simpleks (dansig) usuli

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4-mavzu. simpleks (dansig) usuli tayanch so`z va iboralar: simpleks usul, optimallik bahosi, sun`iy o`zgaruvchilar. dars rejasi 1. simpleks jadvalini tuzish. 2. simpleks jadvalida almashtirishlarni bajarish. 3. optimal yechimni aniqlashga doir teoremalar. 4. maqsad funksiyaning chekli minimumga ega bo`lmaslik sharti. 5. simpleks usuli. dansig yaratgan simpleks usul bilan chpm ning optimal yechimini topish uchun chpm kanonik shaklda va cheklamalar sistemasi keltirilgan tenglamalar sistemasi shaklida bo`lishi kerak. simpleks usuli chpm ning optimal yechimini chekli qadamdan so`ng topishga yordam beradi. bizga quyidagi chpm berilgan bo`lsin. (1) (2) (3) ko`rinib turibdiki bu masalada (4.1) cheklamalar keltirilgan tenglamalar sistemasi ko`rinishidadir. (4.1) sistemani vektor shaklida yozib olamiz: , bu yerda vektorlar sistemasi o`lchovli fazoda chiziqli erkli birlik vektorlar sistemasidan iborat bo`lib, bazis vektorlar sistemasini tashkil etadi. ular m o`lchovli fazoning bazisini tashkil qiladi. ushbu vektorlarga mos keluvchi o`zgaruvchilar «bazis (erksiz) o`zgaruvchilar» deb ataladi. o`zgaruvchilar bazis bo`lmagan (erkli) o`zgaruvchilar. agar erkli o`zgaruvchilarga 0 qiymat bersak, bazis o`zgaruvchilar …

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… … … … 0 0 … 0 … … … … … … … … … … … … … … 0 0 … 1 … … (5) formuladan ko`rinib turibdiki, simpleks jadvaldagi bazis vektorlarga mos lar har doim 0 ga teng. agar ustunlarga mos barcha lar uchun shart bajarilsa, u holda yechim optimal yechim bo`ladi. chiziqli funksiyaning minimal qiymati ga teng bo`ladi. shunday qilib, shart (1)-(3) chpm uchun optimallik sharti deyiladi. agar kamida bitta j uchun bo`lsa, u holda masalaning optimal yechimi bo`la olmaydi. bunday holatda topilgan bazis rejani optimal rejaga yaqin bo`lgan boshqa bazis rejaga almashtirish kerak. yangi bazisga kiritiladigan vektorni (6) shart asosida aniqlaymiz. masalan, bo`lsin. demak, yangi bazislar sistemasida vektor bazis vektor sifatida qatnashishi kerak. agar bazisga kiritilsa, u holda eski bazis vektorlardan birortasini bazisdan chiqarish kerak, chunki (1) sistemaga mos matritsaning rangi: . bazisdan chiqariladigan vektorni aniqlash uchun nisbat orqali aniqlovchi koeffitsient tushunchasini kiritamiz. …

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ekshirib boramiz. shunday qilib quyidagi teoremalar o`rinli. 1-teorema. agar biror bir bazis reja uchun tengsizlik o`rinli bo`lsa, u holda bu reja optimal reja bo`ladi. 2- teorema. agar bazis rejada biror bir uchun shart o`rinli bo`lib qolsa, u holda optimal reja bo`lmaydi va uholda shunday rejani topish mumkin bo`ladiki, uning uchun tengsizlik o`rinli bo`ladi. agar biror bir uchun tengsizlik o`rinli bo`lib, bu ustundagi barcha elementlar uchun bo`lsa, u holda masalaning maqsad funksiyasi chekli ekstremumga ega bo`lmaydi. shuning uchun quyidagi shartlarga: 1. ; 2. (1)-(3) masalaning optimal yechimga ega bo`lmaslik sharti deyiladi. agar chpmda maqsad funksiyasi ko`rinishda bo`lsa, u holda masalaning optimallik sharti sifatida: tengsizlikni; masalaning optimal yechimga ega bolmaslik sharti sifatida esa: 1. ; 2. tengsizliklarni qabul qilamiz. misol. quyidagi masalani simpleks usul bilan yeching. yechish. belgilashlar kiritamiz va simpleks jadvalni to`ldiramiz. 0 1 -3 0 2 0 a.k. 0 7 1 3 -1 0 -2 0 - 0 12 0 …

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76.bin oleobject77.bin oleobject78.bin oleobject79.bin oleobject80.bin oleobject81.bin oleobject4.bin oleobject82.bin oleobject83.bin oleobject84.bin oleobject85.bin oleobject86.bin oleobject87.bin oleobject88.bin oleobject89.bin oleobject90.bin oleobject91.bin image5.wmf oleobject92.bin oleobject93.bin oleobject94.bin oleobject95.bin oleobject96.bin oleobject97.bin oleobject98.bin image53.wmf oleobject99.bin image54.wmf oleobject5.bin oleobject100.bin image55.wmf oleobject101.bin image56.wmf oleobject102.bin image57.wmf oleobject103.bin image58.wmf oleobject104.bin image59.wmf image6.wmf oleobject105.bin image60.wmf oleobject106.bin image61.wmf oleobject107.bin image62.wmf oleobject108.bin image63.wmf oleobject109.bin image64.wmf oleobject6.bin oleobject110.bin image65.wmf oleobject111.bin image66.wmf oleobject112.bin image67.wmf oleobject113.bin oleobject114.bin image68.wmf oleobject115.bin image7.wmf oleobject116.bin oleobject117.bin image69.wmf oleobject118.bin image70.wmf oleobject119.bin image71.wmf oleobject120.bin oleobject121.bin image72.wmf oleobject7.bin oleobject122.bin image73.wmf oleobject123.bin image74.wmf oleobject124.bin image75.wmf oleobject125.bin image76.wmf oleobject126.bin oleobject127.bin image8.wmf image77.wmf oleobject128.bin image78.wmf oleobject129.bin image79.wmf oleobject130.bin image80.wmf oleobject131.bin image81.wmf oleobject132.bin oleobject8.bin oleobject133.bin image82.wmf oleobject134.bin oleobject135.bin image83.wmf oleobject136.bin image84.wmf oleobject137.bin image85.wmf oleobject138.bin image9.wmf image86.wmf oleobject139.bin oleobject140.bin oleobject141.bin oleobject142.bin oleobject143.bin oleobject144.bin oleobject145.bin oleobject146.bin oleobject147.bin oleobject9.bin oleobject148.bin oleobject149.bin oleobject150.bin oleobject151.bin oleobject152.bin oleobject153.bin oleobject154.bin oleobject155.bin oleobject156.bin oleobject157.bin image10.wmf oleobject158.bin oleobject159.bin oleobject160.bin image87.wmf oleobject16

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4-mavzu. simpleks (dansig) usuli tayanch so`z va iboralar: simpleks usul, optimallik bahosi, sun`iy o`zgaruvchilar. dars rejasi 1. simpleks jadvalini tuzish. 2. simpleks jadvalida almashtirishlarni bajarish. 3. optimal yechimni aniqlashga doir teoremalar. 4. maqsad funksiyaning chekli minimumga ega bo`lmaslik sharti. 5. simpleks usuli. dansig yaratgan simpleks usul bilan chpm ning optimal yechimini topish uchun chpm kanonik shaklda va cheklamalar sistemasi keltirilgan tenglamalar sistemasi shaklida bo`lishi kerak. simpleks usuli chpm ning optimal yechimini chekli qadamdan so`ng topishga yordam beradi. bizga quyidagi chpm berilgan bo`lsin. (1) (2) (3) ko`rinib turibdiki bu masalada (4.1) cheklamalar keltirilgan tenglamalar sistemasi ko`rinishidadir. (4.1) sistemani vektor shaklida yozib ola...

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