Transport masalasining matematik modeli

4.3.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 c_m+1,_j=0 ёки c_i,n+1=0.
Misol. Quyidagi ochiq modelli transport masalasini yeching.

bk ai	3	3	3	2	2
4	3	2	1	2	3
5	5	4	3	1	1
7	0	2	3	4	5

Bu masalada

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

bk ai	3	3	3	2	2	3
4	3	2	1	2	3	0
5	5	4	3	1	1	0
7	0	2	3	4	5	0

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,
y_min=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, В₃ ,В₄ bazalarga mos ravishda в₁, в₂, в₃, в₄ tonnadan taqsimlash zarur. Agar bir tonna paxtani tashish narxi d_ij 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
b₄=210