TRANSPORT MASALASINING MATEMATIK MODELI VA OPTIMAL YECHISH USULLARINI TAHLIL QILISH
Keywords:
Kalit so‘zlar: transport masalasi, chiziqli dasturlash, Shimoliy-g‘arbiy burchak usuli, Vogel usuli, MODI, logistika, optimallashtirish, transport xarajatlari, operatsion tadqiqotlarAbstract
ANNOTATSIYA
Ushbu maqolada transport masalasining matematik modeli, uning chiziqli
dasturlash bilan bog‘liqligi va optimal yechish usullari ilmiy-amaliy nuqtai nazardan
tahlil qilindi. Nazariy qismda logistika va transport tizimlarining iqtisodiyotdagi roli,
xarajatlarni kamaytirishning korxona samaradorligiga ta’siri hamda transport
masalasining operatsion tadqiqotlardagi o‘rni yoritildi. Amaliy qismda 3 ta ta’minotchi
va 4 ta iste’molchidan iborat muvozanatlangan transport jadvali tuzildi. Shimoliy-
g‘arbiy burchak usuli yordamida boshlang‘ich joiz reja, Vogel approksimatsiya usuli
yordamida yaxshilangan reja hamda potensiallar usuli (MODI) orqali optimal reja
topildi. Hisob-kitoblar shuni ko‘rsatdiki, boshlang‘ich rejaning umumiy xarajati 890
birlikni, Vogel usuli bilan olingan rejaning xarajati 730 birlikni, yakuniy optimal
rejaning xarajati esa 725 birlikni tashkil etdi. Bu natijalar transport masalalarida
boshlang‘ich reja sifatining muhimligini, MODI usulining esa optimal yechimni qat’iy
tekshirish va yakunlashdagi samaradorligini tasdiqlaydi.
References
ADABIYOTLAR
1. Taha, H. A. (2017). Operations research: An introduction (10th ed.). Pearson.
2. Hillier, F. S., & Lieberman, G. J. (2021). Introduction to operations research
(11th ed.). McGraw-Hill Education.
3. Dantzig, G. B. (1963). Linear programming and extensions. Princeton University
Press.
4. Malacký, P., & Madleňák, R. (2023). Transportation problems and their
solutions: Literature review. Transportation Research Procedia, 74, 323-329.
https://doi.org/10.1016/j.trpro.2023.11.151
5. Korukoğlu, S., & Ballı, S. (2011). An improved Vogel's approximation method
for the transportation problem. Mathematical and Computational Applications, 16(2),
370-381. https://doi.org/10.3390/mca16020370
6. Pratihar, J., Kumar, R., Edalatpanah, S. A., & Dey, A. (2021). Modified Vogel’s
approximation method for transportation problem under uncertain environment.
Complex & Intelligent Systems, 7, 29-40. https://doi.org/10.1007/s40747-020-00153-
4
7. Juman, Z. A. M. S., Hoque, M. A., & Buhari, M. I. (2013). A sensitivity analysis
and an implementation of the well-known Vogel’s approximation method for solving
an unbalanced transportation problem. Malaysian Journal of Science, 32(1), 66-72.
8. Lasić, T., Rožić, T., & Stanković, R. (2023). Optimization of transport network
using mathematical methods. Transportation Research Procedia, 73, 5-16.
https://doi.org/10.1016/j.trpro.2023.11.885
9. Kumar, A., & Thakur, S. K. (2025). Comparative analysis of optimization
models for transportation problems. Science & Technology Journal, 13(1).
https://doi.org/10.22232/stj.2025.13.01.21
10. Sarvirova, N., & Samatov, U. (2022). Optimization of transport and logistics
services in servicing the export potential of the Republic of Uzbekistan. Universum:
Technical Sciences, 98(5-11). https://doi.org/10.32743/UniTech.2022.98.5.13617
11. Raimova, S. R., & Mamatova, Z. X. (2025). Transport masalasini boshlang‘ich
rejalashtirish va optimal yechimga keltirish. Ilm Fan Xabarnomasi, 7(1).
