILLUSTRATED
.
92
3.5.3
REVISED
SIMPLEX
ALGORITHM
.
93
3.5.4
COMPUTATIONAL
REMARKS
.
96
3.6
NOTES
&
SELECTED
BIBLIOGRAPHY
.
97
3.7
PROBLEMS
.
98
4
INTERIOR-POINT
METHODS
113
4.1
BASIC
CONCEPTS
.
115
4.2
PRIMAL
AFFINE
/
DIKIN
'
S
METHOD
.
118
4.3
INITIAL
SOLUTION
.
121
4.4
NOTES
&
SELECTED
BIBLIOGRAPHY
.
122
4.5
PROBLEMS
.
124
5
DUALITY
129
5.1
DUAL
AND
PRIMAL
PROBLEMS
.
129
5.1.1
VON
NEUMANN
SYMMETRIC
FORM
.
129
5.1.2
TUCKER
DIAGRAM
.
130
5.1.3
DUALS
OF
MIXED
SYSTEMS
.
130
5.1.4
THE
DUAL
OF
THE
STANDARD
FORM
.
132
5.1.5
PRIMAL-DUAL
FEASIBLE-INFEASIBLE
CASES
.
133
5.2
DUALITY
THEOREMS
.
134
5.3
COMPLEMENTARY
SLACKNESS
.
135
5.4
OBTAINING
A
DUAL
SOLUTION
.
136
5.5
NOTES
&
SELECTED
BIBLIOGRAPHY
.
138
5.6
PROBLEMS
.
139
CONTENTS
XI
6
EQUIVALENT
FORMULATIONS
145
6.1
RESTRICTED
VARIABLES
.
145
6.2
UNRESTRICTED
(FREE)
VARIABLES
.
146
6.3
ABSOLUTE
VALUES
.
147
6.4
GOAL
PROGRAMMING
.
150
6.5
MINIMIZING
THE
MAXIMUM
OF
LINEAR
FUNCTIONS
.
152
6.6
CURVE
FITTING
.
154
6.7
PIECEWISE
LINEAR
APPROXIMATIONS
.
157
6.7.1
CONVEX/CONCAVE
FUNCTIONS
.
157
6.7.2
PIECEWISE
CONTINUOUS
LINEAR
FUNCTIONS
.
159
6.7.3
SEPARABLE
PIECEWISE
CONTINUOUS
LINEAR
FUNCTIONS
.
160
6.8
NOTES
&
SELECTED
BIBLIOGRAPHY
.
162
6.9
PROBLEMS
.
162
7
PRICE
MECHANISM
AND
SENSITIVITY
ANALYSIS
171
7.1
THE
PRICE
MECHANISM
OF
THE
SIMPLEX
METHOD
.
172
7.1.1
MARGINAL
VALUES
OR
SHADOW
PRICES
.
173
7.1.2
ECONOMIC
INTERPRETATION
OF
THE
SIMPLEX
METHOD
.
174
7.1.3
THE
MANAGER
OF
A
MACHINE
TOOL
PLANT
.
175
7.1.4
THE
AMBITIOUS
INDUSTRIALIST
.
181
7.1.5
SIGN
CONVENTION
ON
PRICES
.
183
7.2
INTRODUCING
A
NEW
VARIABLE
.
184
7.3
INTRODUCING
A
NEW
CONSTRAINT
.
186
7.4
COST
RANGING
.
188
7.5
CHANGES
IN
THE
RIGHT-HAND
SIDE
.
190
7.6
CHANGES
IN
THE
COEFFICIENT
MATRIX
.
192
7.7
THE
SUBSTITUTION
EFFECT
OF
NONBASIC
ACTIVITIES
ON
BASIC
ACTIVITIES
.
198
7.8
NOTES
AND
SELECTED
BIBLIOGRAPHY
.
199
7.9
PROBLEMS
.
199
8
TRANSPORTATION
AND
ASSIGNMENT
PROBLEM
205
8.1
THE
CLASSICAL
TRANSPORTATION
PROBLEM
.
205
8.1.1
MATHEMATICAL
STATEMENT
.
206
8.1.2
PROPERTIES
OF
THE
SYSTEM
.
206
8.2
STANDARD
TRANSPORTATION
ARRAY
.
212
8.3
FINDING
AN
INITIAL
SOLUTION
.
214
8.3.1
TRIANGULARITY
RULE
.
214
8.3.2
THE
LEAST
REMAINING
COST
RULE
.
217
8.3.3
VOGEL
'
S
APPROXIMATION
METHOD
.
217
8.3.4
RUSSEL
'
S
APPROXIMATION
METHOD
.
218
8.3.5
COST
PREPROCESSING
.
219
8.4
FAST
SIMPLEX
ALGORITHM
FOR
THE
TRANSPORTATION
PROBLEM
.
222
8.4.1
SIMPLEX
MULTIPLIERS,
OPTIMALITY,
AND
THE
DUAL
.
222
XII
CONTENTS
8.4.2
FINDING
A
BETTER
BASIC
SOLUTION
.
224
8.4.3
ILLUSTRATION
OF
THE
SOLUTION
PROCESS
.
225
8.5
THE
ASSIGNMENT
PROBLEM
.
229
8.6
EXCESS
AND
SHORTAGE
.
233
8.6.1
MATHEMATICAL
STATEMENT
.
234
8.6.2
PROPERTIES
OF
THE
SYSTEM
.
236
8.6.3
CONVERSION
TO
THE
CLASSICAL
FORM
.
236
8.6.4
SIMPLEX
MULTIPLIERS
AND
REDUCED
COSTS
.
238
8.7
PRE-FIXED
VALUES
AND
INADMISSIBLE
SQUARES
.
239
8.8
THE
CAPACITATED
TRANSPORTATION
PROBLEM
.
240
8.9
NOTES
&
SELECTED
BIBLIOGRAPHY
.
244
8.10
PROBLEMS
.
245
9
NETWORK
FLOW
THEORY
253
9.1
TERMINOLOGY
.
253
9.2
FLOWS
AND
ARC-CAPACITIES
.
258
9.3
AUGMENTING
PATH
ALGORITHM
FOR
MAXIMAL
FLOW
.
.
262
9.4
CUTS
IN
A
NETWORK
.
275
9.5
SHORTEST
ROUTE
.
277
9.6
MINIMAL
SPANNING
TREE
.
282
9.7
MINIMUM
COST-FLOW
PROBLEM
.
286
9.8
THE
NETWORK
SIMPLEX
METHOD
.
288
,9.9
THE
BOUNDED
VARIABLE
PROBLEM
.
299
9.10
NOTES
&
SELECTED
BIBLIOGRAPHY
.
301
9.11
PROBLEMS
.
,
.
304
A
LINEAR
ALGEBRA
315
A.L
SCALARS,
VECTORS,
AND
MATRICES
.
315
A.2
ARITHMETIC
OPERATIONS
WITH
VECTORS
AND
MATRICES
317
A.3
LINEAR
INDEPENDENCE
.
320
A.4
ORTHOGONALITY
.
321
A.5
NORMS
.
321
A.6
VECTOR
SPACES
.
324
A.7
RANK
OF
A
MATRIX
.
I
.
326
A.8
MATRICES
WITH
SPECIAL
STRUCTURE
.
326
A.9
INVERSE
OF
A
MATRIX
.
329
A.10
INVERSES
OF
SPECIAL
MATRICES
.
330
A.
11
DETERMINANTS
.
'
.
331
A.
12
EIGENVALUES
.
333
A.
13
POSITIVE-DEFINITENESS
.
336
A.
14
NOTES
&
SELECTED
BIBLIOGRAPHY
.
337
A.
15
PROBLEMS
.
337
CONTENTS
XIII
B
LINEAR
EQUATIONS
341
B.L
SOLUTION
SETS
.
341
B.2
SYSTEMS
OF
EQUATIONS
WITH
THE
SAME
SOLUTION
SETS
343
B.3
HOW
SYSTEMS
ARE
SOLVED
.
345
B.4
ELEMENTARY
OPERATIONS
.
346
B.5
CANONICAL
FORMS,
PIVOTING,
AND
SOLUTIONS
.
349
B.6
PIVOT
THEORY
.
354
B.7
NOTES
&
SELECTED
BIBLIOGRAPHY
.
357
B.8
PROBLEMS
.
357
REFERENCES
361 |
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| id | DE-604.BV023623075 |
| illustrated | Illustrated |
| index_date | 2024-07-02T22:44:22Z |
| indexdate | 2024-07-09T21:25:48Z |
| institution | BVB |
| isbn | 0387948333 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016940285 |
| oclc_num | 722835376 |
| open_access_boolean | |
| owner | DE-521 |
| owner_facet | DE-521 |
| physical | XXXVIII, 435 S. graph. Darst. 25 cm |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer series in operations research |
| spelling | Dantzig, George Bernard 1914-2005 Verfasser (DE-588)124788734 aut Linear programming 1. Introduction Buch. George B. Dantzig ; Mukund N. Thapa New York [u.a.] Springer 1997 XXXVIII, 435 S. graph. Darst. 25 cm txt rdacontent n rdamedia nc rdacarrier Springer series in operations research Literaturverz. S. 361 - 419 Thapa, Mukund Narain Verfasser (DE-588)124788696 aut (DE-604)BV011292956 1 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016940285&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dantzig, George Bernard 1914-2005 Thapa, Mukund Narain Linear programming |
| title | Linear programming |
| title_auth | Linear programming |
| title_exact_search | Linear programming |
| title_exact_search_txtP | Linear programming |
| title_full | Linear programming 1. Introduction Buch. George B. Dantzig ; Mukund N. Thapa |
| title_fullStr | Linear programming 1. Introduction Buch. George B. Dantzig ; Mukund N. Thapa |
| title_full_unstemmed | Linear programming 1. Introduction Buch. George B. Dantzig ; Mukund N. Thapa |
| title_short | Linear programming |
| title_sort | linear programming |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016940285&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011292956 |
| work_keys_str_mv | AT dantziggeorgebernard linearprogramming1introductionbuch AT thapamukundnarain linearprogramming1introductionbuch |