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Mathematics programmers - Nakonechny S.I.

5.7. Dvahhetapna transport task

In the classic setting of transport tasks, you can be allowed to be transported without intermediaries to post-graduates. Alya to practice often dystrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr At such times, the tasks of the tasks are sub-divided into two stages: the spoiler must know the optimal plan for transporting the providers from the posts to the middle, and then - from the mediators to the local people. Such a task is called a dual-purpose transport task .

Nehai in m points of post-office A 1, A 2, ..., Аm є відповідно Odnitsyn products, yaku neobhіdno to transport up to l mediadzhnikih firm , Місткості сховищ яких вищаться , And sweep to deliver її to spizhivacham , The need to become . Відомі також витрати на перевезення одниці продукції від of the skin supplier to the middle of the day - Та від посередників до споживачів - . Potrbno viznachiti optimal scheme of transporting products with a minimum of total vitrates. Якщо обсяг продукції, що it is transported from the i- th senior supplier to the k -ої фірми, through , And the oath of vandage, sho be transported to and from the k- th firmi j- mu spizivachev - through , Then the mathematical model of problems and mathematicians:

For the mind:

;

;

;

;

.

Significantly, if the zagalny oath Дорівнює місткості всіх складів і of bases , And takozh sumarnіy potrebnosti vsіh spizhivachіv , Tobto = = , Then such a dual transport problem can be unleashed by two-way vehicles. In the shortest possible time, optimal planning for two tasks is not necessary with an optimal plan of goals.

The method of rozv'yazuvannya dvuhetapnoy transportovy problems , rozrobleny Order-March , polagoye vrahuvannі mistkostey srednednikіv dvіchі - yak postachalnikov i yak spizhivachіv. Умови задачі подаються у вигляді таблиці, in the rows of anchors about the posts, and about takozh about the middlemen, and in the stations - the dans about the mediators and the spozhivachiv. At klitinah, yakі rozmіcheny on peretinі rowkіv-postachalnikov that stovpcіv-spizhivachіv, fіksyut real spend on transporting odinnitsi produktsii. In dagonalnyh klitinah on peretinі rowkіv і stovptsіv, yakі vіdpovidayut posadrednitskim firmam, to put zero values ​​of costs. Reshto klіtin tablitsi blocking, tobto vartosty perevezen pririvnyut to action to milk the great number of M. In the process of rozv'yazuvannya tasks in tsich klitinah not vobachachit pereveznania produktsii, sho vidpіdіda umvam dvuhhetapnoy transportnoy zadachi.

Виробниче об'єднання складається з трьох філіалів: А 1, А 2, А 3, які виготовляють однорідну продукцію in the obligations відповідно 1000, 1500 and 1200 odnitsy on місяць. The product is managed in two warehouses: D 1 і D 2 mіstкістю відповідно 2500 т 1200 od., And потім - до п'яти споживачів B 1, B 2, ..., B 5, which populate some of the 900, 700, 1000, 500 і 600 od. Vartostі perevezen odinnitsi produkcii (in witches' wits) vіd vibroknіv in a warehouse, and potim - zі storіv before spozhivachіv are induced in tab. 5.23 and tab. 5.24.

Table 5.23

Table 5.24

Moreover, for indivydualnymi contracts can takozh bezposerednyi supply products from the first fіlіialu to another spizhivacha, and takozh from the third fіlіialu - up to the fourth spizhivacha. Vartizst transportuvannya odinnitsi produktsii and transit route A 1 B 2 дорівнює 3 ум. One, and for the route A 3 B 4 - 4 minds. Od. The transfer of products to the warehouse at the warehouse is inadmissible.

Formulate the problem posed yak transportnu promizhnimi items (dvuhhetapnu) ta viznachiti її optimal plan.

Rozvjazannya. In the delivered tasks, the leather warehouse can be filed by a whiphead point in the direction of the product and the yak item of recognition. Tom in the transport table grants the role of the producer of goods, and the business.

Перевезення продукції безпосередньо від філіалів до споживачів (крім випадків, взначих в умові задачі), а and takozh zі warehouse in the warehouse blocking the input of the goods in the warehouse to bring the great vartes moving the odinnitsi produktsii - M.
Probudovan z urauvuvannam tsiogo transportnoy table of two-purpose tasks is imposed lower (Table 5.25).

Table 5.25

Зауважимо, що в клітинках D 1 D 1 і D 2 D 2 розміщується нульова вартість перевезення продукції. Tse admit nevne vikoristannya єmnost szhovishch u zv'yazku zmotlivim transitnym transportuvannannyam produktsii.

The transport task is balanced, bo:

Od.,

But also Od.,

That is, no need to enter the transport of a table of a phisical postal worker.

The first basic plan of transport tasks is motivated by the method of minimum wintry. Розрахуємо загальну вартість перевезень, що відповідає цьому планну:

Z 1 = 2 x 1000 + 3 x 300 + 5 x 1200 + 1 x 1200 + 1 x 900 + 3 x 700 +

+ 8 x 900 + 5 x 100 + 3 x 500 + 1 x 600 = 22 900 (dd).

Tse the basic task plan and the non-optimal. Perehіd vіd ynogo before another plan vikonuemo, zapovnemichi empty klіtinku D 1 D 1 zgіdno z impulled by the cycle (Table 5.26).

Table 5.26

Viznachimo vartizhest transport zgіdno ot another basic plan:

Z 2 = 2 x 300 + 3 x 700 + 3 x 300 + 5 x 1200 + 1 x 1200 +

+ 1 x 900 + 8 x 900 + 5 x 100 + 3 x 500 + 1 x 600 = 21 500 (dd).

Tablitsa, scho vidpіdіїє third basic plan of tasksі, має such viglyad:

Table 5.27

In Table. 5.27 maemo optimal plan of transport tasks:

Z min = 2 x 300 + 3 x 700 + 3 x 300 + 5 x 1200 + 1 x 700 + 4 x 500 + + 1 x 900 + 8 x 400 + 5 x 600 + 1 x 600 = 20 000 .).

For більшої наочності an optimal plan for transporting products of two-purpose transport tasks is submitted in the framework of the visa (fig 5.1):

Fig. 5.1. Optimal plan for transporting products

On the diagrams, it is shown that in the first warehouse, 300 + 300 + 700 = 1300 od. Products, tobto yogo mіstkіst vikoristvuyutsya not obnynstyu ( D 1 D 1 = 1200 od.). It is cured by direct deliveries of products for routes A 1 B 2 in the scope of 700 od. І А 3 В 4 - у обсьзі 500 од.

The transport task is the most attractive one for an alternative optimal plan, which is to be observed in the first place through transport of products and warehouses up to the third one.

Krim rozglyanutoї in transport problems із promizhimnymi mozhut zusstrіchatisya і так такііції:

1. Unbalanced transport tasks ( ). In the course of time, it is necessary to introduce a phobic post-worker, an abiotic foster person, who is known to have such a task before the closed type.

2. Місткість проміжних пунктів не дорівнює загально обсягу продукції почальників: a) the number of (In order to introduce a fictitious industrial item, a product tax, a "transportable" to a new one, a mere dorivnuvati of an unimproved part of the product of a supplier, or to allow transit to be transported for a voucher, not just a yak (Od.)); B) the number (In the case of a variety of imports, enter a fictitious postmaster ─ zrozumilo, but the volume of industrial items should not be vikoristivuvatimsya).

3. Місткість проміжних пунктів не відповідає загальній потребі споживачів: а) (In order to introduce a fictitious industrial item, a product tax, and a "transportable" one to one prior to a dispute, Vj , moe means misappropriation of a drink of a spodivacha, abo permission to directly transport products from suppliers to spozhivachyv for the oath not mensh yak (Od.)); B) (Analogous to item 2b).