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

Mathematics programmers - Nakonechny S.I.

1.2. Mathematical formulation of problems and mathematical programming

Submitted schematically to the economical system in such a vigil (Fig. 1.1):

Fig. 1.1. Scheme of Economical Systems

The parameter ck ( k = 1, 2, ..., l ) is the characteristic characteristics of the systems. Napriklad, Yakscho just past about Taku ekonomіchnu system, yak sіlskogospodarske pіdpriєmstvo then yogo parameters Je nayavnі resources (zemelnі ugіddya, robochem force sіlskogospodarska tehnіka, tvarinnitskі that skladskі primіschennya) rіven urozhaynostі sіlskogospodarskih cultures produktivnostі tvarin, normalized vitrat resursіv, tsіni that sobіvartіst Promiizhnoi and kintsevoi products, rates of taxes, interest for a loan, prices for a coupon of a resource.

Chastina parametrіv ck for pevnoї Sistemi Mauger Buti became quantities napriklad, normalized visіvu Nasinnya sіlskogospodarskih cultures, norms spozhivannya tvarinami kormіv toscho and Chastina - zmіnnimi, tobto zalezhatime od Pevnyi minds yak, skazhіmo, urozhaynіst sіlskogospodarskih cultures sobіvartіst produktsії, realіzatsіynі tsіni on Roslinnitsku y tvarinnitsku product.

Zmіnnі magnitudes boivayut nezalezhnimi chi solvzhnimi, discrete chi neperervnimi, determinovanimi abo vipadkovymi. Napriklad, fallow zmіnnoyu Je sobіvartіst produktsії, by the Independent od Process funktsіonuvannya pіdpriєmstva the size Je Pochatkova rozmіr statutory fund, discrete - Quantity korіv, neperervnoyu - Ploscha posіvu ozimoї pshenitsі, determіnovanoyu - rate visіvu Nasinnya Kukurudza per hectare vipadkovoyu - Quantity calves SSMSC narodyatsya have planned Period.

Вхідні змінні економічної системи бувають двох видів: кереноі xj ( j = 1, 2, ..., n ), meaningfulness of which can be entered into the activity list; І некероваі змінні yi ( і = 1, 2, ..., m ), meaning not to lie in the wolves of people, and to be identified by the call of the middle. Overlay, the oath of the palm fir is kerovana, and the temperature is unchanged. Zalezhno vіd realo situatsії kerovіі zmіnnі mozut go from a group of nekoredovy i navpaki. Napriklad, in razi raznchenogo rink otsyagi pidbannya diesel fuel є kerenovuyu zmіnnoyu size, and for the minds of the deficit of a resource - unkerned.

Skin economical system maє pevnu metu its function. Tse mozhe bouti, napriklad, otrymnya the maximum of pure pribudku. Ступінь досягнення мети, здебільшого, має кількісну міру, тобто може бути descriptions is mathematical.

Nekhay F is the vibration of meta (tsil). For the cynicism of minds, as a rule, insert the fallowness of the quantity F, which is supposed to be meticulously meticulous, with the following parameters in the systems:

F = f ( x1 , x2 , ..., xn; y1 , y2 , ..., ym ; c1 , c2 , ..., c1 ). (1.1)

The function F is called a function , the function of a function . For ekonomichnoy system - the function of efektivnosti її functііонування та розвитку, оскільки значення F відображує ступінь досягнення певної мети.

In the case of a perverse vigil, the problem of mathematical programming is formulated as follows:

To know the value of keroviyah zmіnnih xj, shchob tsil'ova function nabuvala ekstremalnogo (maximum chi mіnimalnogo znachennya).

Otzhe, potrebno vidshukati znachennya

. (1.2)

Можливості вибору xj зажжен обвжені звнішніми щодо системи umovami, parametres виробничо-економічної системи тощо.

Napriklad, area is posіvu ozimoї pshenitsі obmezhena nayavnіstyu rіllі that іnshih resursіv, sіvozmіnami, mozhlivіstyu realіzatsії grain neobhіdnіstyu vikonannya dogovіrnih zobov'yazan toscho. These processes can be described by the system of mathematic equations of the same kind:

(1.3)

Here nabir symbol ( , =, ) Means, for actual people, the meaning of the flow-through and the viciousness of the type , For інших - рівності (=), and for the sake of - type .

The system (1.3) is called the system of interchange , the system of minds of tasks. Vaughn opisuє vnutrіshnі tehnologіchnі that ekonomіchnі processes funktsіonuvannya th rozvitku virobnicho-ekonomіchnoї system, and takozh processes zovnіshnogo seredovischa, SSMSC vplivayut the result dіyalnostі system. For ekonomichnyh systems zmіnnі xj miyut bouti nevіd'єmnimi:

. (1.4)

Залежності (1.2) - (1.4) utomlyuyut ekonomiko-mathematic model of economical systems. Rozroblyayuchi taku model, slid dottrimuvatis pivnyh rules:

1. Model maee adequately describe the real technologic and economical processes.

2. In the model, potrybno vrahovuvaty all істотне, сутєве в досліджуваному явищі чи processes, nehtuychy vsyіm odnoprjadnim, neistotnim u nyomu. Mathematicians modelyuvannya - tse myssteztvo, vuzka stozh mizh peresproshchennyam ta peresusladnenyam. Spravdі, prostі modelі not zabezpechuyut vіdpovіdnoї tochnostі, i "optimalnі" rozv'yazki for such models, yak usually not vіdpovіdayut real situatsіyam, dezorієntuyut koristuvacha and pereuskladnenі modelі vazhko realіzuvati on AMR yak s look around at nemozhlivіst їh іnformatsіynogo zabezpechennya, so i through Відсутність відповідних метоів оптимізації.

3. A model of moe bouti zrozumiloy for korostustacha, zruchnoyu for realizatsii on EOM.

4. It is necessary, but the multiplicity of the zhinni xj bula is not empty. By using the method in economical and mathematical models for zmogi slid uniquely interchange type "=", and takozh superechlivichih obmezhen. Napriklad, be placed in the same manner as vikonannya contract, ala resursiv not enough, abi ikh vikonati. The system (1.3), (1.4) of the èdinium rozvjazok, it does not meet the set of rіznyh planіv, and ozhe, th tasks viboru optimal of them.

For example, suppose that x 1, x 2, ..., xn , scho are pleased with (1.3) and (1.4), call it a permissible plan , or a plan . Obviously, the dummy permissive plan is a strategic strategy for economy, a program for children . To the leather allowable plan for the performance of the value of the function, yak is to be calculated for the formula (1.1).

Sukupnist sostіh rozv'yakіv sistemi obmezhen (1.3) i (1.4), tobto multiplication of all permissive planiv utoulyovoy region іsnuvannya planiv .

The plan, for some kind of function, nabuvae ekstremalnogo znachennya, nazivaetsya optimal . The optimal plan is the problem of mathematical problems (1.2) - (1.4).