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Mathematics programmers - Nakonechny S.I.

ROSDIL 9. DYNAMICHNE PROGRAMMANNNAYA

"A mathematician can vvazhati his problem rozv'yanoyu, lsche if zbugne essence of the optimal approach to rozv'yazannya."

R. Belman

9.1. The economical nature of the tasks of dynamical programming

All the economical processes are those that are dynamical, the problems of the will of function and growth are not in the open spaces, ale th y h in the hour. For national Gospodarstwa in tsіlomu, yogo Galuzo, regіonіv chi okremih of companies s metoyu їh stabіlnogo funktsіonuvannya that rozvitku neobhіdno rozroblyati strategіchnі that taktichnі plan. Strategic planning for the parametrization of business, yak characterize їх віддалене майбутнє. Otzhe, stink maiyu rozroblyatsya on the basis dinamichnyh models, for vozhodozhennya rozv'yakіv yakih zastosovuyutsya method dinamichnogo programvannya.

Dinamіchne programuvannya yavlyaє him ically mathematical aparata scho daє zmogu zdіysnyuvati planuvannya bagatokrokovih kerovanih protsesіv and takozh protsesіv, SSMSC rozvivayutsya in chasі.

Otzhe, dinamіchne programuvannya not Je okremim method rozv'yazuvannya tasks and yavlyaє him teorіyu scho poєdnuє number of similar іdey that priyomіv, SSMSC zastosovuyutsya for rozv'yazuvannya dosit rіznih for zmіstom tasks.

Before tasks dinamіchnogo programuvannya nalezhat takі scho pov'yazanі s optimally rozpodіlom kapіtalovkladen, rozpodіlom produktsії mіzh rіznimi regіonami, viznachennyam naykorotshogo high road imported tovarіv spozhivacham, zadachі schodo zamіni ustatkuvannya optimal inventory upravlіnnya toscho.

Economical processes can be dealt with by collapses in several stages (krokiv). On the skin of them zdіysnyuetsya vplyv on rozvitok vsоgo process. Tom at razі planuvannya bagatoetapnih protsesіv rіshen of acceptance on the dermal etapі Got vrahovuvati poperednі zmіni that Buti pіdporyadkovanim kіntsevomu result. Динамічне програмування дає змогу прийняти number послідовних рішень, що забезпечує оптимильність розвитку процесу в цілому.

Slid zaznachiti, sho optimally planned plodders okremih vidrizkiv the planned period do not zavzhdi - optimal for vsogogo interval planning. On the contrary, it is not enough to excel the optimal plan of the vibrobitztva for one month and then to go on a three-hour stretch. Dosit ymovіrno, scho in nastupnі mіsyatsі virobnitstvo himself up for Tim Mauger Why not optimal for yogo oskіlki rozroblennya mozhlivostі further rozvitku not vrahovuvalis. Доцільніше визначати оптимальні плани на нажен місяць з урахуванням змін у попередніх періодах. Lisha Todi rіchny optimal plan виробництва буде sumarnym result optimal rіshen, scho priimalisya dermal місяця.

The task of dynamical programming in a fictitious vigilance is posible.

Nehai analizuetsya active kerovaniya process, filed yakogo admit decomposition on the post-itepi (crocs), the number of such n is given. Effectiveness of the fast process Z can be submitted to the sum of the effects Okremi krokiv, tobto:

,

I call the adictive criterion Okremič krokіv u viglyadі: , Which I call the multiplicative criterion).

In the skin of the tasks (krok) of tasks, in the days of the reception of the first stage, the so-called crooked control Scho viznachaє yak effektivnnist danogo etapu, so i vsoygo protsentu v tsilomu.

Rozv'yazuvannya tasks in the dynamic programming of the field in the know-how of such management By the process of culm, yak maximize zagalnu efektivnist: (Max ).

Optimal rozv'yazkom tsієї problems є managly Що складається з сукупності оптимальних покрокових управлінь:

І уможливлює досягнення максимаї ефективності: