ENDÜSTRİDE BİLGİSAYAR UYGULAMALARI - 2 New potential hubs in the South-Atlantic market. A problem of location Journal  of ...
İçerik: <ul><li>Tesis Planlama Kavramı </li></ul><ul><li>Tesis Planlamanın Amaçları </li></ul><ul><li>Tesis Planlama Tiple...
TESİS PLANLAMA KAVRAMI: <ul><li>TESİS :  Mal ve hizmetlerin fiilen üretildiği fiziksel birimlerdir.  </li></ul><ul><li>TES...
TESİS PLANLAMA AMAÇLARI: <ul><li>Kaynakların kullanımı </li></ul><ul><li>Darboğazların belirlenmesi </li></ul><ul><li>Tesi...
TESİS PLANLAMA TİPLERİ: <ul><li>Basit Yerleşim  </li></ul><ul><li>Çoklu Yerleşim </li></ul><ul><li>Tesis Oluşturulması ve ...
TESİSİN KURULACAĞI BÖLGENİN SEÇİLMESİ: <ul><li>Yerleşim Kararlarını Etkileyen Faktörler : </li></ul><ul><li>Ülke seçimi (k...
ALTERNATİFLERİ DEĞERLENDİRME   YÖNTEMLERİ: <ul><ul><li>Faktör Oranlama Metodu  </li></ul></ul><ul><ul><li>Başa-baş Analizi...
Problem: <ul><li>Güney Amerika–Avrupa arasında </li></ul><ul><li>düzenlenen uçuş seferlerinde optimum </li></ul><ul><li>ak...
 
Veriler: <ul><li>1) Şehirler arası mesafeler </li></ul>0 4000 4100 24400 23100 21100 BUONES AIRES 4000 0 7000 21100 19500 ...
Veriler: <ul><li>2) Şehirler arası yolcu sayısı </li></ul>0 0 0 83000 270051 110000 BUONES AIRES 0 0 0 143977 126851 73847...
min  Σ   (d   E i  H x   + d   H x  S j   )   T   E i  S j H x  E u S   E i   E   T  *      S j    S
Problemin Lingo Modeli: <ul><li>SETS: </li></ul><ul><li>AIRPORT/LISBON MADRID PARIS SANTIAGO SAOPAULO BUONESAIRES/:HUB,K; ...
Lingo Çözümü: <ul><li>Rows=  1 Vars=  5 No. integer vars=  5  ( all are linear) </li></ul><ul><li>Nonzeros=  6 Constraint ...
Lingo Çözümü: <ul><li>DIST( LISBON, LISBON)  0.0000000E+00  0.0000000E+00 </li></ul><ul><li>DIST( LISBON, MADRID)  1000.00...
Lingo Çözümü: <ul><li>DIST( SAOPAULO, LISBON)  17600.00  0.0000000E+00 </li></ul><ul><li>DIST( SAOPAULO, MADRID)  19500.00...
Lingo Çözümü: <ul><li>PASS( PARIS, LISBON)  0.0000000E+00  0.0000000E+00 </li></ul><ul><li>PASS( PARIS, MADRID)  0.0000000...
Lingo Çözümü: <ul><li>  Row  Slack or Surplus  Dual Price </li></ul><ul><li>1  0.2743843E+11  -1.000000 </li></ul><ul><li>...
Problem: <ul><li>Avrupa – Güney Amerika arasında </li></ul><ul><li>düzenlenen uçuş seferlerinde; biri Amerika </li></ul><u...
 
min  Σ   (d  E j E x  + d   E x S y   +  d  S y S j  ) T  E i  S j E x ,S y  E x S   E i   E   T  *      S j    S
Problemin Lingo Modeli: <ul><li>SETS: </li></ul><ul><li>S1/LISBON MADRID PARIS/; </li></ul><ul><li>S2/SANTIAGO SAOPAULO BU...
Lingo Çözümü: <ul><li>Rows=  1 Vars=  8 No. integer vars=  8  ( all are linear) </li></ul><ul><li>Nonzeros=  9 Constraint ...
Lingo Çözümü: <ul><li>DIST2( SANTIAGO, SANTIAGO)  0.0000000E+00  0.0000000E+00 </li></ul><ul><li>DIST2( SANTIAGO, SAOPAULO...
Lingo Çözümü: <ul><li>PASS( PARIS, SANTIAGO)  156000.0  0.0000000E+00 </li></ul><ul><li>PASS( PARIS, SAOPAULO)  384190.0  ...
Lingo Çözümü: <ul><li>  Row  Slack or Surplus  Dual Price </li></ul><ul><li>1  0.4630561E+11  -1.000000 </li></ul><ul><li>...
TEŞEKKÜRLER :))
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Facility Location Problem

  1. 1. ENDÜSTRİDE BİLGİSAYAR UYGULAMALARI - 2 New potential hubs in the South-Atlantic market. A problem of location Journal of Transport Geography Volume 11, Issue 2 , June 2003, Pages 139-149 FERİDE SEVLİ – 2000503052 AYTÜL ŞENER – 200503056 İLKEM YALINER – 2000503067
  2. 2. İçerik: <ul><li>Tesis Planlama Kavramı </li></ul><ul><li>Tesis Planlamanın Amaçları </li></ul><ul><li>Tesis Planlama Tipleri </li></ul><ul><li>Tesisin Kurulacağı Bölgenin Seçimi </li></ul><ul><li>Alternatiflerin Değerlendirilme Yöntemleri </li></ul><ul><li>Havacılık Sektöründe Tesis Planlama Uygulamaları </li></ul>
  3. 3. TESİS PLANLAMA KAVRAMI: <ul><li>TESİS : Mal ve hizmetlerin fiilen üretildiği fiziksel birimlerdir. </li></ul><ul><li>TESİS PLANLAMA : Tesislerin düzenleme çalışmalarının yapılması, tesisin kurulması ve faaliyete geçirilmesi aşamalarında gerçekleştirilecek olan faaliyetlerin bugünden eşgüdümlerinin yapılmasıdır. </li></ul>
  4. 4. TESİS PLANLAMA AMAÇLARI: <ul><li>Kaynakların kullanımı </li></ul><ul><li>Darboğazların belirlenmesi </li></ul><ul><li>Tesis faaliyetleri </li></ul><ul><li>Optimum yerleşim düzeni </li></ul><ul><ul><ul><ul><li>Maliyet </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Mesafe </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Zaman </li></ul></ul></ul></ul>
  5. 5. TESİS PLANLAMA TİPLERİ: <ul><li>Basit Yerleşim </li></ul><ul><li>Çoklu Yerleşim </li></ul><ul><li>Tesis Oluşturulması ve Kapasite Atama </li></ul><ul><li>Tesis Seçimi ve Kapasite Atama </li></ul><ul><li>Tesis İçi Yerleşim(QAP) </li></ul>
  6. 6. TESİSİN KURULACAĞI BÖLGENİN SEÇİLMESİ: <ul><li>Yerleşim Kararlarını Etkileyen Faktörler : </li></ul><ul><li>Ülke seçimi (kanunlar, pazar, işgücü, tedarik, alım gücü vb.) </li></ul><ul><li>Bölge seçimi (maliyet, çevre kuralları, müşteri&hammadde erişimi vb.) </li></ul><ul><li>Yer seçimi (yerin alan&maliyeti, ulaşım kolaylığı vb.) </li></ul>
  7. 7. ALTERNATİFLERİ DEĞERLENDİRME YÖNTEMLERİ: <ul><ul><li>Faktör Oranlama Metodu </li></ul></ul><ul><ul><li>Başa-baş Analizi </li></ul></ul><ul><ul><li>Ağırlık Merkezi Metodu </li></ul></ul><ul><ul><li>Ulaştırma Metodu </li></ul></ul>
  8. 8. Problem: <ul><li>Güney Amerika–Avrupa arasında </li></ul><ul><li>düzenlenen uçuş seferlerinde optimum </li></ul><ul><li>aktarma noktası seçimi </li></ul>
  9. 10. Veriler: <ul><li>1) Şehirler arası mesafeler </li></ul>0 4000 4100 24400 23100 21100 BUONES AIRES 4000 0 7000 21100 19500 17600 SAO PAULO 4100 7000 0 26200 24000 24000 SANTIAGO 24400 21100 26200 0 2500 3200 PARIS 23100 19500 24000 2500 0 1000 MADRID 21100 17600 24000 3200 1000 0 LISBON BUONES AIRES SAO PAULO SANTIAGO PARIS MADRID LİSBON TO FROM
  10. 11. Veriler: <ul><li>2) Şehirler arası yolcu sayısı </li></ul>0 0 0 83000 270051 110000 BUONES AIRES 0 0 0 143977 126851 73847 SAO PAULO 0 0 0 82000 80054 95000 SANTIAGO 85000 155036 74000 0 0 0 PARIS 240213 126137 81220 0 0 0 MADRID 121000 69238 62000 0 0 0 LISBON BUONES AIRES SAO PAULO SANTIAGO PARIS MADRID LİSBON TO FROM
  11. 12. min Σ (d E i H x + d H x S j ) T E i S j H x  E u S E i  E T *  S j  S
  12. 13. Problemin Lingo Modeli: <ul><li>SETS: </li></ul><ul><li>AIRPORT/LISBON MADRID PARIS SANTIAGO SAOPAULO BUONESAIRES/:HUB,K; </li></ul><ul><li>A(AIRPORT,AIRPORT):DIST,PASS; </li></ul><ul><li>ENDSETS </li></ul><ul><li>DATA: </li></ul><ul><li>DIST=0 1000 3200 24000 17600 21100 </li></ul><ul><li>1000 0 2500 24000 19500 23100 </li></ul><ul><li>3200 2500 0 26200 21100 24400 </li></ul><ul><li>24000 24000 26200 0 7000 4100 </li></ul><ul><li>17600 19500 21100 7000 0 4000 </li></ul><ul><li>21100 23100 24400 4100 4000 0 ; </li></ul><ul><li>PASS=0 0 0 62000 69238 121000 </li></ul><ul><li>0 0 0 81220 126137 240213 </li></ul><ul><li>0 0 0 74000 155036 85000 </li></ul><ul><li>95000 80054 82000 0 0 0 </li></ul><ul><li>73847 126851 143977 0 0 0 </li></ul><ul><li>110000 270051 83000 0 0 0 ; </li></ul><ul><li>ENDDATA </li></ul><ul><li>MIN=@SUM(AIRPORT(I):HUB(I)*K(I)); </li></ul><ul><li>@FOR(AIRPORT(I):@SUM(A(J,K)|J#NE#I #AND# #NE#K:(DIST(J,I)+DIST(I,K))*PASS(J,K))=HUB(I)); </li></ul><ul><li>IFA=@MIN(AIRPORT(I):HUB(I)); </li></ul><ul><li>@FOR(AIRPORT(I)|HUB(I)#LE#IFA:K(I)=1); </li></ul><ul><li>@FOR(AIRPORT(I):@BIN(K(I))); </li></ul>
  13. 14. Lingo Çözümü: <ul><li>Rows= 1 Vars= 5 No. integer vars= 5 ( all are linear) </li></ul><ul><li>Nonzeros= 6 Constraint nonz= 0( 0 are +- 1) Density=1.000 </li></ul><ul><li>Smallest and largest elements in absolute value= 0.317284E+11 0.481254E </li></ul><ul><li>No. < : 0 No. =: 0 No. > : 0, Obj=MIN, GUBs <= 0 </li></ul><ul><li>Single cols= 5 </li></ul><ul><li>Optimal solution found at step: 0 </li></ul><ul><li>Objective value: 0.2743843E+11 </li></ul><ul><li>Branch count: 0 </li></ul><ul><li>Variable Value Reduced Cost </li></ul><ul><li>IFA 0.2743843E+11 0.0000000E+00 </li></ul><ul><li>HUB( LISBON) 0.3455933E+11 0.0000000E+00 </li></ul><ul><li>HUB( MADRID) 0.2743843E+11 0.0000000E+00 </li></ul><ul><li>HUB( PARIS) 0.3879355E+11 0.0000000E+00 </li></ul><ul><li>HUB( SANTIAGO) 0.4812541E+11 0.0000000E+00 </li></ul><ul><li>HUB( SAOPAULO) 0.3371716E+11 0.0000000E+00 </li></ul><ul><li>HUB( BUONESAIRES) 0.3172843E+11 0.0000000E+00 </li></ul><ul><li>K( LISBON) 0.0000000E+00 0.3455933E+11 </li></ul><ul><li>K( MADRID) 1.000000 0.0000000E+00 </li></ul><ul><li>K( PARIS) 0.0000000E+00 0.3879355E+11 </li></ul><ul><li>K( SANTIAGO) 0.0000000E+00 0.4812541E+11 </li></ul><ul><li>K( SAOPAULO) 0.0000000E+00 0.3371716E+11 </li></ul><ul><li>K( BUONESAIRES) 0.0000000E+00 0.3172843E+11 </li></ul>
  14. 15. Lingo Çözümü: <ul><li>DIST( LISBON, LISBON) 0.0000000E+00 0.0000000E+00 </li></ul><ul><li>DIST( LISBON, MADRID) 1000.000 0.0000000E+00 </li></ul><ul><li>DIST( LISBON, PARIS) 3200.000 0.0000000E+00 </li></ul><ul><li>DIST( LISBON, SANTIAGO) 24000.00 0.0000000E+00 </li></ul><ul><li>DIST( LISBON, SAOPAULO) 17600.00 0.0000000E+00 </li></ul><ul><li>DIST( LISBON, BUONESAIRES) 21100.00 0.0000000E+00 </li></ul><ul><li>DIST( MADRID, LISBON) 1000.000 0.0000000E+00 </li></ul><ul><li>DIST( MADRID, MADRID) 0.0000000E+00 0.0000000E+00 </li></ul><ul><li>DIST( MADRID, PARIS) 2500.000 0.0000000E+00 </li></ul><ul><li>DIST( MADRID, SANTIAGO) 24000.00 0.0000000E+00 </li></ul><ul><li>DIST( MADRID, SAOPAULO) 19500.00 0.0000000E+00 </li></ul><ul><li>DIST( MADRID, BUONESAIRES) 23100.00 0.0000000E+00 </li></ul><ul><li>DIST( PARIS, LISBON) 3200.000 0.0000000E+00 </li></ul><ul><li>DIST( PARIS, MADRID) 2500.000 0.0000000E+00 </li></ul><ul><li>DIST( PARIS, PARIS) 0.0000000E+00 0.0000000E+00 </li></ul><ul><li>DIST( PARIS, SANTIAGO) 26200.00 0.0000000E+00 </li></ul><ul><li>DIST( PARIS, SAOPAULO) 21100.00 0.0000000E+00 </li></ul><ul><li>DIST( PARIS, BUONESAIRES) 24400.00 0.0000000E+00 </li></ul><ul><li>DIST( SANTIAGO, LISBON) 24000.00 0.0000000E+00 </li></ul><ul><li>DIST( SANTIAGO, MADRID) 24000.00 0.0000000E+00 </li></ul><ul><li>DIST( SANTIAGO, PARIS) 26200.00 0.0000000E+00 </li></ul><ul><li>DIST( SANTIAGO, SANTIAGO) 0.0000000E+00 0.0000000E+00 </li></ul><ul><li>DIST( SANTIAGO, SAOPAULO) 7000.000 0.0000000E+00 </li></ul><ul><li>DIST( SANTIAGO, BUONESAIRES) 4100.000 0.0000000E+00 </li></ul>
  15. 16. Lingo Çözümü: <ul><li>DIST( SAOPAULO, LISBON) 17600.00 0.0000000E+00 </li></ul><ul><li>DIST( SAOPAULO, MADRID) 19500.00 0.0000000E+00 </li></ul><ul><li>DIST( SAOPAULO, PARIS) 21100.00 0.0000000E+00 </li></ul><ul><li>DIST( SAOPAULO, SANTIAGO) 7000.000 0.0000000E+00 </li></ul><ul><li>DIST( SAOPAULO, SAOPAULO) 0.0000000E+00 0.0000000E+00 </li></ul><ul><li>DIST( SAOPAULO, BUONESAIRES) 4000.000 0.0000000E+00 </li></ul><ul><li>DIST( BUONESAIRES, LISBON) 21100.00 0.0000000E+00 </li></ul><ul><li>DIST( BUONESAIRES, MADRID) 23100.00 0.0000000E+00 </li></ul><ul><li>DIST( BUONESAIRES, PARIS) 24400.00 0.0000000E+00 </li></ul><ul><li>DIST( BUONESAIRES, SANTIAGO) 4100.000 0.0000000E+00 </li></ul><ul><li>DIST( BUONESAIRES, SAOPAULO) 4000.000 0.0000000E+00 </li></ul><ul><li>DIST( BUONESAIRES, BUONESAIRES 0.0000000E+00 0.0000000E+00 </li></ul><ul><li>PASS( LISBON, LISBON) 0.0000000E+00 0.0000000E+00 </li></ul><ul><li>PASS( LISBON, MADRID) 0.0000000E+00 0.0000000E+00 </li></ul><ul><li>PASS( LISBON, PARIS) 0.0000000E+00 0.0000000E+00 </li></ul><ul><li>PASS( LISBON, SANTIAGO) 62000.00 0.0000000E+00 </li></ul><ul><li>PASS( LISBON, SAOPAULO) 69238.00 0.0000000E+00 </li></ul><ul><li>PASS( LISBON, BUONESAIRES) 121000.0 0.0000000E+00 </li></ul><ul><li>PASS( MADRID, LISBON) 0.0000000E+00 0.0000000E+00 </li></ul><ul><li>PASS( MADRID, MADRID) 0.0000000E+00 0.0000000E+00 </li></ul><ul><li>PASS( MADRID, PARIS) 0.0000000E+00 0.0000000E+00 </li></ul><ul><li>PASS( MADRID, SANTIAGO) 81220.00 0.0000000E+00 </li></ul><ul><li>PASS( MADRID, SAOPAULO) 126137.0 0.0000000E+00 </li></ul><ul><li>PASS( MADRID, BUONESAIRES) 240213.0 0.0000000E+00 </li></ul>
  16. 17. Lingo Çözümü: <ul><li>PASS( PARIS, LISBON) 0.0000000E+00 0.0000000E+00 </li></ul><ul><li>PASS( PARIS, MADRID) 0.0000000E+00 0.0000000E+00 </li></ul><ul><li>PASS( PARIS, PARIS) 0.0000000E+00 0.0000000E+00 </li></ul><ul><li>PASS( PARIS, SANTIAGO) 74000.00 0.0000000E+00 </li></ul><ul><li>PASS( PARIS, SAOPAULO) 155036.0 0.0000000E+00 </li></ul><ul><li>PASS( PARIS, BUONESAIRES) 85000.00 0.0000000E+00 </li></ul><ul><li>PASS( SANTIAGO, LISBON) 95000.00 0.0000000E+00 </li></ul><ul><li>PASS( SANTIAGO, MADRID) 80054.00 0.0000000E+00 </li></ul><ul><li>PASS( SANTIAGO, PARIS) 82000.00 0.0000000E+00 </li></ul><ul><li>PASS( SANTIAGO, SANTIAGO) 0.0000000E+00 0.0000000E+00 </li></ul><ul><li>PASS( SANTIAGO, SAOPAULO) 0.0000000E+00 0.0000000E+00 </li></ul><ul><li>PASS( SANTIAGO, BUONESAIRES) 0.0000000E+00 0.0000000E+00 </li></ul><ul><li>PASS( SAOPAULO, LISBON) 73847.00 0.0000000E+00 </li></ul><ul><li>PASS( SAOPAULO, MADRID) 126851.0 0.0000000E+00 </li></ul><ul><li>PASS( SAOPAULO, PARIS) 143977.0 0.0000000E+00 </li></ul><ul><li>PASS( SAOPAULO, SANTIAGO) 0.0000000E+00 0.0000000E+00 </li></ul><ul><li>PASS( SAOPAULO, SAOPAULO) 0.0000000E+00 0.0000000E+00 </li></ul><ul><li>PASS( SAOPAULO, BUONESAIRES) 0.0000000E+00 0.0000000E+00 </li></ul><ul><li>PASS( BUONESAIRES, LISBON) 110000.0 0.0000000E+00 </li></ul><ul><li>PASS( BUONESAIRES, MADRID) 270051.0 0.0000000E+00 </li></ul><ul><li>PASS( BUONESAIRES, PARIS) 83000.00 0.0000000E+00 </li></ul><ul><li>PASS( BUONESAIRES, SANTIAGO) 0.0000000E+00 0.0000000E+00 </li></ul><ul><li>PASS( BUONESAIRES, SAOPAULO) 0.0000000E+00 0.0000000E+00 </li></ul><ul><li>PASS( BUONESAIRES, BUONESAIRES 0.0000000E+00 0.0000000E+00 </li></ul>
  17. 18. Lingo Çözümü: <ul><li> Row Slack or Surplus Dual Price </li></ul><ul><li>1 0.2743843E+11 -1.000000 </li></ul><ul><li>2 0.0000000E+00 0.0000000E+00 </li></ul><ul><li>3 0.0000000E+00 1.000000 </li></ul><ul><li>4 0.0000000E+00 0.0000000E+00 </li></ul><ul><li>5 0.0000000E+00 0.0000000E+00 </li></ul><ul><li>6 0.0000000E+00 0.0000000E+00 </li></ul><ul><li>7 0.0000000E+00 0.0000000E+00 </li></ul><ul><li>8 0.0000000E+00 0.0000000E+00 </li></ul><ul><li>9 0.0000000E+00 -0.2743843E+11 </li></ul>
  18. 19. Problem: <ul><li>Avrupa – Güney Amerika arasında </li></ul><ul><li>düzenlenen uçuş seferlerinde; biri Amerika </li></ul><ul><li>diğeri Avrupa’da olmak üzere iki tane </li></ul><ul><li>aktarma noktası seçimi </li></ul>
  19. 21. min Σ (d E j E x + d E x S y + d S y S j ) T E i S j E x ,S y  E x S E i  E T *  S j  S
  20. 22. Problemin Lingo Modeli: <ul><li>SETS: </li></ul><ul><li>S1/LISBON MADRID PARIS/; </li></ul><ul><li>S2/SANTIAGO SAOPAULO BUONESAIRES/; </li></ul><ul><li>B1(S1,S1):DIST1; </li></ul><ul><li>B2(S2,S2):DIST2; </li></ul><ul><li>A(S1,S2):DIST,PASS,HUB,AFI; </li></ul><ul><li>ENDSETS </li></ul><ul><li>DATA: </li></ul><ul><li>DIST1= 0 1000 3200 </li></ul><ul><li>1000 0 2500 </li></ul><ul><li>3200 2500 0 ; </li></ul><ul><li>DIST2= 0 7000 4100 </li></ul><ul><li>7000 0 4000 </li></ul><ul><li>4100 4000 0 ; </li></ul><ul><li>DIST= 24000 17600 21100 </li></ul><ul><li>24000 19500 23100 </li></ul><ul><li>26200 21100 24400; </li></ul><ul><li>PASS= 157000 143085 231000 </li></ul><ul><li>161274 252988 425087 </li></ul><ul><li>156000 384190 168000; </li></ul><ul><li>ENDDATA </li></ul><ul><li>MIN=@SUM(A(I,J):HUB(I,J)*AFI(I,J)); </li></ul><ul><li>@FOR(A(I,J):@SUM(A(K,L):(DIST1(K,I)+DIST(I,J)+DIST2(J,L))*PASS(K,L))=HUB(I,J)); </li></ul><ul><li>IFA=@MIN(A(I,L):HUB(I,L)); </li></ul><ul><li>@FOR(A(M,N)|HUB(M,N)#LE#IFA:AFI(M,N)=1); </li></ul><ul><li>@FOR(A(I,J):@BIN(AFI(I,J))); </li></ul>
  21. 23. Lingo Çözümü: <ul><li>Rows= 1 Vars= 8 No. integer vars= 8 ( all are linear) </li></ul><ul><li>Nonzeros= 9 Constraint nonz= 0( 0 are +- 1) Density=1.000 </li></ul><ul><li>Smallest and largest elements in absolute value= 0.494510E+11 0.670984E </li></ul><ul><li>No. < : 0 No. =: 0 No. > : 0, Obj=MIN, GUBs <= 0 </li></ul><ul><li>Single cols= 8 </li></ul><ul><li>Optimal solution found at step: 0 </li></ul><ul><li>Objective value: 0.4630561E+11 </li></ul><ul><li>Branch count: 0 </li></ul><ul><li>Variable Value Reduced Cost </li></ul><ul><li>IFA 0.4630561E+11 0.0000000E+00 </li></ul><ul><li>DIST1( LISBON, LISBON) 0.0000000E+00 0.0000000E+00 </li></ul><ul><li>DIST1( LISBON, MADRID) 1000.000 0.0000000E+00 </li></ul><ul><li>DIST1( LISBON, PARIS) 3200.000 0.0000000E+00 </li></ul><ul><li>DIST1( MADRID, LISBON) 1000.000 0.0000000E+00 </li></ul><ul><li>DIST1( MADRID, MADRID) 0.0000000E+00 0.0000000E+00 </li></ul><ul><li>DIST1( MADRID, PARIS) 2500.000 0.0000000E+00 </li></ul><ul><li>DIST1( PARIS, LISBON) 3200.000 0.0000000E+00 </li></ul><ul><li>DIST1( PARIS, MADRID) 2500.000 0.0000000E+00 </li></ul><ul><li>DIST1( PARIS, PARIS) 0.0000000E+00 0.0000000E+00 </li></ul>
  22. 24. Lingo Çözümü: <ul><li>DIST2( SANTIAGO, SANTIAGO) 0.0000000E+00 0.0000000E+00 </li></ul><ul><li>DIST2( SANTIAGO, SAOPAULO) 7000.000 0.0000000E+00 </li></ul><ul><li>DIST2( SANTIAGO, BUONESAIRES) 4100.000 0.0000000E+00 </li></ul><ul><li>DIST2( SAOPAULO, SANTIAGO) 7000.000 0.0000000E+00 </li></ul><ul><li>DIST2( SAOPAULO, SAOPAULO) 0.0000000E+00 0.0000000E+00 </li></ul><ul><li>DIST2( SAOPAULO, BUONESAIRES) 4000.000 0.0000000E+00 </li></ul><ul><li>DIST2( BUONESAIRES, SANTIAGO) 4100.000 0.0000000E+00 </li></ul><ul><li>DIST2( BUONESAIRES, SAOPAULO) 4000.000 0.0000000E+00 </li></ul><ul><li>DIST2( BUONESAIRES, BUONESAIRE 0.0000000E+00 0.0000000E+00 </li></ul><ul><li>DIST( LISBON, SANTIAGO) 24000.00 0.0000000E+00 </li></ul><ul><li>DIST( LISBON, SAOPAULO) 17600.00 0.0000000E+00 </li></ul><ul><li>DIST( LISBON, BUONESAIRES) 21100.00 0.0000000E+00 </li></ul><ul><li>DIST( MADRID, SANTIAGO) 24000.00 0.0000000E+00 </li></ul><ul><li>DIST( MADRID, SAOPAULO) 19500.00 0.0000000E+00 </li></ul><ul><li>DIST( MADRID, BUONESAIRES) 23100.00 0.0000000E+00 </li></ul><ul><li>DIST( PARIS, SANTIAGO) 26200.00 0.0000000E+00 </li></ul><ul><li>DIST( PARIS, SAOPAULO) 21100.00 0.0000000E+00 </li></ul><ul><li>DIST( PARIS, BUONESAIRES) 24400.00 0.0000000E+00 </li></ul><ul><li>PASS( LISBON, SANTIAGO) 157000.0 0.0000000E+00 </li></ul><ul><li>PASS( LISBON, SAOPAULO) 143085.0 0.0000000E+00 </li></ul><ul><li>PASS( LISBON, BUONESAIRES) 231000.0 0.0000000E+00 </li></ul><ul><li>PASS( MADRID, SANTIAGO) 161274.0 0.0000000E+00 </li></ul><ul><li>PASS( MADRID, SAOPAULO) 252988.0 0.0000000E+00 </li></ul><ul><li>PASS( MADRID, BUONESAIRES) 425087.0 0.0000000E+00 </li></ul>
  23. 25. Lingo Çözümü: <ul><li>PASS( PARIS, SANTIAGO) 156000.0 0.0000000E+00 </li></ul><ul><li>PASS( PARIS, SAOPAULO) 384190.0 0.0000000E+00 </li></ul><ul><li>PASS( PARIS, BUONESAIRES) 168000.0 0.0000000E+00 </li></ul><ul><li>HUB( LISBON, SANTIAGO) 0.6183313E+11 0.0000000E+00 </li></ul><ul><li>HUB( LISBON, SAOPAULO) 0.4630561E+11 0.0000000E+00 </li></ul><ul><li>HUB( LISBON, BUONESAIRES) 0.5203010E+11 0.0000000E+00 </li></ul><ul><li>HUB( MADRID, SANTIAGO) 0.6102913E+11 0.0000000E+00 </li></ul><ul><li>HUB( MADRID, SAOPAULO) 0.4945099E+11 0.0000000E+00 </li></ul><ul><li>HUB( MADRID, BUONESAIRES) 0.5538335E+11 0.0000000E+00 </li></ul><ul><li>HUB( PARIS, SANTIAGO) 0.6709839E+11 0.0000000E+00 </li></ul><ul><li>HUB( PARIS, SAOPAULO) 0.5427308E+11 0.0000000E+00 </li></ul><ul><li>HUB( PARIS, BUONESAIRES) 0.5958185E+11 0.0000000E+00 </li></ul><ul><li>AFI( LISBON, SANTIAGO) 0.0000000E+00 0.6183313E+11 </li></ul><ul><li>AFI( LISBON, SAOPAULO) 1.000000 0.0000000E+00 </li></ul><ul><li>AFI( LISBON, BUONESAIRES) 0.0000000E+00 0.5203010E+11 </li></ul><ul><li>AFI( MADRID, SANTIAGO) 0.0000000E+00 0.6102913E+11 </li></ul><ul><li>AFI( MADRID, SAOPAULO) 0.0000000E+00 0.4945099E+11 </li></ul><ul><li>AFI( MADRID, BUONESAIRES) 0.0000000E+00 0.5538335E+11 </li></ul><ul><li>AFI( PARIS, SANTIAGO) 0.0000000E+00 0.6709839E+11 </li></ul><ul><li>AFI( PARIS, SAOPAULO) 0.0000000E+00 0.5427308E+11 </li></ul><ul><li>AFI( PARIS, BUONESAIRES) 0.0000000E+00 0.5958185E+11 </li></ul>
  24. 26. Lingo Çözümü: <ul><li> Row Slack or Surplus Dual Price </li></ul><ul><li>1 0.4630561E+11 -1.000000 </li></ul><ul><li>2 0.0000000E+00 0.0000000E+00 </li></ul><ul><li>3 0.0000000E+00 1.000000 </li></ul><ul><li>4 0.0000000E+00 0.0000000E+00 </li></ul><ul><li>5 0.0000000E+00 0.0000000E+00 </li></ul><ul><li>6 0.0000000E+00 0.0000000E+00 </li></ul><ul><li>7 0.0000000E+00 0.0000000E+00 </li></ul><ul><li>8 0.0000000E+00 0.0000000E+00 </li></ul><ul><li>9 0.0000000E+00 0.0000000E+00 </li></ul><ul><li>10 0.0000000E+00 0.0000000E+00 </li></ul><ul><li>11 0.0000000E+00 0.0000000E+00 </li></ul><ul><li>12 0.0000000E+00 -0.4630561E+11 </li></ul>
  25. 27. TEŞEKKÜRLER :))

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