n
b1, . . . , bn j bj > 0
m
i i = 1, . . . , m
m n
ai ai > 0 ai e" bj d1, . . . , dm
i=1 j=1
di > 0 c1, . . . , cm
ci > 0
C = [cij]
m × n cij > 0
X = [xij] xij
i j
Å„Å‚
m n m n
ôÅ‚
ôÅ‚
ôÅ‚
(ci + cij)xij + di sgn xij min
ôÅ‚
ôÅ‚
ôÅ‚
ôÅ‚
i=1 j=1 i=1 j=1
ôÅ‚
ôÅ‚
ôÅ‚
ôÅ‚
ôÅ‚
ôÅ‚
ôÅ‚
n
òÅ‚
xij d" ai, i = 1, . . . , m,
ôÅ‚j=1
ôÅ‚
ôÅ‚
ôÅ‚
m
ôÅ‚
ôÅ‚
ôÅ‚
ôÅ‚
xij = bj, j = 1, . . . , n,
ôÅ‚
ôÅ‚
ôÅ‚
ôÅ‚
i=1
ôÅ‚
ôÅ‚
ółxij e" 0, i = 1, . . . , m, j = 1, . . . , n.
Å„Å‚
m n m
ôÅ‚
ôÅ‚
ôÅ‚ (ci + cij)xij + diyi min
ôÅ‚
ôÅ‚
ôÅ‚
i=1 j=1 i=1
ôÅ‚
ôÅ‚
ôÅ‚
ôÅ‚
ôÅ‚
ôÅ‚
ôÅ‚
n
ôÅ‚
ôÅ‚
ôÅ‚
ôÅ‚
xij d" aiyi, i = 1, . . . , m,
ôÅ‚
òÅ‚
j=1
m
ôÅ‚
ôÅ‚
ôÅ‚
ôÅ‚ xij = bj, j = 1, . . . , n,
ôÅ‚
ôÅ‚
ôÅ‚
i=1
ôÅ‚
ôÅ‚
ôÅ‚x e" 0, i = 1, . . . , m, j = 1, . . . , n,
ôÅ‚
ôÅ‚ ij
ôÅ‚
ôÅ‚
ôÅ‚0 d" yi d" 1, i = 1, . . . , m,
ôÅ‚
ôÅ‚
ôÅ‚
ół
yi " Z, i = 1, . . . , m.
yi i
xij
ci cij di > 0 i = 1, . . . , m j = 1, . . . , n
aibj
xij =
m
ai
i=1
yi = 1 i = 1, . . . , m j = 1, . . . , n
n
yi = 1 xij = 0
j=1
(X , y )
n
yi = sgn x ij , i = 1, . . . , m.
j=1
2n n
2n
 b1 = 6 b2 = 4
a1 = 7 a2 = 6 a3 = 8
d1 = 112 d2 = 168 d3 = 192 c1 = 15 c2 = 22
c3 = 11
îÅ‚ Å‚Å‚
4 2
ðÅ‚ ûÅ‚
C = 2 4 .
1 5
Å„Å‚
ôÅ‚19x11 + 17x12 + 24x21 + 26x22 + 12x31 + 16x32 + 112y1 + 168y2 + 192y3 min
ôÅ‚
ôÅ‚
ôÅ‚
ôÅ‚
ôÅ‚
ôÅ‚
ôÅ‚
ôÅ‚
ôÅ‚x11 + x12 d" 7y1, x21 + x22 d" 6y2, x31 + x32 d" 8y3,
ôÅ‚
òÅ‚
x11 + x21 + x31 = 6, x12 + x22 + x32 = 4,
ôÅ‚
ôÅ‚x , x12, x21, x22, x31, x32 e" 0,
ôÅ‚
ôÅ‚
11
ôÅ‚
ôÅ‚
ôÅ‚0 d" y1, y2, y3 d" 1,
ôÅ‚
ôÅ‚
ôÅ‚
ôÅ‚
óły , y2, y3 " Z.
1
5 5
(x11, x12, x21, x22, x31, x32, y1, y2, y3) = (1, 4, 0, 0, 5, 0, , 0, ).
7 8
yi
(x 11, x 12, x 21, x 22, x 31, x 32, y1, y2, y3) = (0, 2, 0, 0, 6, 2, 1, 0, 1)