n F1, . . . , Fn
m N1, . . . , Nm
Å„Å‚
ôÅ‚
ôÅ‚cx min
ôÅ‚
òÅ‚
ôÅ‚Ax e" b,
ôÅ‚
ôÅ‚
ół
x e" 0,
cj - j Fj, j = 1, . . . , n,
bi - i
Ni, i = 1, . . . , m,
aij - Ni Fj ,
i = 1, . . . , n, j = 1, . . . , m,
xj - Fj , j = 1, . . . , n.
1 900 7 2000
2 1000 8 1500
3 2000 9 1200
4 3000 10 2000
5 4000 11 1800
6 3700 12 1800
n
s0 s0 e" 0 s0
 s0 = 0
s0 (s0 e" 0)
rt (rt e" 0) t t = 1, . . . , n
xt (xt e" 0) t t = 1, . . . , n
st (st e" 0) t t = 1, . . . , n
xt, st " R,
t = 1, . . . , n
n
st-1 + xt - st = rt, t = 1, . . . , n.
xt - xt-1, t = 1, . . . , n (x0 := s0)
xt - xt-1 = yt - zt, yt, zt e" 0, t = 1, . . . , n,
yt (yt e" 0) t t = 1, . . . , n
zt (zt e" 0) t t = 1, . . . , n
t - 1 t
a a > 0
b b > 0
n n
a yt + b st min .
t=1 t=1
a
 = > 0
b
Å„Å‚
n n
ôÅ‚
ôÅ‚ yt + st min
ôÅ‚
ôÅ‚
ôÅ‚
ôÅ‚
t=1 t=1
ôÅ‚
ôÅ‚
òÅ‚
ôÅ‚st-1 + xt - st = rt, t = 1, . . . , n;
ôÅ‚
ôÅ‚
ôÅ‚
ôÅ‚xt - xt-1 - yt + zt = 0, t = 1, . . . , n;
ôÅ‚
ôÅ‚
ôÅ‚
ół
xt, yt, zt, st e" 0 t = 1, . . . , n.
st = 0 t = 1, . . . , n
{xt, yt, zt, st}td"n yt zt
t = 1, . . . , n
4n 2n
n
Å„Å‚
ôÅ‚
òÅ‚xt = rt + st - st-1
xt-1 = rt-1 + st-1 - st-2 Ò! rt - st-1 + st - rt-1 + st-2 - st-1 = yt - zt
ôÅ‚
ółx - xt-1 = yt - zt
t
yt - zt + 2st-1 - st - st-2 = rt - rt-1, t = 1, . . . , n s-1 := 0, r0 := 0.
n xt t = 1, . . . , n n
s0 rt t = 1, . . . , n
Å„Å‚
n n
ôÅ‚
ôÅ‚ yt + st min
ôÅ‚
ôÅ‚
ôÅ‚
ôÅ‚
òÅ‚
t=1 t=1
, s-1 := 0, r0 := 0.
ôÅ‚
ôÅ‚y - zt + 2st-1 - st - st-2 = rt - rt-1;
ôÅ‚
ôÅ‚
t
ôÅ‚
ôÅ‚
óły , zt, st e" 0 t = 1, . . . , n.
t
yt
zt n
3n
 n
sn = 0
s0 s0
st t = 1, . . . , n
n n n
a yt + b st + c zt min,
t=1 t=1 t=1
c > 0 t - 1
t
m i i = 1, . . . , m
n j j = 1, . . . , n
ai ai > 0 i i = 1, . . . , m
bj bj > 0 j j = 1, . . . , n
cij i j
C = [cij]
m n
ai = bj,
i=1 j=1
 X = [xij]m×n
xij i j
Å„Å‚
m n
ôÅ‚
ôÅ‚
ôÅ‚
cijxij min
ôÅ‚
ôÅ‚
ôÅ‚
ôÅ‚
i=1 j=1
ôÅ‚
ôÅ‚
ôÅ‚
ôÅ‚
ôÅ‚
ôÅ‚
ôÅ‚
n
òÅ‚
xij = 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.
ai i = 1, . . . , m bj j = 1, . . . , n
ai i = 1, . . . , m bj j = 1, . . . , n