1. Transport masalasining matematik modeli Transport masalasini yechish usullari Ochiq turdagi transport masalasini yechish


Ochiq turdagi transport masalasini yechish


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26 Transport masalalariga keltiriladigan taqsimot masalalari

3.Ochiq turdagi transport masalasini yechish
Ba'zi transport masalalarida yuk zapaslari talablar yig‘indisidan kichik yoki katta bo‘lishi mumkin. Bunday masalalar ochiq turdagi transport masalasi deyiladi. Bunday hollarda soxta (fiktiv) m+1 jo‘natish yoki n+1 qabul (iste’mol) qiluvchi punktlari kiritiladi, ya'ni
yoki

Bu punktlarda transport xarajatlari nolga teng qilib olinadi, ya'ni cm+1,j=0 ёки ci,n+1=0.
Misol. Quyidagi ochiq modelli transport masalasini yeching.

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Bu masalada

Shuning uchun oltinchi soxta talabgorni kiritamiz, uning talabi b6=16-13=3 bo‘ladi. Bu soxta punktni kiritib, masalani quyidagicha yozamiz.

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Bu masalani yechib 7-siklda optimal yechimni topamiz, ya'ni
x12=1, x13=3,x24=2,
x25=2, x26=1,x31=3, x32=2, x36=2,
ymin=1·2+1·3+1·2+1·2+1·0+0·3+2·2+2·0=13


Amaliy mashg‘ulot uchun misollar
Uchta А1, А2, А3 paxta punktlarida mos ravishda а1, а2, а3 tonnadan paxta bor. Bu paxtalarni В1, В2, В34 bazalarga mos ravishda в1, в2, в3, в4 tonnadan taqsimlash zarur. Agar bir tonna paxtani tashish narxi dij bulsa, tashishning optimal planini tuzing.
1. a1=330 b1 =180 10 13 16 9
a2=260 b2= 220 d= 11 14 17 8
a3= 310 b3 =300 12 15 18 7
b4=200


2. a1=240 b1 =150 9 12 15 18
a2=230 b2= 160 d= 10 13 16 19
a3= 230 b3 =170 11 14 17 10
b4=220


3. a1=390 b1 =240 18 15 12 15
a2=290 b2= 230 d = 17 13 16 17
a3= 320 b3 =310 16 9 17 16
b4=220


4. a1=330 b1 =320 19 11 18 12
a2=420 b2= 210 d = 16 9 15 10
a3= 350 b3 =290 13 17 14 20
b4=280
5 . a1=340 b1 =270 20 13 15 12
a2=410 b2= 260 d = 19 17 10 13
a3= 350 b3 =290 9 16 11 14
b4=280


6. a1=200 b1 =180 6 9 10 8
a2=250 b2= 120 d = 4 5 9 7
a3= 150 b3 =130 7 6 14 21
b4=170

7. a1=250 b1 =130 12 15 14 17


a2=200 b2= 110 d = 13 8 11 20
a3= 150 b3 =190 19 16 12 21
b4=170
8. a1=280 b1 =180 3 20 15 16
a2=220 b2= 270 d = 12 14 21 10
a3=300 b3 =310 16 19 17 13
b4=200
9. a1=250 b1 =180 20 15 16 13
a2=200 b2= 120 d = 3 14 21 10
a3= 150 b3 =130 12 16 19 17
b4=170

10. a1=350 b1 =230 15 16 13 10


a2=400 b2= 270 d = 20 14 21 17
a3= 250 b3 =200 3 12 16 19
b4=300

11. a1=250 b1 =200 16 13 10 17


a2=250 b2= 120 d = 15 21 14 19
a3= 250 b3 =180 20 3 12 16
b4=250

12. a1=250 b1 =170 13 10 17 19


a2=270 b2= 160 d = 16 21 14 16
a3= 170 b3 =110 15 20 5 12
b4=250

13. a1=350 b1 =320 10 17 19 16


a2=300 b2= 260 d = 13 14 21 12
a3= 370 b3 =215 16 15 20 5
b4=225
14. a1=250 b1 =190 7 9 16 10
a2=350 b2= 210 d = 13 13 18 12
a3= 300 b3 =230 19 9 10 13
b4=270

15. a1=230 b1 =200 17 13 17 20


a2=400 b2= 280 d = 10 9 15 6
a3= 280 b3 =250 7 13 21 7
b4=180
16. a1=290 b1 =200 6 14 18 14
a2=310 b2= 180 d = 13 7 5 15
a3= 240 b3 =220 16 10 16 9
b4=240

17. a1=330 b1 =130 12 5 16 11


a2=370 b2= 280 d = 21 10 7 23
a3= 300 b3 =230 19 13 17 18
b4=360
18. a1=340 b1 =200 8 7 12 15
a2=260 b2= 240 d = 11 9 14 13
a3= 280 b3 =180 10 6 16 9
b4=260

19. a1=300 b1 =190 8 12 10 15


a2=280 b2= 170 d = 4 13 15 14
a3= 220 b3 =240 9 16 17 11
b4=200

20 . a1=400 b1 =225 8 9 14 17


a2=250 b2= 230 d = 9 5 11 22
a3= 350 b3 =335 4 17 18 21
Foydalanilgan adabiyotlar
1.Акулич И.Л. Математическое программирование в примерах и задачах. - М.: Высшая школа, 1996.
2.Badalov F.B. Optimallash nazariyasi va matеmatik dasturlash. “O‘qituvchi”, T. 1989 y.
3.Кузнецов А.В., Новикова Г.И., Холод Н.И. Сборник задач по математическому программированию. Минск, Вышэйшая школа, 1985.
4.Курицкий Б.Я. Поиск оптимальных решений средствами Excel. “Санкт-Перербург”, 1997г.
5.Safaеva K., Bеknazarova N. Opеratsiyalarni tеkshirishning matеmatik usullari. “O‘qituvchi”, 1984y. 1 qism.
6.Лесин В.В., Лисовец Ю.П. Основы методов оптимизации. М. Изд. МАИ 1998.
7.Хазанова Л.Э. Математическое моделирование в эканомике. М. БЕК, 1998.
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