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Matematika

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decision making with help of hyerarchy method

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Matematika

  1. 1. gadawyvetilebis miReba ierarqiis analizis meTodiT
  2. 2. <ul><li>Tanamedrove biznesis samyaroSi menejers xSirad uxdeba ama Tu im problemis alternatiuli variantebis Sefaseba garkveuli kriteriumebis mixedviT da maT safuZvelze gadawyvetilebis miReba. </li></ul>
  3. 3. amerikelma mecnierma tomas saatim Cvens codvaSi Cadga fexi da daamuSava midgoma romlis mixedviTac gadawyvetilebis miRebis procesi warmoidgineba ierarqiis saxiT.
  4. 4. I done menejeris mizani II done kriteriumebi III done alternetivebi daaxloebiT ase iwvala saatim
  5. 5. problemis gadaWris sami etapi I etapi: kriteriumebis prioritetebis mixedviT dalageba <ul><li>II etapi: ToToeuli kriteriumis mixedviT alternetivebis Sedareba </li></ul><ul><li>III etapi: alternativebis ganzogadebuli Sefasebis miReba kriteriumebis wonebis gaTvaliswinebiT </li></ul>
  6. 6. saatis Skala situacia roca saWiroa kompromisi Sualeduri mniSvnelobebi or mezobel msjelobebs Soris 2, 4, 6, 8 erT alternativas meoresTan SedarebiT gaaCnia aSkara upirateso-ba absoluturi upiratesoba 9 erTi alternativis upiratesoba meoresTan SedarebiT eWvs ar iwvevs cxadi upiratesoba 7 gamocdileba da msjeloba iZleva erTi alternativis arsebitT upiratesobas meoresTan SedarebiT arsebiTi upiratesoba 5 erT alternativas gaaCnia araarse-biTi upiratesoba meoresTan Seda-rebiT araarsebiTi mniSvneloba 3 orive alternativas miznis misaR-wevad Seaqvs erTnairi wyvili erTnairi mniSvneloba 1 axsna gansazRvreba fardobiTi mniSvnelobebis intensivoba
  7. 7. <ul><li>eqsperti saatis skalis mixedviT avsebs wyvil-wyvilad Sedarebis Sebrunebad simetriul C matricas romelic Seicavs n 2 elements Tumca azris gamoTqma mas mxolod n(n-1)/2 jer uwevs </li></ul>menejeri iwvevs eqsperts romelic pirvel etapze alagebs kriteriumebs prioritetebis mixedviT, xolo meore etapze afasebs erTi alternativis upiratesobis xarisxs sxvebTan SedarebiT yoveli kriteriumis mixedviT da TviT kriteriumebis upiratesobis xarisxsac.
  8. 8. wyvil-wyvilad Sedarebis matrica <ul><li>C aris Sedarebis matrica. misi elementebi akmayofileben pirobas </li></ul><ul><li>c ij >0, c ii =1, c ij =1/c ji </li></ul><ul><li>Tu c ij >1 , es niSnavs, rom i - uri alternativa ufro mniSvnelovania, vidre j - uri alternativa da c ij ricxvi am upiratesobis gamomxatveli sididea. </li></ul><ul><li>maSin bunebrivia , c ji =1/c ij <1 </li></ul><ul><li>cxadia, rom C matrica aris Sebrunebulad simetriuli. </li></ul>
  9. 9. kolejis kursdamTavrebuls SesTavazes samuSao adgili sam ( α , β , γ ) firmaSi. cota xnis fiqris Semdeg mas Camouyalibda Semdegi kriteriumebi 1.kolegebi 2.Tanamdeboba 5.adgilmdebareoba 6.dawinaureba zrda 3.reputacia , imiji 4.Semosavali
  10. 10. kmayofileba samuSaoTi α β γ I done: mizani II done: kriteriumebi III done: alternativebi Tanamdeboba kolegebi dawinaureba zrda mdebareoba reputacia Semosavali
  11. 11. am amocanaSi n = 3 (alternativebis raodenoba) m = 6 (kriteriumebis raodenoba) eseigi man unda Seavsos m +1=7 wyvil wyvilad Sedarebis matrica : B, A 1 , A 2 , ...,A 6 . matricebis Sevsebisas is xelmZRvanelobda saatis skaliT da miiRo Sesabamisi matrica Sesabamisi wonebis veqtorebiT
  12. 12. kriteriumebis wonis veqtoris miReba 1 3 3 3 2 1/4 6 4 1 5 6 3 1 5 1/3 1/5 1 2 2 1/3 4 1/3 1/6 1/2 1 1/4 1/8 3 1/2 1/3 1/2 4 1 1/3 2 4 1 3 8 3 1 1 6 5 4 3 2 1 B=
  13. 13. wonis veqtoris miReba <ul><li>C matricis </li></ul><ul><li>yoveli j </li></ul><ul><li>svetisTvis </li></ul><ul><li>viTvliT </li></ul><ul><li>elementebis jams: </li></ul>j=1,2,...,n Σ S 1 S 2 S 3 S 4 S 5 S 6
  14. 14. I. etapi <ul><li>vadgenT axal Č=||č ij || matricas, sadac </li></ul>i,j=1,2,...,n
  15. 15. vadgenT wonis veqtors sadac
  16. 16. II etapi: TiToeuli kriteriumis mixedviT wonebis veqtorebis miReba <ul><li>1) kriteriumi “kariera” A A 1 =||a ij ||, i,j=1,2,3 </li></ul>|| || || S 1 S 2 S 3 S 1 =1+1/2+3= 9/2 S 2 =2+1+2= 5 S 3 =1/3+1/2+1= 11/6 vipovoT svetebis elementTa jamebi
  17. 17. maSin Σ =d 1 Σ =d 2 Σ =d 3 d 1 =2/9+2/5+2/11= 398/495 d 2 =1/9+1/5+3/11= 289/495 d 3 =6/9+2/5+6/11= 798/495 sabolood miviRebT radgan gvaqvs 3 alternativa vyofT samze
  18. 18. 2) kriteriumi: “Semosavali” miviRebT
  19. 19. 3) kriteriumi “kolegebi” miviRebT
  20. 20. 4) kriteriumi “adgilmdebareoba” miviRebT
  21. 21. 5) kriteriumi “reputacia ” miviRebT
  22. 22. 6) kriteriumi “Tanamdeboba” miviRebT
  23. 23. <ul><li>III etapi saboloo Sefasebis veqtoris miReba </li></ul>SevadginoT V matrica, romlis striqonebia miRebuli veqtorebi
  24. 24. axla ganvixiloT U veqtorisa da V matricis namravli
  25. 25. miviReT alternativebis integraluri SefasebaTa wonis veqtori e.i yvelaze didi wona aqvs γ alternativas. amitom kolejis kursdamTavrebuli iRebs gadawyvetilebas  firmaSi muSaobis Sesaxeb. aRvniSnoT, rom  - s upiratesoba aqvs α -ze koeficientiT w 3 /w 1 =1.2 da β -ze w 3 /w 2 =1.4
  26. 26. menejeris mizani kriteriumebi alternativebi III I II II II III III III
  27. 27. I kriteriumiT nxn
  28. 30. <ul><li>aRvniSnoT i -uri kriteriumiT alternativebis Sefasebis Sedegad miRebuli wonis veqtori </li></ul>- I kriteriumiT yvela alternativis Sefaseba -II kriteriumiT yvela alt.-is Sefaseba - i -uri kriteriumiT yvela alt.-is Sefaseba - m -uri kriteriumiT yvela alt.-is Sefaseba ) ... ( ) ... ( ) ... ( ) ... ( , , 2 , 1 , , 2 , 1 2 , , 22 , 21 2 1 , , 12 , 11 1 mn m m m in i i i n n v v v V v v v V v v v V v v v V          
  29. 31. pirveli alternativis Sefasebis veqtori II alternativis Sefasebis veqtori j -uri alternativis Sefasebis veqtori n -uri alternativis Sefasebis veqtori I alternativis Sefasebis veqtori
  30. 32. k -uri alternativis Sefaseba i -uri kriteriumi cxadia: 1 , ,..., 1 , ,..., 1 , 0 1       n k V ik n k m i V ik
  31. 33. -veqtorisa da V matricis gadamravlebiT vadgenT SefasebaTa wonis veqtors
  32. 34. yvela alternativis integraluri Sefasebis safuZvelze menejeri iRebs gadawvetilebas alternativis arCevis Sesaxeb (airCeva maqsimaluri komponentis Sesabamisi alternativa)
  33. 35. vin ver gaigo???

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