ϳ
ϳ , t- dt, at . , t- bt (t = 0, 1,...) .
Ct (xt, it), ' , C(xt) h*it, ' , Ct (xt, it) = C(xt) + h*it, xt - t, it - t, h -, ' .
: N , .
г:
. , N.
.. , 1 N- , 2- - N-1- .., N- - 1- .
' t k, t=N-k+1.
jk - k- , xk(jk) - k- jk, k- ik = jk + xk(jk) - dk, dk - k- .
, - k- jk .
fk(jk) = min {ck [xk(jk); jk + xk(jk) - dk] + fk-1(jk+xk(jk) - dk)} (1.21)
xk(jk)
. k=N.
fN(j1) = min {c1 [x1(j1); j1 + x1(j1) - d1] + fN-1(j1+x1(j1) - d1)} (1.22)
x1(j1)
k =1
f1(jN) = min {cN [xN(jN); jN + xN(jN) - dN]} = N [bN + dN - jN; bN]=
xN(jN)
= C(bN + dN - jN) + h. bN. (1.23)
N- bN = jN + xN(jN) - dN = xN(jN) = bN + dN - jN.
: N=3; dt, at, bt, : dt = 3 + n1
at = 5 + n1; bt = 4 + n1; h = 1 + n1; C(xt) =
K = n2; m = 2 + n1, n1 - , n2 - . b0 = b3 = 0,
n1 = n2 = 0, k = 13 .
() |
г , N=3
(3) f1(j3) = C(3-j3) 0 < 3-j3 < 5 0 < j3 < 4 Þ 0 < j3 < 3
j3 | |||||
f1(j3) |
|
|
(2)
f2(j2) = min {[c(x2(j2)+ j2+ x2(j2)- d1]+f1(j2+x2(j2)- 3)}
x(j2)
0 < j2+x2(j2)-3 < 4 3 < x2+j2 < 7; 3-j2 < x2 < 7-j2 Þ 0 < j2 < 3
j2 = 0
3 < x2 < 5
j2 = 2 1 < x2 < 4, f1(2+5-3) = f1(4) .
j2 = 3 0 < x2 < 3, f1(3+4-3) = f1(4) .
j2 | |||||
f2(j2) |
f3(j1), j1- 1- . j1 = 0. 0 < x1-3 < 4 = 3 < x1 < 5.
, min 47 ..
.
1- 3 , x10 = 3, 1- 0 ., i1 = 0 , j2 = 0, 0 . .
2- x20 = 3, 3- (1- ) , i30 = 0.
3- 30 = 3.
. ̳ 47 .. x10 = x20 = 30 = 3, .
- , .
N- Si (i = 1,..., N) . Ui, Vi(Si; Ui). , N- ,
SN-1 = VN (SN; UN)
SN-2 = VN-1 (SN-1; UN-2) (1.24)
.....................................................
S = V1 (S1; U1)
, Sk, SN:
Sk = V1 (V2(V3(... VN-1(VN(SN; UN); UN-1); UN-2...) (1.25)
UN, UN-1,..., U1, (1.24), 㳺. , 㳺 .
N-
max W = qi (Si; Ui) ,
fN(SN) = max [qN(SN; UN) + fN-1(SN-1)]
UN
fN(SN) = max {qN(SN; UN) + fN-1[VN(SN; UN)]} (1.26)
UN
f1(S1) = max q(S1; U1)
U1
. W , W, , , . .. . , , .