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1. Îáùàÿ ÇËÏ.

1. = (X1, X2, …,Xn)

Xk  0, k = 1, 2, …,t;

Xk ~, k = t + 1, …, n.

Îãðàíè÷åíèÿ

aikXk = aio (i = 1, …, l) (k = 1, …, n);

aikXk  aio (i = l + 1, …, s) (k = 1, …, n);

aikXk  aio (i = s + 1, …, m) (k = 1, …, n).

Z = CkXk + C0 (max, min).



Êàíîíè÷åñêàÿ ìîäåëü ÇËÏ.

Ñèñòåìà îãðàíè÷åíèé çàäàåòñÿ ñ ïîìîùüþ ñèñòåìû ëèíåéíûõ óðàâíåíèé.

Xk  0, k = 1, 2, …,n.

Îãðàíè÷åíèÿ

aikXk = aio (i = 1, …, n).

Z = CkXk + C0 (max).



Ñòàíäàðòíàÿ ìîäåëü. Óäîáíà äëÿ òåîðåòè÷åñêîãî èçó÷åíèÿ.

1. Xk  0, k = 1, 2, …, n.

Îãðàíè÷åíèÿ

aikXk  aio (i = 1, …, n).

Z = CkXk + C0 (max).

Ïåðåéäåì îò îáùåé ìîäåëè ê ñòàíäàðòíîé.

X1  0, X2  0, X3~.

2X1 – X2 + X3 = 5;

X1 + X2 – X3  2;

3X1 – X2 + 2X3  2;

Z = 2X1 + 5X2 – X3 + 4 (min).

Ýòî áûëà îáùàÿ ìîäåëü.

Ïåðåéäåì ê ñòàíäàðòíîé.

X10;

X2 = –X2’;

X3 = X3’ – X3’’ (X3’0, X3’’0).

2X1 + X2’ + X3’ – X3’’ = 5;

X1 – 2X2’ – X3’ + X3’’  2;

3X1 + X2 + 2X3’ – 2X3’’  2;

Ïðèâåäåì âñå âûðàæåíèÿ ñèñòåìû ê íåðàâåíñòâàì ñî çíà÷êîì “”.

2X1 + X2’ – X3’’  5;

X1 – 2X2’ – X3’ + X3’’  2;

– 3X1 – X2 – 2X3’ + 2X3’’  – 2;

Z’ = – Z;

Z’ = – 2X1 + 5X2 +X3’ – X3’’ – 4 (max).