home Other disciplines Books Mathematics programmers - Nakonechny S.I.

Mathematics programmers - Nakonechny S.I.

5.6. Transport problem with extraordinarial powers

In practice, in tasks that have been dealt with in hiring, it is often necessary to teach doctors how to do things: the inconvenience of overland transportation beyond the routes; Neobhідність перевезень разнорідної продукції тощо. So you can set up a mathematical formulation of transport tasks, and you can apply them to the country.

Розглянемо кілька особливостей відкритих transport problems with додатковими умов .

1. Dodatkov's mind, take care of the transfer of a freelancer to a spivovach. In this way, in the optimal plan for the protection of the clay, it is obovyazykovo to smell the buti vlnimi ( ).

Rozv'yazuchi transport problem with dodatkovuyu I'm on the fence in the past postakan, neobhidno u vpdpіdnih klіtinakh zmіniti znachennosti vartostey perevezen odіmnitsі productіїї on the act of a great number (to be put to a large number of M ). Oskilki vygljagnuti vische method of rozv'yannya transport tasks udozhlilyuyut organizatsiyu transport in such a way, so mnimizuyetsya zagalnaya vartit vitrat on transportuvannya, then it is possible to suspend the exclamation from the sight of transportation in large quantities, but to avoid the vikonannya of such dodatkoi ymovi.

2. Dodatkov's mind is transported for enlarging the routes of a strictly vigilant product, toto vikonannya obovyazykovykh postochany. In the optimal plan for the transport tasks, such a dodatkovuyu umovoi klitinii vidpodіdnih fiktivno vvedenih postachalnikov chi spizhivachiov majut bouti vіlnimi.

Rozv'yazuchi this type of transport problem, neobhidno u vidpovidnih klitinah takozh zbilshiti znachennosti vartostey perevezen (to be put large number of M ).

3. Додаткова умова необхідності перевезення від і- я почальника j- mu spizhivachevі not less kij odіnitsі product, tobto enter додаткове обмеження вид: .

Rozv'yazuchi transport problem with such dodatkovuyu I'm thinking, neobhidno zmіniti kachatkovi umovi: the oath of post-office kij in the payment of the reserve to the reserve of the i- th successor ( ) That for the consumption of the j- th cohabiting . Znaydzhny optimal plan for transport problems and zmіnenimi umovami (de vikoristani znachennya ) To swallow, vrahovoychi millet .

4. Додаткова умова необхідності перевезення від і- я почальника j- mu spizhivachevі not more than kij odnitsyn products, tobto enter dodatkov obmezhenya mind: .

For vikonannya takoї dodatkovo ymovi neobhimdno in the transport table j- th spizivacha write dvichi. Once yogo is consumed by the value of kij , and the other time - by the divisor . Vitraty for transporting the odinnitsi products in obozh sovptsyah povinni buti nevertheless for the vinyatkom klitini on the renegotiation of the i- th steward і j- th spizivacha z demand . In this case, the number M should be raised. In this way, the task is to be explored visually.

5. In practice, often potrybno viznachiti optimal plan for the transportation of non-food products, tobto rozv'yati bahatoproduku problem. A mathematical model is such a visage:

De k - indeks to the form of production, but it is necessary to transport it.

Rozv'yazuchi bagatoproduku transport problem, potiblobno zablokuvati ti klіtini, yakі zv'yazuyut postavchiliv і spozhivachіv schodo postachan riznoi produkcii. Take blokuvannya zdіysnyuyutsya introduced to dos vysokikh vartostey perevezen odinnitsi produktsii (great number M ), ali slіd zauvazhiti, scho nayavnist zablokovanih klitin mozhe can call to nemozhivolistі rozv'yannya zadachi. Tom at such a time neobhіdіno perevіryati, chi є dostatnya kіlkіst nezablokovani переi transport for the motives of the basic task planі, який повинен містити Додатну змінну.

Three naftopereobrobnyh backwaters A 1, A 2 and A 3 and 3 with the maximum yield productivity of 30, 20 and 15 yew. T gasoline zabezpechuyot chotiri benzohshchascha B 1, B 2, B 3, B 4, schodenna kotorba some of which become 10, 20, 25 and 20 tis. Gasoline. Gasoline is supplied to the gasoline stations by pipelines. Vartosty perekachuvannya 1000 tons of gasoline from plants to shovishch (in wits odinitsah) are induced in Table. 5.19.

Table 5.19

Formulaty ta vozv'yati vidpovidnu transport problem with neodminnim vikonannyam such minds:

1) I will need a gasoline B 4;

2) for the shortage of gasoline to the grasshopper B 2 zgіdno with the contract perebacheni penalnі sanktsії: 5 mind. Od. For kozhni 1000 tons of gasoline;

3) at the call of the repair workers on the pipelines to the gasoline from the plant A 1 to the shoe B 1, a time-thinned out.

Rozvjazannya . Viznachimo, up to a type of nalezhit transport problem:

, .

For the transport task, the mission is to meet, unbalanced. Zvedennya її to zakritogo type need to be introduced dodatkovogo fictitious postavalnika А 4 з продуктивністю а 4 = 75 - 65 = 10 (тисяч tons). Kilkist gasoline, sho "vidpravlyaetsya" fictitious plant to benzoshovisch, in the optimal plani meaning of the vigilance of an uninhanced popita in the clause of the confession. Tomu for vikonannya persoshoy dodatkovoy vimogi zadachi neobhіdno zablokuvati klіtinku fiktivnogo postavalnika A 4 ta spizhivacha B 4, having written down in ni dovit visoku vartizhest vereviznennya M. Todi mozhno bouti vpevnenim, scho in the optimal planі transportnoy tasks klyotinka obovyazyakovo bude nezapovnenoyu.

Vikonannya drugovi izvi tasks i zabezpechuyutsya tim, scho in a row of a fictitious supplier in the stock B 2 vartitst transportuvannya 1000 tons of gasoline dorivnyuatime 5 mind. Od. Zmist zero.

Oskilki nemozhlivo transportuyuti gasoline from plant A 1 to shovishcha B 1, then neobhidno takozh blocking route A 1 B 1. For the right in the designated klіinttsi zistosti C 11 = 4 the value of M is recorded.

Z I will look at the table. 5.20 In the first plan of transport tasks, such a vigil (the swinging support plan is motivated by the method of Vogel approximating):

Table 5.20

Otzhe, the first supportive plan of problems and non-optimal. Naybіlis porushennya uchiv optimіnostіі vіdpііdіі інжінім клінкамм А 4 B 1 та А 4 B 3 таблиці. Оскільки обидві вони мають однакові коефіціннти With 41 = С 43 = 0, then for zapovnennya you can vibrate be yaku them, for example, A 4 B 1. Perehid to another plan vikonuetsya for this cycle:

Після цього кроку заблокована клітинка А4B4 стає порожньоюю.

Next rozv'yazuvannya tasks submitted to the vigilat table. 5.21 ta Table. 5.22.

In Table. 5.22 maemo optimal plan of transport tasks, de:

.

Zmin = 5 x 5 + 3 x 25 + 5 x 20 + 3 x 15 = 245 mind. Od.

Through nezalansovannіst tsієї transportnoї problemyi sposterygatimyetsya nedopostachannya gasoline to the first benzoshovische in the 10,000 tonne of communications. For legal reasons, transportation for such a plan will be naimenshimi i stanovitimut 245 mind. Od.

The alternative optimal plan is dystanemo, having filled the A 4 B 3 (for ne 4 + v 3 = c 43) clique with such a cycle:

You can also write:

.

Zmin = 5 x 15 + 3 x 15 + 5 x 20 + 1 x 10 + 3 x 5 = 245 minds. Od.

Mіnіmalnі zagalnі vitrati for transportuvannya by the oath 245 minds. Od. To meet the third optimal plan of tasks, zgіdno z yakim tretє benzoskhovische otrimaє on 10000 tons of gasoline less than, nizh demanded.

Існування дух альтернатиних оптимальних планів розглянутої транспортної задачі розшієє mozlovistі stosovno residual priyonyattya рішення.