home Other disciplines books Ically mathematical programuvannya - Nakonechny S.І.

Ically mathematical programuvannya - Nakonechny S.І.

8. ROZDІL ZADACHІ NELІNІYNOGO PROGRAMUVANNYA. OSNOVNІ Method ЇH ROZV'YAZUVANNYA TA ANALІZU

"Mathematics is similar to Charivny Mlyn, yaky peremelyuє all scho zavgodno, i to whether yakoї drіbnostі. However, those scho vie dіstaєte, deposits od of scho zasiplete vi, yak i have naychudovіshy svіtі Mlyn not vidast you pshenichnoї semolina s Loboda, so i do not storіnki formulas vidadut you Pevnyi result of sumnіvnimi danimi ".

T. Gekslі

In poperednіh rozdіlah Bulo rozglyanuto methodological problems rozv'yazuvannya lіnіynogo programuvannya that deyakі tipi tasks scho Pevnyi awkward peretvorennyami zvodyatsya to lіnіynih. Tsі methodological naykrasche rozroblenі easily realіzuyutsya on PEOM and to Nabeul wide zastosuvannya in bagatoh Galuzo science tehnіki is the Economy. Prote lіnіynі modelі vіdobrazhayut deprivation Pevnyi th Velma obmezhenu sukupnіst vlastivostey navkolishnogo svitu. Aje, skazhіmo, sotsіalno-ekonomіchnі processes perevazhno not Je lіnіynimi. The Branch, ob'єdnannya that okremі pіdpriєmstva national Gospodarstwa funktsіonuyut i rozvivayutsya for neviznachenostі minds, and to adequately їh mozhna opisati nelіnіynimi, stochastics, dinamіchnimi models. Otzhe for efektivnosti upravlіnnya folk Gospodarstwa in tsіlomu, i yogo Galuzo okremimi ob'єktami gospodaryuvannya potrіbne zastosuvannya nelіnіynih ekonomіko-ically mathematical models that metodіv.

Zauvazhimo scho Suchasnyj rіven rozvitku komp'yuternoї tehnіki i metodіv ically mathematical modelyuvannya stvoryuє peredumovi for zastosuvannya nelіnіynih metodіv and Tse Mauger suttєvo pіdvischiti yakіst rozroblyuvanih planіv, nadіynіst that efektivnіst rіshen, SSMSC priymayutsya.

8.1. Ekonomichna i ically mathematical formulation zadachі nelіnіynogo programuvannya

Dosit detail rozglyanuta in rozdіlah, prisvyachenih lіnіynomu programuvannyu task Poshuk optimally obsyagіv virobnitstva ґruntuєtsya on assumptions about lіnіynіst zv'yazku mіzh vitratami resursіv i obsyagami vigotovlenoї produktsії; mіzh tsіnoyu, advertising that popitom toscho. Ale takі zv'yazki naspravdі nelіnіynimi Yea, that tochnіshі matematichnі modelі dotsіlno formulyuvati in termіnah nelіnіynogo programuvannya.

Let him for deyakoї virobnichoї Sistemi neobhіdno viznachiti produktsії Key infrastructure plan for a process of minds naykraschogo vikoristannya її resursіv. Vіdomі zagalnі reserves skin resource normalized vitrat skin resource on odinitsyu produktsії that tsіni realіzatsії odinitsі vigotovlenoї produktsії. Kriterії optimalnostі shaping can Buti rіznimi, napriklad, maksimіzatsіya viruchki od realіzatsії produktsії. Such Umov podaєtsya lіnіynoyu zalezhnіstyu zagalnoї viruchki od obsyagіv Prodan product that tsіn on odinitsyu produktsії.

However, Je zagalnovіdomim fact scho minds of rinkovoї konkurentsії power realіzatsії produktsії Je dosit folding. Obsyag zbutu produktsії viznachaєtsya peredusіm її tsіnoyu, otzhe, yak tsіlovu funktsіyu dotsіlno brati maksimіzatsіyu not vsієї vigotovlenoї and deprivation realіzovanoї produktsії. Neobhіdno viznachati takozh i optimally rіven tsіni on odinitsyu produktsії for yakoї obsyag zbutu LUVs bi Maximum. For tsogo її potrіbno enter task yak nevіdomu value and obmezhennya zadachі toil vrahovuvati zv'yazki mіzh tsіnoyu, advertising that obsyagami zbutu produktsії. Tsіlova funktsіya in such razі bude Virage dobutkom dvoh nevіdomih values: optimalnoї tsіni odinitsі produktsії at optimal obsyag vіdpovіdnogo produktsії mind tobto bude nelіnіynoyu. Otzhe, maєmo task nelіnіynogo programuvannya.

Takozh good vіdoma transport problems staє nelіnіynoyu, Yakscho vartіst transported odinitsі product deposits od zagalnogo obsyagu transported the route product. Tobto koefіtsієnti at nevіdomih in tsіlovіy funktsії, scho in lіnіynіy modelі steel boule values ​​zalezhatimut od values ​​nevіdomih (otzhe, samі stayut nevіdomimi) scho lead to znovu nelіnіynostі in funktsіonalі.

The I nareshtі, whether yak task staє nelіnіynoyu, Yakscho in matematichnіy modelі neobhіdno vrahovuvati minds neviznachenostі that rizik. Yak pokaznik riziku often vikoristovuyut dispersіyu, that for vrahuvannya obmezhenostі riziku potrіbno vvoditi nelіnіynu funktsіyu in obmezhen system and mіnіmіzatsіya riziku Pevnyi processes dosyagaєtsya doslіdzhennyam matematichnoї modelі s nelіnіynoyu tsіlovoyu funktsієyu.

Zagalna ically mathematical problem programuvannya formulyuєtsya this: Know takі zmіnnih values xj , Dwellers tsіlova funktsіya nabuvala ekstremalnogo (maximum chi mіnіmalnogo) Value:

(8.1)

of minds:

( ); (8.2)

. (8.3)

Yakscho OAO All funktsії that . Je lіnіynimi, the tse challenge lіnіynogo programuvannya, іnakshe (Yakscho Hoch b a s funktsіy Je nelіnіynoyu) maєmo task nelіnіynogo programuvannya.