, .
n , m . i- j- ij , cij . xij i- , j- ij () , , Ni i- ().
.
:
.
.
:
xij 0, xij - , .
(1) , j- .
(2) i- .
3.5
. , .
, 300, 200, 1000 500 .
I | II | III | IV | ||
I | II | III | IV | |
.
:
15x11+20x12+25x13+40x14+70x21+28x22+15x23+45x24+40x31+70x32+40x33+65x34 min,
:
15x11+30x21+25x31 300,
10x12+25x22+50x32 200,
20x13+10x23+30x33 1000,
50x14+17x24+45x34 500,
x11+x12+x13+x14=50,
x21+x22+x23+x24=20,
x31+x32+x33+x33=30,
xij 0, ().
Excel, , . 31. xij B4:E6 (. . 3.14). , B18:E20. B12:E14. - B7:E7 F4:F6.
F8 B8:E8 ( ), F4:F6 ( ) (. . 3.14 3.15). . 3.15.
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(. . 3.16) , , ( ), , ( xij) . .
. 3.14.
. 3.14
. 3.15
. 3.16
, n , . m , , , .. ij - i- j- , bi- , .. xj j- , . , cj j.
.
:
.
.
:
xj 0, xj- , .
(1) , .
3.6
, . , , .. aij i- j- , cj - j- (). , .
1 | 2 | 3 | 4 | ||
I | |||||
II | |||||
III | |||||
.
:
3x1+4x2+3x3+3x4→ max,
:
3x1+3x2+5x3+2x4 1000,
4x1+2x2+4x3+4x4 600,
3x1+5x2+4x3+3x4 600,
xj 0, , .
Excel, , . 34. xij B3:E3 (. . 3.17). , B6:E6. B9:E11. H9:H11.
. 3.17
F6 F9:E11 ( ) (. . 3.17 3.18). . 318.
" " . 3.19.
. 3.17.
. 3.18
. 3.19
n . 1, 1.
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, : , , .. C=||cij|| .
xij=1, i j, i j;
xij=0, ,
.
.
:
.
.
:
ui, - .
(1) , , (2)- .
(3), , . , 1, , 3.20.
. 3.20
3.7
, , . . (. .) . , : .
.
:
0x11+270x12+430x13+160x14+70x21+0x22+160x23+10x24+200x31+130x32+0x33+ +350x34+210x41+160x42+250x43+0x44 min,
:
x11+x21+x31+x41=1,
x12+x22+x32+x42=1,
x13+x23+x33+x43=1.
x14+x24+x34+x44=1,
x11+x12+x13+x14=1,
x21+x22+x23+x24=1,
x31+x32+x33+x34=1,
x41+x42+x43+x44=1,
u2-u3+3x23 2,
u2-u4+3x24 2,
u3-u2+3x32 2,
u3-u4+3x34 2,
u4-u2+3x42 2,
u4-u3+3x43 2.
, , . 3.21. xij B3:E6. , ( ) , . ( B11:E14). n ( ) - F16.
. 3.21
F8. B7:E7 ( ) F3:F6 ( ) (. . 3.21 3.22). . 3.22. ui (. ). B17:E19. B8:E8.
. 3.23 " ". , , , xij, , .
. , , <Ctrl> , , , ui. ";" (. . 3.23).
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. 3.22
, . 42: $C$4=0; $D$5=0; $E$6=0; $F$3:$F$6=1.
. 3.23
ui. (. . 3.22 . ), , n-2, F18. , $B$17:$D$19 2 (4-2=2).
i j. xij , xij, i=j ( ), 0 . : $B$3=0, $C$4=0, $D$5=0, $E$6=0.
: , , , . 610 . . (. . 3.21).