TRANSPORT MASALASINI BOSHLANG‘ICH REJALASHTIRISH VA OPTIMAL YECHIMGA KELTIRISH

Аннотация

В статье рассматривается концепция транспортной задачи, ее математическая модель и методы поиска оптимальных решений — метод северо- западного угла, метод аппроксимации Фогеля (VAM) и методы MODI (модифицированного распределения). Алгоритм каждого метода проиллюстрирован примерами иоцененаего практическая значимость. Annotation: This article discusses the concept of the transportation problem, its mathematical model, and methods for finding optimal solutions — the Northwest Corner Method, the Vogel Approximation Method (VAM), and the MODI (Modified Distribution) methods. The algorithm of each method is illustrated with examples and its practical significance isassessed. Kalit so‘zlar: Transport masalasini matematik modeli, Boshlang‘ich yechim topish usullari,optimalyechim topish. Ключевые слова: Математическая модель транспортной задачи, Методы нахожденияначальногорешения,Нахождениеоптимального решения. Keywords: Mathematical model of the transportation problem, Methods for finding an initial solution, finding an optimal solution. 760 Kirish. Transport masalasi – bu chiziqli dasturlashning keng qo‘llaniladigan masalalaridan biri bo‘lib, maqsad – berilgan manbalar va talab nuqtalari o‘rtasida tashish xarajatlarini Originalarticle ISSN:3030-3931, Impact factor: 7,241 Volume 7,issue1,Aprel 2025 https://worldlyjournals.com/index.php/Yangiizlanuvchi worldly knowledge OAKIndex bazalari : research gate, research bib. Qo’shimchaindex bazalari:zenodo,open aire. googlescholar. minimallashtirishdan iborat. Ushbu masala ishlab chiqarish, logistika va resurslar taqsimoti sohalarida muhimahamiyatga ega. Transportmasalasining matematik modeli Berilgan: -m tayetkazibberuvchi (manbalar), har biri birlikmahsulotga ega. -ntaiste’molchi (talab nuqtalari), har biri b i rlikmahsulot talab qiladi. -Har biri-manbadan j-iste’molchiga yetkazish xarajati . Maqsad:Tashish xarajatlari yig‘indisiniminimallashtiruvchi reja ni topish: MinZ= =1 =1 × cheklovlar: = = 0 Yechishusullari: Boshlang‘ichyechim topishusullari a)Shimol-gʻarb burchak usuli: Bu usulda jadvalning chap yuqori burchagidan boshlab talab va taklif bo‘yicha ketma-ket taqsimlashamalga oshiriladi. b)Vogel taxminiy usuli(VAM): Har bir satr va ustundagi ikki eng kichik qiymat orasidagi farq hisoblanadi. Eng katta farqli yo‘nalish tanlanadi. Optimalga yaqin boshlang‘ichyechim beradi. Transport masalasining optimal usullarinitopish Optimal yechim topish:MODI usuli MODIusuli boshlang‘ich asosiy yechimni optimallashtirishuchun qo‘llaniladi: 1.Potensiallar , ni topish. 761 2.Bo‘shkataklar uchun = -( + )hisoblash. Originalarticle ISSN:3030-3931, Impact factor: 7,241 Volume 7,issue1,Aprel 2025 https://worldlyjournals.com/index.php/Yangiizlanuvchi worldly knowledge OAKIndex bazalari : research gate, research bib. Qo’shimchaindex bazalari:zenodo,open aire. googlescholar. 3.Agar barcha 0bo‘lsa –yechim optimal. Aks holda, eng salbiy bo‘yicha yangi bazisga o‘tish. ∆ ≥ ∆ Amaliy misol : 6 ta ta’minotchi va 7 ta iste’molchi mavjud bo‘lgan quyidagi transport masalasini ko‘rib chiqamiz. Berilgan transport jadvali (qiymatlar –xarajatlar). a)Shimoliy-g‘arb burchak usulidayechilishiniko‘ramiz: 1-jadval Bu yerdan biz ni qiymatlarini vaZni topamiz. min(a,b) deb olamiz. = 762 Originalarticle ISSN:3030-3931, Impact factor: 7,241 Volume 7,issue1,Aprel 2025 https://worldlyjournals.com/index.php/Yangiizlanuvchi worldly knowledge OAKIndex bazalari : research gate, research bib. Qo’shimchaindex bazalari:zenodo,open aire. googlescholar. 2-jadval Shimol-g‘arb usuli asosidaboshlang‘ich taqsimot: min(40,100)=40 = =0 11 = 40 12 = 0 13 =0 14 = 0 15 = 0 16 = 0 17 = 0 21 = 60 22 = 10 23 =30 24 = 0 25 = 0 26 = 0 27 = 0 31 = 0 32 = 70 33 =40 34 = 0 35 = 0 36 = 0 37 = 0 41 = 0 42 = 0 43 =0 44 = 50 45 = 0 46 = 0 47 = 0 51 = 0 52 = 0 53 =0 54 = 50 55 = 0 56 = 0 57 = 0 61 = 0 62 = 0 63 64 = 20 65 = 50 66 = 80 77 = 70 Xarajat ni topishuchun: MinZ= formuladan foydalanamiz. =1 =1 × barcha elementlarini ning moselementlariga ko‘paytirib qo‘shamiz. 763 =16 40+17 60+20 10+22 70+18 30+13 40+22 50+20 50+23 20+10 50+22 80+15 70= $ 1 × × × × × × × × × × × × 10330 Originalarticle ISSN:3030-3931, Impact factor: 7,241 Volume 7,issue1,Aprel 2025 https://worldlyjournals.com/index.php/Yangiizlanuvchi worldly knowledge OAKIndex bazalari : research gate, research bib. Qo’shimchaindex bazalari:zenodo,open aire. googlescholar. Amaliy misol : 6 ta ta’minotchi va 7 ta iste’molchi mavjud bo‘lgan quyidagi transport masalasini ko‘rib chiqamiz. Berilgan transport jadvali (qiymatlar –xarajatlar). b)Vogel taxminiyusuli (VAM) dayechilishini ko‘ramiz: 1-jadval Minimal elementusuliniqo‘llash tartibi: 1. Xarajatlarni tekshirib chiqish: Har bir manba uchun har bir manzilga transport xarajatlarini taqqoslash. 2. Eng kichik xarajatni topish: Har bir manba va manzil juftligi bo‘yicha eng kichik transport xarajatini aniqlash. 3. Manba va manzillarni to‘ldirish: Eng kichik xarajat bo‘