transport masalasining matematik modeli va xossalari

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16-ma’ruza. transport masalasining matematik modeli va xossalari reja: 1. transport masalasi 2. transport masalasining matematik modeli. 3. transport masalasining xossalari. tayanch so'z va iboralar :transport masalasi, yopiq modelli transport masalasi, "band katakchalar", "bo'sh katakchalar", "shimoliy g'arb burchak" usuli, "minimal xarajatlar" usuli, xarajatlar matritsasi, potentsiallar, potentsial tenglama, yopiq kontur, xos transport masalasi, xos bazis echim, tsikllanish, e-usul, ochiq modelli transport masalasi, differentsial rentalar usuli, shartli optimal echim, qator va ustun xarakteristikalari, tartiblanuvchi belgilar. 1.transport masalasi. transport masalasi chiziqli dasturlash masalalari ichida nazariy va amaliy nuqtai nazardan eng yaxshi o'zlashtirilgan masalalar dan biri bo'lib, undan sanoat va qishloq xo'jalik mahsulotlarini tashishni optimal rejalashtirish ishlarida muvaffaqiyatli ravishda foydalanilmoqda. transport masalasi maxsus chiziqli dasturlash masalalari sinfiga tegishli bo'lib, uning chegaralovchi shartlaridagi koeffitsientlardan tuzilgan (aij) matritsaning elementlari 0 va 1 raqamlardan iborat bo'ladi va har bir ustunda faqat ikkita element 0 dan farqli, qolganlari esa 0 ga teng bo'ladi. transport masalasini echish uchun uning maxsus …

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doriga teng, ya'ni tenglik o'rinli bo'lsin deb faraz kilamiz deylik, har bir ishlab chiqarish punkti ai dan hamma iste'mol qiluvchi punktga mahsulot tashish imkoniyati mavjud hamda ai, punktdan vj punktga mahsulotni olib borish uchun sarf qilinadigan xarajat sij pul birligiga teng bo'lsin. xij bilan rejalashtirilgan vaqt oralig'ida ai punktdan vj punktga olib boriladigan mahsulotning umumiy miqdorini belgilaymiz. transport masalasining berilgan parametrlarini va belgilangan noma'lumlarni quyidagi jadvalga joylashtiramiz. b1 b2 bn i/ch mahsulotlar miqdori a1 c11 x11 c12 x12 c1n x1n a1 a2 c21 x21 c22 x22 c2n x2n a2 am cm1 xm1 cm2 xm2 cmn xmn am talab miqdori b1 b2 bn 1-jadval. masalaning iqtisodiy ma'nosi yuk tashishning shunday rejasini tuzish kerakki: 1) har bir ishlab chiqarish punktidagi mahsulotlar to'la taqsimlansin; 2) har bir iste'molchining mahsulotga bo'lgan talabi to'la qanoatlantirsin va shu bilan birga sarf qilinadigan yo'l xarajatlarining umumiy qiymati minimal bo'lsin. masalaning birinchi shartini quyidagi tenglamalar sistemasi orqali ifodalash …

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yig'indisi unga bo'lgan talablar yig'indisiga teng bo'lsa, u holda bu masalani yopiq modelli transport masalasi deb aytamiz. 1-teorema. har qanday yopiq modelli transport masalasi echimga ega. isbot. shartga ko'ra , u holda berilgan transport masalasining rejasi bo'ladi. haqiqatdan ham, ab chunki ai≥0, bj≥0, a>0. , . demak, transport masalasining hamma shartlarini qanoatlantiradi. shuning uchun bu miqdor masalaning rejasi bo'ladi. 2-teorema. transport masalasinng shartlaridan tuzilgan matritsaning r(a) rangi ga teng. isbot. haqiqatdan ham, bu matritsa kengaytirilgan holda quyidagi ko'rinishga ega bo'ladi: bu matritsaning ixtiyoriy qatori (masalan, 1-qatori) qolgan qatorlarning chiziqli kombinatsiyasidan iborat ekanligini ko'rsatish mumkin. buning uchun m+1, m+2, ..., m+n qatoridan o'zaro qo'shib, natijasidan 2, 3, ..., (m+n) qatorlarni ayirsak 1-qatorni hosil qilamiz. demak, r(a)=n+m-1. endi 2, 3, ..., (m+n) - qatorlar o'zaro chiziqli bog'liq bo'lmagan sistemani tashkil qilishini ko'rsatamiz. buning uchun ixtiyoriy a2, a3,….,am , 1 2… n, sonlar olib ularga moe ravishda 2, 3, ..., m, (m+n) - …

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n chegaralangan bo'ladi va uning qiymati mos ai va bj larning qiymatidan oshmaydi. shunday qilib, transport masalasi rejalaridan tashkil topgan to'plam bo'sh to'plam bo'lmaydi, u chegaralangan to'plam bo'ladi. demak, transport masalasi optimal rejaga ega. nazorat sovollari: 1. transport masalasi 2. transport masalasining matematik modeli. 3. transport masalasining xossalari. adabiyotlar ro’yxati 1.ts.safaeva. matematik dasturlash. toshkent, «ibn sino»-2004. 2.prof. sara billey.discrete mathematical modeling. university of washington, winter quarter, 2011. � prof. sara billey.discrete mathematical modeling. university of washington, winter quarter, 2011, pp.73-87. � prof. sara billey.discrete mathematical modeling. university of washington, winter quarter, 2011, pp.73-87. � prof. sara billey.discrete mathematical modeling. university of washington, winter quarter, 2011, pp.73-87. _1554207694.unknown _1554207702.unknown _1554207706.unknown _1554207708.unknown _1554207710.unknown _1554207712.unknown _1554207713.unknown _1554207711.unknown _1554207709.unknown _1554207707.unknown _1554207704.unknown _1554207705.unknown _1554207703.unknown _1554207698.unknown _1554207700.unknown _1554207701.unknown _1554207699.unknown _1554207696.unknown _1554207697.unknown _1554207695.unknown _1554207690.unknown _1554207692.unknown _1554207693.unknown _1554207691.unknown _1554207688.unknown _1554207689.unknown _1554207687.unknown 11 mn ij ij ab == = åå 111211 21222 12 ... ... ........................... ... n n …

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11 1000100100 0100010010 0001001001 00...010...00, 00...0 ij ij nn ijji ijj jj ij ij mn ab ximjn a abba xb aa ab x a a aaabbb aa == === === = æö ç÷ ç÷ ç÷ ç÷ ç÷ = ç÷ ç÷ ç÷ ç÷ ç÷ ç÷ èø ×+×+×+×+×+×= ×+×+ å åå 12 2312 01...00, ........................................ .............................. 00...000...10, mn mn abbb aaabbb ì ï ×+×+×+×= ï í ï ï ×+×+×+×+×+×= î 11 11 0 mn ij aba == ==> åå (1,;1,) ij ij ab ximjn a === (1,;1,) ij ij ab ximjn a === 1 111 nnn ij i iji jjj ab a xba aa === === ååå 11 nn ijji ijj jj abba xb aa == === å åå ij ij ab x a = 1 m p +- 1111000000 0000111000 0000000111 1000100100 0100010010 0001001001 a æö ç÷ ç÷ ç÷ ç÷ ç÷ = ç÷ ç÷ ç÷ ç÷ ç÷ ç÷ èø b b …

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16-ma’ruza. transport masalasining matematik modeli va xossalari reja: 1. transport masalasi 2. transport masalasining matematik modeli. 3. transport masalasining xossalari. tayanch so'z va iboralar :transport masalasi, yopiq modelli transport masalasi, "band katakchalar", "bo'sh katakchalar", "shimoliy g'arb burchak" usuli, "minimal xarajatlar" usuli, xarajatlar matritsasi, potentsiallar, potentsial tenglama, yopiq kontur, xos transport masalasi, xos bazis echim, tsikllanish, e-usul, ochiq modelli transport masalasi, differentsial rentalar usuli, shartli optimal echim, qator va ustun xarakteristikalari, tartiblanuvchi belgilar. 1.transport masalasi. transport masalasi chiziqli dasturlash masalalari ichida nazariy va amaliy nuqtai nazardan eng yaxshi o'zlashtirilgan masalalar dan biri bo'l...

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