.
Mavzu:
FAN: jarayonlarni matematik modellashtirish
Reja:
- Transport masalasining qo`yilishi.
- Transport masalasining boshlang`ich yechimini topish.
- Transport masalasining optimal yechimini topish.
1. Transport masalasining qo`yilishi.
Yuk zaxiralari ๐1, ๐2, . . . ๐๐ boโlgan m ta joโnatish punkti, yukka boโlgan talab ๐1, ๐2, . . . ๐๐ boโlgan n ta qabul punktlari berilgan boโlib, joโnatish punktlaridan qabul punktlariga birlik yukni tashish harajatlari ๐๐๐, ๐ = 1 โฆ ๐; ๐ = 1 โฆ , ๐ boโlsin. . Bu yerda i- joโnatish punkti nomeri, j- qabul punkti nomerini bildiradi. Umumiy yuk tashish xarajatlari quyidagi formula orqali beriladi:
๐ ๐
๐ง = โ โ ๐๐๐๐ฅ๐๐
๐=1 ๐=1
Bu yerda ๐ฅ๐๐- i nomerli joโnatish punktidan j nomerli qabul
punktiga tashiladigan yuk hajmi. Yuk tashish harajatlarini iloji boricha kamaytirish uchun z funktsiyaning minimumini hisoblaymiz:
โ๐
๐ง = โ๐
๐=1 ๐=1
๐๐๐๐ฅ๐๐ โ ๐๐๐ (1)
Yuqoridagi masala jadval koโrinishida quyidagicha ifodalanadi:
Qabul
punktlari Joโnatish punktlari
|
1
| |
2
| |
โฆ
|
n
| |
Yuk
zaxiralari
|
1
|
x11
|
c11
|
x12
|
c12
|
โฆ
|
x1n
|
c1n
|
a1
|
2
|
x21
|
c21
|
x22
|
c22
|
โฆ
|
x2n
|
c2n
|
a2
|
โฆ
|
โฆ
| |
โฆ
| |
โฆ
|
โฆ
| |
โฆ
|
m
|
xm1
|
cm1
|
xm2
|
cm2
|
โฆ
|
xmn
|
cmn
|
am
|
Yukka boโlgan talab
|
b1
| |
b2
| |
โฆ
|
bn
| | |
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