Введение в специальность / Vv_v_sp_11
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zik+1 = zik − X aijk xjk + qik , i = |
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k = |
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:25!2; |
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1, m, |
1, s. |
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j=1 |
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=/ %'+: *0;0$1*#) '0-0&# =)&(=&+, /',)&'*# ! |
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:25!); |
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2 &/$( +0=0*/;)**+&'/ |
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0 ≤ xjk ≤ fjk, j = |
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:25!4; |
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1, n, k = 1, s; |
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X X cjk xjk − X X pik zik → max. |
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k=1 j=1 |
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u(t) = (xtj , j = 1, n) !
2,)#): ,)9'+=*+3:0'=/;*#) +<+'*0;)*/% A(t) = E B(t) = (−atij , i =
1, m j = 1, n)# q(t) = (qit, i = 1, m) p(t) = (pti, i = 1, m) d(t) = (dti, i =
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'0#0;( :25!2; :25!+; :+. *+ '0-/&0'1 , &$)#( ): ,/#) ! |
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J (u) = X (−p 0 (t)z(t) + c 0 (t)u(t)) → max, |
:25!6; |
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t=1 |
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z(t + 1) = A(t)z(t) + B(t)u(t) + q(t), |
t T = {1, 2, . . . , s}, |
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z(1) = z0, |
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:25!1; |
0 ≤ z(t) ≤ d(t), |
t T {s + 1}; |
0 ≤ u(t) ≤ f (t), t T. |
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'0'/;)&90% :+#)$1 :).+'=0&$),+0+ <0$0*&0 <#$0 =0&&:+'=)*0 , - ! = |
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#0% +'=0&$1 -=+/',+#/' +#*+=+#*( -=+#(9./ / |
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=0'*#) +'=0&$/ -=+/',+#%' =0 |
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6#)&1 aij - +<$): -=+#(9.// i3+- +'=0&$/ *)+</+#/:#- #$% -=+/',+#&',0 +#*+- )#/*/.# -=+#(9.// j3+- +'=0&$/ !
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-=+#(9.// j30+ ,/#0 ,#-(&90):+- , -)=/+# ]t −1, t] j = 1, n! 2 *0;0$1*#- :+:)*' /:) '&% *0;0$1*#) '0-0&# -=+#(9.//
xj (0) = x0j , j = 1, n.
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yi(t) = X aij xj (t)
j=1
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y(t) = Ax(t)
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y(t) ≤ x(t − 1).
+&$)#*)) *)=0,)*&',+ #+$. *+ ,#-+$*%'1&% #$% ,&)/ -)=/+#+, t =
1, 2, . . . , z !
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&&/+#% /' ,#$)/'$+.)**+0+ -+$(;0): &$)#( ( :0'):0'/;)&9( :+#)$1 #/*0:/;)&9+0+ :).+'=0&$),+0+ <0$0*&0!
p 0 x(z) → max; Ax(t) ≤ x(t − 1), x(t) ≥ 0, t = 1, 2, . . . , z; x(0) = x0.
8'0 :+#)$1 %,$%)'&% #/*0:/;)&9/: 0*0$+0+: &'0'/;)&9+- :+#)$/ 2! )+*'1),0 7'0'=0'#3,#-(&9> :&: ! - ! = =0'#)$0 II;! **0 #+&'0'+;*+ (-=+3
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