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Ically mathematical programuvannya - Nakonechny S.І.

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11.6. Institution matrichnoї gris to zadachі lіnіynogo programuvannya

Yakscho gras 2 x n m x 2 abo Mauger Buti rozv'yazana geometrically, then vipadku gris 3 x n (m x 3) is geometric іnterpretatsіya move from Prostir, scho yak uskladnyuє її pobudovu so i spriynyattya. In vipadku Well, if n> 3 the, m> 3, geometric іnterpretatsіya vzagalі nemozhliva. For rozv'yazuvannya gris m x n vikoristovuyut Priya Institution її to zadachі lіnіynogo programuvannya.

Nekhay rozglyadaєtsya Parn gras Zi strategіyami And that for gravtsya strategіyami for i platіzhnoyu gravtsya The Matrix . Neobhіdno Know optimalnі zmіshanі strategії that de . .

Znaydemo spochatku optimally strategіyu gravtsya A. For basic theorems teorії Igor such strategіya Got zabezpechiti gravtsevі vigrash not Mensch for tsіnu gris (Pokey scho nevіdomu value) u, for whether yakoї povedіnki gravtsya in.

Acceptable, scho Gravets A zastosovuє its optimal strategіyu and Gravets B - a "pure» j -tu strategіyu Bj, todі serednіy vigrash gravtsya A dorіvnyuvatime:

. (11.10)

For Tsikh obstavin vigrash Got Booty not less then, nіzh Cena gris. Otzhe to whether the value of j yakogo the value of the form (11.10) Got Booty not less then, nіzh u:

OAO All Rozdіlivshi obmezhennya on u, otrimaєmo:

Items marked maєmo:

.

Vrahovuyuchi minds scho , otrimuєmo .

Neobhіdno zrobiti vigrash Maximum. Tsogo mozhna dosyagti, if viraz nabuvatime mіnіmalnogo values. Otzhe, vreshtі maєmo zvichaynu task lіnіynogo programuvannya.

Tsіlova funktsіya:

(11.11)

of minds:

(11.12)

. (11.13)

Rozv'yazuyuchi qiu problem simplex method, znahodimo values and takozh value i values Scho Yea optimally rozv'yazkom pochatkovoї zadachі. Otzhe, viznacheno zmіshanu optimally strategіyu And for gravtsya.

For analogієyu mozhna zapisati task lіnіynogo programuvannya for viznachennya optimalnoї strategії gravtsya in. W tsієyu metoyu poznachimo:

Maєmo Taku lіnіynu model zadachі:

of minds:

Obviously, scho problem lіnіynogo programuvannya for gravtsya In Je dvoїstoyu to zadachі gravtsya A, and to optimally rozv'yazok odnієї h takozh viznachaє them optimally rozv'yazok spryazhenoї.

Rozglyanemo butt zastosuvannya metodіv lіnіynogo programuvannya znahodzhennya for optimal rozv'yazku gris.

Agrofіrma "Zorya" rozrobila shіst BIZNES-planіv (X 1, X 2, X 3, X 4, X 5, X 6) in the following їh zdіysnennya rotsі. Od zovnіshnіh fallow minds (the weather will, market analysis toscho) vidіleno p'yat situatsіy (Y 1, Y 2, Y 3, Y 4, Y 5). For skin varіanta Xi BIZNES plan that zovnіshnoї situatsії Yj obchislenі pributki, SSMSC navedenі in Table. 11.2:

table 11.2

Varіant BIZNES plan

Zovnіshnya situatsіya

Y 1

Y 2

Y 3

Y 4

Y 5

pributki, yew. UAH

X 1

1.0

1.5

2.0

2.7

3.2

X 2

1.2

1.4

2.5

2.9

3.1

X 3

1.3

1.6

2.4

2.8

2.1

X 4

2.1

2.4

3.0

2.7

1.8

X 5

2.4

2.9

3.4

1.9

1.5

X 6

2.6

2.7

3.1

2.3

2.0

Neobhіdno vibrato naykraschy varіant BIZNES plan abo kombіnatsіyu іz rozroblenih planіv.

Rozv'yazannya.

Maєmo GRU platіzhnoyu matrix yakoї Je vіdpovіdnі Elements vischenavedenoї tablitsі. Easy perekonuєmosya scho domіnuyuchih strategіy in tsіy grі Absent.

Potіm viznachaєmo:

and takozh

Otzhe, Absent tobto sіdlovoї point and oznachaє Tse, scho neobhіdno zastosuvati method Institution gris to zadachі lіnіynogo programuvannya:

of minds:

Rozv'yazuєmo qiu problem simplex method. Optimally rozv'yazok zadachі: ; . Zvіdsi otrimaєmo optimally rozv'yazok for pochatkovoї zadachі: ; . Cena gris .


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