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Ically mathematical programuvannya - Nakonechny S.І.

5.9.1. Transport problems in merezhevіy formі

Let him set the Count іz skіnchennoyu kіlkіstyu vertex i edges. Postavimo in vіdpovіdnіst kozhnіy vershinі deyake number (I = 1, 2, ..., m), yak nazvemo іntensivnіstyu i -oї top and kozhnіy duzі (іj) - number - Throughput zdatnіst (іj) -oї arc vіdnosyachi tsі value to Pevnyi vіdrіzka t hour (0 <t < ) Napriklad to pevnoї odinitsі hour. For Tsikh minds skіnchenny Count peretvoryuєtsya in trammel (sіt). Poznachimo through nevіdomu value scho oznachaє obsyag deyakoї produktsії, yak peremіschayut at (ij) th duzі for deyaky vіdrіzok hour. Todі to tsogo hour to most vіdrіzka kozhnoї k -oї top of graph can be zapisati Taku carrying rіvnіst:

. (5.42)

Spravdі, Persha scrip oznachaє sumarno obsyag pevnoї produktsії scho protyagom aforesaid hour pribuvaє in k -tu the top on arcs, and other scrip oznachaє sumarno obsyag tsієї produktsії scho vibuvaє on arcs h k -oї top in that samy hour. Otzhe, Je obsyagom rozglyaduvanoї produktsії, yaky spozhivaєtsya (akumulyuєtsya) in the k -іy vershinі and Je obsyagom tsієї produktsії, yaky vidіlyaєtsya (produkuєtsya) top of zgadany vіdrіzok hour. The top for yakoї , Nazivatimemo drain, and the top, for yakoї - Jerel. Top, yakih , Nazvemo neutral.

Natural vvazhati zmіnnі i nevіd'єmnimi i obmezhenimi zverhu numbers i So scho:

. (5.43)

In his Cherga can vvazhati scho quantities i mozhut zmіnyuvatisya in these furrows:

. (5.44)

Rіvnyannya (5.42) can be traktuvati yak rіvnyannya bezperervnostі flow rozglyaduvanoї produktsії on pevnіy MEREZHI (dorіg, truboprovodіv i t. N.) In deyakomu okolі k -oї apex (point). Butt Mauger Buti rіvnyannya zberezhennya kіlkostі rіdini scho held on truboprovіdnіy MEREZHI.

Mozhna postaviti vimogu, dwellers of the reference value is the іntensivnostey Jerel stokіv i values ​​throughput zdatnostey arcs found values ​​nevіdomih zadovolnyali deyaky kriterіy optimalnostі, napriklad, slapped mіnіmalnogo values ​​lіnіynіy funktsії:

. (5.45)

Easy pomіtiti scho sformulovana sіtova transportation problem (5.42) - (5.45) Je uzagalnennyam zvichaynoї transportnoї zadachі (5.1) - (5.4) for the minds nayavnostі promіzhnih punktіv transported i obmezhenih throughput zdatnostey shlyahіv spoluchennya.