Mathematics programmers - Nakonechny S.I.

5.3. Methods of motivating the basic plan of transport tasks

Як і в звичайному симплексному методі, розв'язування транспортної задачиі полягає в цілеспрямованому переборі та перевірці on optimality of the basic plan. The obtuse of such an iterative process is motivated by the first basic plan.

The first basic plan for transport tasks , which can be motivated by a method, is a boule that is rooted in the growth of a rope, up to the necessity of folding rozraunki. Zavshyaki vischezgadanim osoblivostym budomi mathematicheskoi model of transport problems and simulate the simple method of motivations of the basic plan. Розглянемо method північно-західного kuta, мінімальної вартості, подвійної переваги and the method of approximating Vogel. Pobudov supporting plan zerno podavati viglyadі tablitsi, in yakii postachalniki produktsii vidpovidayut row, and spizhivachi - stovpchikam.

Nekhay pomoti specific transportovye tasks submitted in Table. 5.2.

Іode to the method of північно-західного a kut of the field in that, поо заповнення таблиці починають, не враховуючи витостей перевезень, з лівого верхнього (північно-західного) a kut. At klitinu zapiskuyut less than two numbers a 1 and b 1. Dali pass to the onset of the cliche in the life of the family at the store, and zapovnoyut її, і т. Д. Закінчимть заповнення таблиці у правій нижній клітинці. Such a supply of supplies will be delivered on the basis of the table.

Розглянемо цей процес детальніше на прикладі.

Spotka, not vrahovoychi vartosty transfer, zavzhdi zagovolnyayut consumer first spyzhivacha B1, vikoristoyuchi stock first akademika A. 1. In our application (Table 5.2) consumer spizhivacha In 1 to become = 110, and the reserve of the litter - = 150 oditnits (tobto and reserve of the first postmaster can be worried about the satisfaction of the consumer of the first spozhivacha), that in the cliche A 1 V 1 note is less than the value , , Tobto 110. Now the consumer of the first spozhivacha pobnistyu zadovoleni, i is transferred to the satisfaction of the needs of the oncoming (another) spozhivacha B2. The yogis of yogo consumption = 50. Pislya zadovolennya needs of the first spozhivacha filling of the reserves of the first post-bureaucrat become 150 - - 110 = 40. Otzhe, vіd the first vibrochnika another spozhivachevіi can transfer the product 40 oditnits products, the volume A 1 V 2 note number 40. Pislya chyogo, okkilki reserve The first post-office worker will be hung up, will be transferred to the Vicoristan Reserve of the step-by-step hedge-maker A 2. Yogo stock = 60, and unhappy with the consumption of another spozhivacha 50 - 40 = 10, the volume in the A 2 B 2 note number 10, і other spozhivach at such a way takozh pobnistju otrimav neobhіdnu kilkist product. Moved to the satisfaction of the needs of the approaching mate V 3. In the result of the partial vicarities of other yogo suppliers, the potting of the product becomes 60 - 10 = 50. The otze, from the other vibrokeeper to the third spozhivacha, you can transport 50 odnitsyn products. Klіitinka A 2 V 3 mіstimime zatshenchene number 50, і tsim stock of the post-holder A 2 budut ponnistyu vycherpanі. It is transferred to the stand-alone storage of the remaining (third) A3 stand-by. Were consumed by third-party consumers in the 60 -50 = 10 mix. For them, the satisfaction is with the stocks of the A 3. The clerk A 3B 3 has a number 10, i is consuming the spies. In 3, they are happy. Movable to the rest of the co-habitat In 4 c the needs b 4 = 80, whichever is better for the ravine, filling in the stockpile of the third steward: 90 - 10 = 80.

Table 5.2

Otzhe, in the table 5.2 in zapovnenyh klіtinkah numbers are meant, sho ozozyayut mozhlivy plan for the transfer of products. The sum of numbers (transfer) in rows is equal to the levels of supply of posts, and the sum of the numbers for the posts - the requirements for the needs of the individuals.

Analogic result can be returned, yakshcho pochati from the right lower kut table, rihayuchis to lyvogo top. The procedure of the method can be zastosovuvati takozh, prichinauchi rozpodil supplies in the lower lower kuta and rihayuchis to the upper right on the dagagoni. In such times, the rospodil can be transported by a method called pivdenno-zahidnogo kuta, to which the method is called diagonal. Method північно-західного кута є найпростішим, one and і namensh efektivnim. Process vidushkanya optimal plan nislya povchatkovogo support, viznachenogo method pivnichno-zahidnogo kuta, pozhyazany zі znachnim otsygom obsoblyuvualnyh robot, the yogo realizuyut on EOM.

Vignichno zagalnu vartіst transporting zgіdno z povatkovkim oborimnym plan. From the first post-lord to the first spozhivacha neobhіdno carry 110 oditynits products for tsinoyu 4 mind. Od. (The price is written in the upper right part of the skin clotinium), otze, koshtuvatime mind. Od. In addition, it is necessary to transport one of the first post-earners 40 oditnits products to another spizivacha for tsinoyu 4 mind. Od. І t. D. In such a way, the vistigiousness of the transport of goods is vividly vague:

(Dd).

THEOREM 5.4. The basic plan of transport problems, knowledge by the method of the peasants and zakhidny kut, the manager of the acyclic.

Beforehand . By using the method of induction number . For The theorem is obvious: the plan Acyclical, okkilki warehousing Element. So the very acyclic is the plan for , Oskilki vin zagradaetsya lishe z dvoh klitin.

The theorem is valid for the active . The fairness for the number .

It is permissible for assignments, in transport tasks (5.1) - (5.4) , Tobto pislya first crocus for the method of pivnichno-zahidnogo kuta otrimaemo , Всі інші . Dalshi kroki to the method of povyazhenі із yogo zastosuvannam up to the table of rozmіrnistyu , De , a , Prichomu vsya zapisi і consumer's tables zbіgayutsya with stocks and needs of the time, крім . For pripuschennjam індукції the plan, знайжений by a method північно-західного a kuta for , Tobto in the new table, acyclic. Obviously, if we adjoin to the first plan of the first row with a non-zero element, do not set the cycle, or vidushkaniy in such a way the plan will be for the plan of tasks for , And the theorem is given.

Induced in the power of the basic plan, one hundred and fifty planivities, and otrimanі rozglyanutimi in lower ways, yakі pevnoyu mirovu є modifikatsyami method pivnichno-zahidnogo kuta.

Obviously, as for the motivations of the supporting plan, physicians vartosty transfer, then the sum total of all posts can be changed, and the otrimanie of the basic plan will be reduced to optimum.

Іode to the method of minimally vartosty polyagay in that, on the leather crochet zapovnjut klіtinku tabli, yaka maє naimenshu vartim esteem odinnitsi produkcii. So, I repeat the doti, the docks will not be rozpodileno all products mizzh postavalnikami ta spizhivachami.

Foldable for the third method of the plan of problems with high visibility (Table 5.3).

Naimenshu vartіst mayut transporting, yakі zdіysnayutsya vіd A 2 to B 3 ta Vіd A 3 to B 2 (tsіna vereviznya oditytsi produktsii - 1 mind od). You can be a prisoner for them, for example, A 2 V 3. Oskilki postavilnik maє 60 oditnits produkії, a spizhivach need same takoї ії kіlostі, then in klіtinu A 2 V 3 nalichno znachennya 60. In such a way to reserve another postchalnik pobnistyu vycherpanі, and The third consumer is in need of satisfaction. Takozh mіnіmalnoyu - vartіst transfer from a third postpartan to another spizhivacha, that is subject to takozh klitinu A 3 V 2.

З клітинок таблиці, що зашились незапроненими, вибираємо наступне мінімальне значення вартості перевезень, яке дорівнює 2 mind. Od. - for clitin A 1 B 3, A 2 B 4, A 3 B 1 ta A 3 B 4. A cloak of clay A 2 B 4 ta A 1 B 3 nemozhlive, oskilki podachalnik A 2 vzhe pozhnistyu vycherpav vlasniy osnyg spesiv, zdovolonyayuchi consumer spizhivacha In 3, and spizhivach In 3 ponnyostyu having satisfied its own consumers. Otzhe, mozhna zapovniti tilki klіtinu A 3 V 1 chi A 3 B 4. The A 3 B is solicited 1. The reserve of a 3 = 90, prichomu 50 oditytsy produkcii vzhe nadano another spizhivachev. Otzhe, maemo pour 90 - 50 = 40, and the consumer b 1 = 110, then the third postpartan before the first spozhivacha plan to transport 40 oditnits products. Now at the clinic A 3 V 4 can not be recorded be-a kind of a post-office oschanya, oskilki reserve a third post-bell in veche ponynistyu impersonation.

Znovu vibiraeto naimenshu vartit for klitin tables, shochu zalishilisya empty, i prodovzhueto process, leaving all the reserves will not be rozpodileni, and consumers - zadovoleni.

Table 5.3

Bj

Ai

B 1 = 110

B 2 = 50

B 3 = 60

B 4 = 80

And 1 = 150

4

70

4

2

5

80

And 2 = 60

5

3

1

60

2

A 3 = 90

2

40

1

50

4

2

As a result, such mirkuvan otrimali povchatkovy support plan, zagalna vartim transport for yakogo become:

(Dd).

Znachenny tsіlової functіії менше за попередній варіант, mean a short-range plan to the optimal.

Method of subversion . Yaksho rozmіrnіst zadachi dosyat great, then perebir for the method mіnіmalnії vаrtоstі уккладнюється. In such a time proizesti poshuk klitin z namenshimi vartostyami mozhna, zastosoyuchi method podvіynoi perevagi.

Zgіdno z protsedoroju ts'ogo to a method before pochatkom zapovnennja tablitsi neobhіdno poznachiti be-yakimi symbols klіtinki, yakі mistjat naimenshu vartits in row, and potim - beside stovpchikah. Tablitsu pozynayut zapovnyuvaty z klitinok, cognition dvichi (yakі mistjat vartosty, scho і mіnіmalnimi і in a row, і in стовпчику). Далі заповнюють клітинки, позначені once (Що містять мінімальні вартостіі пoвoкo, пo в стовпчику), and вже потім - for the method мінімальної Варгості.

Table 5.4

Bj

Ai

B 1 = 110

B 2 = 50

B 3 = 60

B 4 = 80

And 1 = 150

4

110

4

V 2

5

40

And 2 = 60

5

3

VV 1

60

V 2

A 3 = 90

V 2

VV 1

50

4

V 2

40

(Dd).

Dressing for the motivations of the basic plan for this method is made easy by removing the namenshogo from zistavlennnyi z rozgljanutimi vische znachenny tsil'ovoy funktsii. Otzhe, such a plan є vyblizhchim to optimal.

The method of Vogel approximating . For the cyme method on the leather crochet, the size of the dowry is to be found in the leather row and the stock of the transport table. Ці різниці записують у спеціально відведених місцях таблиці - зню та справа у кілька ряків та стовпчиків, що відповідають крокам заповнення таблиці. З-поміж усіх різниць vibirajut naybіlshu у уідповідномуномуку chi стовпчику заповнять клітинку з найменшою ватістю. Yaksho z nasvoyh naybіlshih rіznits kіlka, vibirayut be-yakyі vіdpііdіchny ря ryadok abo stovpchik. If you fill up the unsecured list, one line is assigned to the stock, then you add to the account, and the spreadsheet is sold for the method of minimum wages.

Dany method of motivating the basic plan vrahovuє not the route with the minimal vitrates transporting the products, ale th spivvodnoshennya vitrat at the row chi stovpchiku, tobto rozrahovuyutsya naskilki, mozhe zbilshitis vartchast postanya on the approaching krokok procedure, yakshchoo not zdіsniti on streaming krotci postachannya in klitinu z mіnimalnoyu vartіstyu.

The method of Vogel's approximating is particularly suitable for the tasks of the great rozmirnosts of the fold, which lays down the basic plan.

Table 5.5

Bj

Ai

B 1 = 110

B 2 = 50

B 3 = 60

B 4 = 80

Різниці order

And 1 = 150

4

110

4

40

2

5

2

2

0

And 2 = 60

5

3

1

60

2

1

2

A 3 = 90

2

1

10

4

2

80

1

1

1

Різниці по стовпцях

2

2

1

3

2

2

1

2

3

At the table 5.5. Навпроти кожного ряка і стовпчика записиі значенияі, які знайдені як різниці між мінімальним значенням вартості та наступним за его по рівню. The maximum value on Perche takoї rіznitsі krotsі vіdpovіdaє fourth stovpchiku i oznachaє, scho in razі, if not bude zadovolena require fourth spozhivacha transported produktsії od tert postachalnika for tsіnoyu 2 d. Od. For oditnitsyu, then on the advancing crooks vartizist transported mozhe bouti on 3 minds. Od. Більшою. Tobto іnakshe Mauger become a scho needful fourth spozhivacha neobhіdno bude zadovolnyati transported produktsії od postachalnika Perche, scho prizvede to zbіlshennya vartostі tsogo transported 2.5 Razi. Vodnochas for all інших споживачів та постачальників такі різниці є меншими. Otzhe, naydotsіlnіshe on Persha krotsі zapovniti klіtinu A 3 4. Pіslya tsogo required in 4 povnіstyu zadovolenі, i OAO All klіtini fourth stovpchika viklyuchayutsya h the following rozrahunku rіznits of order i stovptsyah.

On the other krotsі maximum rіznitsya dorіvnyuє 2 i i vіdpovіdaє Perche Perche other the rows that i stovpchikam another, this can be zapovnyuvati whether yak їh klіtinu s mіnіmalnoyu vartіstyu, napriklad, A 2 B 3 Pіslya tsogo s rozglyadu viklyuchayutsya odrazu OAO All klіtini another order that third Sotvpcya, oskilki consumption of the third spozhivacha ponynistyu zadovoleni, and the reserve of another postavalnika vycherpani.

Ostannіy rozrahunok rіznits (naybіlshe Value 3 vіdpovіdaє another stovpchiku) svіdchit about dotsіlnіst Introduction Contents od the Third postachalnika to another spozhivacha. Reshtu klіtin in the way of the minimalist method of vividly vaginal vartness transfer:

(Dd).

The result is the reduction of the values ​​of the function for the reference plan, but of the folds after the alternating method. Efektivnist method of approximating Vogel, yak vzhe zzadulovalo, - obvious for the problems bilshoy rozmіrnostі.

Zaznachimo scho efektivnіst guidance metodіv mozhna otsіnyuvati deprivation in serednomu, oskіlki mozhliva situatsіya scho method mіnіmalnoї vartostі otrimano support program transportnoї zadachі maintained upstream, nіzh method podvіynoї perevagi.