Location theory: a unified approach ; with 36 tables
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2005
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Auch als Internetausgabe |
| Physical Description: | XX, 437 S. graph. Darst. |
| ISBN: | 3540243216 |
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MARC
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| 100 | 1 | |a Nickel, Stefan |e Verfasser |0 (DE-588)130451479 |4 aut | |
| 245 | 1 | 0 | |a Location theory |b a unified approach ; with 36 tables |c Stefan Nickel ; Justo Puerto |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2005 | |
| 300 | |a XX, 437 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Auch als Internetausgabe | ||
| 650 | 4 | |a Betriebliche Standortwahl / Mathematische Optimierung / Theorie / Theorie | |
| 650 | 4 | |a Standortproblem | |
| 650 | 4 | |a ordered median function / ordered median location problem | |
| 650 | 0 | 7 | |a Standortproblem |0 (DE-588)4301515-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Standortproblem |0 (DE-588)4301515-3 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Puerto, Justo |e Verfasser |4 aut | |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013224887&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
Record in the Search Index
| _version_ | 1805084090321338368 |
|---|---|
| adam_text |
STEFAN NICKEL
JUSTO PUERT
O
LOCATIO
N THEOR
Y
A UNIFIED APPROACH
WITH 116 FIGURES
AND 36 TABLES
4Y SPRI
RINGE
R
CONTENT
S
PAR
T I LOCATIO
N THEOR
Y AN
D TH
E ORDERE
D MEDIA
N FUNCTIO
N
1 MATHEMATICA
L PROPERTIE
S O
F TH
E ORDERE
D MEDIA
N FUNCTIO
N . 3
1.1 INTRODUCTIO
N 3
1.2 MOTIVATIN
G EXAMPL
E 4
1.3 TH
E ORDERE
D MEDIA
N FUNCTIO
N 6
1.4 TOWARDS LOCATIO
N PROBLEM
S 15
PAR
T I
I TH
E CONTINUOU
S ORDERE
D MEDIA
N LOCATIO
N PROBLE
M
2 TH
E CONTINUOU
S ORDERE
D MEDIA
N PROBLE
M 23
2.1 PROBLE
M STATEMEN
T 23
2.2 DISTANC
E FUNCTION
S 27
2.2.1 TH
E PLANA
R CASE 31
2.3 ORDERE
D REGIONS
, ELEMENTAR
Y CONVEX SET
S AN
D BISECTOR
S 34
2.3.1 ORDERE
D REGIONS 34
2.3.2 ORDERE
D ELEMENTAR
Y CONVEX SET
S 35
2.3.3 BISECTORS 39
3 BISECTOR
S 43
3.1 BISECTOR
S - TH
E CLASSICAL CAS
E 43
3.2 POSSIBLE GENERALIZATION
S 44
3.3 BISECTOR
S - TH
E GENERA
L CAS
E 46
3.3.1 NEGATIV
E RESULT
S 47
3.3.2 STRUCTURA
L PROPERTIE
S 48
3.3.3 PARTITIONIN
G OF BISECTOR
S 59
3.4 BISECTOR
S OF POLYHEDRA
L GAUGE
S 65
3.5 BISECTOR
S OF ELLIPTI
C GAUGE
S 74
3.6 BISECTORS OF A POLYHEDRA
L GAUG
E AN
D A
N ELLIPTI
C GAUG
E 83
3.7 APPROXIMATIO
N OF BISECTOR
S 96
X CONTENTS
4 TH
E SINGL
E FACILIT
Y ORDERE
D MEDIA
N PROBLE
M 105
4.1 SOLVING TH
E SINGLE FACILITY OMP BY LINEAR PROGRAMMIN
G 105
4.2 SOLVING TH
E PLANA
R ORDERE
D MEDIA
N PROBLE
M GEOMETRICALL
Y .
. 110
4.3 NON POLYHEDRA
L CAS
E 117
4.4 CONTINUOU
S OMPS WIT
H POSITIV
E AN
D NEGATIV
E LAMBDA
S 123
4.4.1 TH
E ALGORITHM
S 127
4.5 FINDIN
G TH
E ORDERE
D MEDIA
N IN TH
E RECTILINEA
R SPACE 134
5 MULTICRITERI
A ORDERE
D MEDIA
N PROBLEM
S 137
5.1 INTRODUCTIO
N 137
5.2 MULTICRITERI
A PROBLEM
S AN
D LEVEL SETS 138
5.3 BICRITERI
A ORDERE
D MEDIA
N PROBLEM
S 139
5.4 TH
E 3-CRITERI
A CASE 151
5.5 TH
E CASE Q 3 158
5.6 CONCLUDING REMARK
S 162
6 EXTENSION
S O
F TH
E CONTINUOU
S ORDERE
D MEDIA
N PROBLE
M . . . 165
6.1 EXTENSION
S OF TH
E SINGLE FACILITY ORDERE
D MEDIA
N PROBLE
M .
. 165
6.1.1 RESTRICTE
D CASE 165
6.2 EXTENSIO
N T
O TH
E MULTIFACILITY CASE 169
6.2.1 TH
E NON-INTERCHANGEABL
E MULTIFACILITY MODE
L 170
6.2.2 TH
E INDISTINGUISHABL
E MULTIFACILITY MODEL 172
6.3 TH
E SINGLE FACILITY OMP IN ABSTRAC
T SPACES 174
6.3.1 PRELIMINAR
Y RESULT
S 176
6.3.2 ANALYSI
S OF TH
E OPTIMA
L SOLUTIO
N SET 185
6.3.3 TH
E CONVEX OMP AN
D TH
E SINGLE FACILITY LOCATIO
N
PROBLE
M I
N NORME
D SPACES 189
6.4 CONCLUDIN
G REMARK
S 193
PAR
T II
I ORDERE
D MEDIA
N LOCATIO
N PROBLEM
S O
N NETWORK
S
7 TH
E ORDERE
D MEDIA
N PROBLE
M O
N NETWORK
S 197
7.1 PROBLE
M STATEMEN
T 197
7.2 PRELIMINAR
Y RESULT
S 200
7.3 GENERA
L PROPERTIE
S 203
8 O
N FINIT
E DOMINATIN
G SET
S FOR TH
E ORDERE
D MEDIA
N
PROBLE
M 209
8.1 INTRODUCTIO
N 209
8.2 FD
S FOR TH
E SINGLE FACILITY ORDERE
D MEDIA
N PROBLE
M 210
8.3 POLYNOMIA
L SIZE FD
S FOR TH
E MULTIFACILITY ORDERE
D MEDIA
N
PROBLE
M 214
8.3.1 A
N FD
S FOR TH
E MULTIFACILITY ORDERE
D MEDIA
N PROBLE
M
WHEN A = AI = .
. =
AFC ^ AFE+I - .
. = A
M =B 215
CONTENTS XI
8.3.2 A
N FD
S FOR TH
E ORDERE
D 2-MEDIAN PROBLE
M WIT
H
GENERA
L NONNEGATIV
E A-WEIGHTS 225
8.4 O
N TH
E EXPONENTIA
L CARDINALIT
Y OF FD
S FOR TH
E MULTIFACIHT
Y
FACILITY ORDERE
D MEDIA
N PROBLE
M 236
8.4.1 SOME TECHNICAL RESULT
S 239
8.4.2 MAI
N RESULT
S 245
9 TH
E SINGL
E FACILIT
Y ORDERE
D MEDIA
N PROBLE
M O
N NETWORK
S 249
9.1 TH
E SINGLE FACILITY OMP ON NETWORKS
: ILLUSTRATIV
E EXAMPLE
S . . 250
9.2 TH
E FC-CENTRUM SINGLE FACILITY LOCATIO
N PROBLE
M 254
9.3 TH
E GENERA
L SINGLE FACILITY ORDERE
D MEDIA
N PROBLE
M ON
NETWORKS 266
9.3.1 FINDIN
G TH
E SINGLE FACILITY ORDERE
D MEDIA
N OF A
GENERA
L NETWORK 267
9.3.2 FINDIN
G TH
E SINGLE FACILITY ORDERE
D MEDIA
N OF A TREE . . 269
1
0 TH
E MULTIFACIHT
Y ORDERE
D MEDIA
N PROBLE
M O
N NETWORK
S . . 275
10.1 TH
E MULTIFACIHT
Y FC-CENTRUM PROBLE
M 275
10.2 TH
E ORDERE
D P-MEDIA
N PROBLE
M WIT
H A
S
-VECTOR
A
S
= (A,.-.
S
,A,6,.?.,6
) 281
10.3 A POLYNOMIA
L ALGORITH
M FOR TH
E ORDERE
D ^-MEDIA
N PROBLE
M
ON TREE NETWORKS WIT
H A
S
-VECTOR, A
S
= (A, R.
S
, A,B,.
S
.,B) 283
1
1 MULTICRITERI
A ORDERE
D MEDIA
N PROBLEM
S O
N NETWORK
S 289
11.1 INTRODUCTIO
N 289
11.2 EXAMPLE
S AN
D REMARK
S 291
11.3 TH
E ALGORITH
M 293
11.4 POIN
T COMPARISO
N 295
11.5 SEGMENT COMPARISO
N 296
11.6 COMPUTIN
G TH
E SET OF EFHCIENT POINT
S USING LINEA
R
PROGRAMMIN
G 307
1
2 EXTENSION
S O
F TH
E ORDERE
D MEDIA
N PROBLE
M O
N NETWORK
S . . 311
12.1 NOTATIO
N AN
D MODEL DEFINITIONS 312
12.2 TACTICA
L SUBTRE
E WIT
H CONVEX ORDERE
D MEDIA
N OBJECTIV
E 314
12.2.1 FINDIN
G A
N OPTIMA
L TACTICA
L SUBEDG
E 314
12.2.2 FINDIN
G A
N OPTIMA
L TACTICA
L CONTINUOU
S SUBTRE
E
CONTAININ
G A GIVEN NOD
E 315
12.3 STRATEGI
E SUBTRE
E WIT
H CONVEX ORDERE
D MEDIA
N OBJECTIV
E .
. 317
12.3.1 FINDIN
G A
N OPTIMA
L STRATEGI
E SUBEDG
E 318
12.3.2 FINDIN
G A
N OPTIMA
L STRATEGI
E CONTINUOU
S SUBTRE
E
CONTAININ
G A GIVEN NOD
E 318
12.3.3 SUBMODULARIT
Y OF CONVEX ORDERE
D MEDIA
N FUNCTION
S . . 318
12.4 TH
E SPECIAL CASE OF TH
E SUBTRE
E FC-CENTRUM PROBLE
M 320
J
XII CONTENTS
12.4.1 NESTEDNES
S PROPERT
Y FOR TH
E STRATEGI
E AN
D TACTICA
L
DISCRET
E FE-CENTRUM PROBLEM
S 321
12.4.2 A DYNAMI
C PROGRAMMIN
G ALGORITH
M FOR TH
E STRATEGI
E
DISCRET
E SUBTRE
E FC-CENTRUM PROBLE
M 322
12.5 SOLVING TH
E STRATEGI
E CONTINUOU
S SUBTRE
E FE-CENTRUM PROBLEM
. 325
12.6 CONCLUDIN
G REMARK
S 327
PAR
T I
V TH
E DISCRET
E ORDERE
D MEDIA
N LOCATIO
N PROBLE
M
1
3 INTRODUCTIO
N AN
D PROBLE
M STATEMEN
T 331
13.1 DEFINITION OF TH
E PROBLE
M 332
13.2 A QUADRATI
C FORMULATIO
N FOR TH
E DISCRET
E OMP 335
13.2.1 SORTIN
G A
S A
N INTEGE
R LINEA
R PROGRA
M (ILP
) 336
13.2.2 FORMULATIO
N OF TH
E LOCATION-ALLOCATIO
N SUBPROBLE
M . . . 337
13.2.3 QUADRATI
C INTEGE
R PROGRAMMIN
G FORMULATIO
N FOR OMP . 339
1
4 LINEARIZATION
S AN
D REFORMULATION
S 341
14.1 LINEARIZATION
S OF (OMP) 341
14.1.1 A FIRS
T LINEARIZATION
: (OMP
1
) 341
14.1.2 A LINEARIZATIO
N USING LESS VARIABLES
: (OMP
2
) 346
14.1.3 SIMPLIFYING FURTHER
: (OMP
3
) 349
14.1.4 COMPARISO
N BETWEE
N (OMP
2
) AN
D (OMP
3
) 352
14.2 REFORMULATIONS 354
14.2.1 IMPROVEMENT
S FOR (OMP
1
) 356
14.2.2 IMPROVEMENT
S FOR (OMP
3
) 362
14.2.3 IMPROVEMENT
S FOR (OMP
2
) 368
14.2.4 COMPARISO
N BETWEEN (OMP
2
*) AN
D (OMP
3
*) 371
14.3 COMPUTATIONA
L RESULT
S 372
1
5 SOLUTIO
N METHOD
S 381
15.1 A BRANCH AN
D BOUN
D METHO
D 381
15.1.1 COMBINATORIA
L LOWER BOUND
S 382
15.1.2 BRANCHIN
G 387
15.1.3 NUMERICA
L COMPARISO
N OF TH
E BRANCHIN
G RULES 389
15.1.4 COMPUTATIONA
L RESULT
S 390
15.2 TWO HEURISTI
C APPROACHE
S FOR TH
E OMP 393
15.2.1 AN EVOLUTIO
N PROGRA
M FOR TH
E OMP 393
15.2.2 A VARIABL
E NEIGHBORHOO
D SEARCH FOR TH
E OMP 399
15.2.3 COMPUTATIONA
L RESULT
S 407
16 RELATE
D PROBLEM
S AN
D OUTLOO
K 419
16.1 TH
E DISCRET
E OMP WIT
H AE
4 419
16.1.1 PROBLE
M FORMULATIO
N 419
16.1.2 COMPUTATIONA
L RESULT
S 421
CONTENTS XIII
16.2 CONCLUSIONS AN
D FURTHE
R RESEARC
H 422
REFERENCE
S 423
INDE
X 435 |
| any_adam_object | 1 |
| author | Nickel, Stefan Puerto, Justo |
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| dewey-ones | 510 - Mathematics |
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| discipline | Mathematik Wirtschaftswissenschaften |
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| id | DE-604.BV019937423 |
| illustrated | Illustrated |
| indexdate | 2024-07-20T07:58:55Z |
| institution | BVB |
| isbn | 3540243216 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013224887 |
| oclc_num | 254249502 |
| open_access_boolean | |
| owner | DE-20 DE-29T DE-634 DE-2070s |
| owner_facet | DE-20 DE-29T DE-634 DE-2070s |
| physical | XX, 437 S. graph. Darst. |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | Springer |
| record_format | marc |
| spelling | Nickel, Stefan Verfasser (DE-588)130451479 aut Location theory a unified approach ; with 36 tables Stefan Nickel ; Justo Puerto Berlin [u.a.] Springer 2005 XX, 437 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Auch als Internetausgabe Betriebliche Standortwahl / Mathematische Optimierung / Theorie / Theorie Standortproblem ordered median function / ordered median location problem Standortproblem (DE-588)4301515-3 gnd rswk-swf Standortproblem (DE-588)4301515-3 s DE-604 Puerto, Justo Verfasser aut DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013224887&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nickel, Stefan Puerto, Justo Location theory a unified approach ; with 36 tables Betriebliche Standortwahl / Mathematische Optimierung / Theorie / Theorie Standortproblem ordered median function / ordered median location problem Standortproblem (DE-588)4301515-3 gnd |
| subject_GND | (DE-588)4301515-3 |
| title | Location theory a unified approach ; with 36 tables |
| title_auth | Location theory a unified approach ; with 36 tables |
| title_exact_search | Location theory a unified approach ; with 36 tables |
| title_full | Location theory a unified approach ; with 36 tables Stefan Nickel ; Justo Puerto |
| title_fullStr | Location theory a unified approach ; with 36 tables Stefan Nickel ; Justo Puerto |
| title_full_unstemmed | Location theory a unified approach ; with 36 tables Stefan Nickel ; Justo Puerto |
| title_short | Location theory |
| title_sort | location theory a unified approach with 36 tables |
| title_sub | a unified approach ; with 36 tables |
| topic | Betriebliche Standortwahl / Mathematische Optimierung / Theorie / Theorie Standortproblem ordered median function / ordered median location problem Standortproblem (DE-588)4301515-3 gnd |
| topic_facet | Betriebliche Standortwahl / Mathematische Optimierung / Theorie / Theorie Standortproblem ordered median function / ordered median location problem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013224887&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT nickelstefan locationtheoryaunifiedapproachwith36tables AT puertojusto locationtheoryaunifiedapproachwith36tables |