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

Ically mathematical programuvannya - Nakonechny S.І.

10.3. Butt ekonomіchnih tasks stochasticity programuvannya

Nekhay potrіbno zrobiti stock tovarіv n s y obsyagah On SSMSC Je vipadkovy popit . For nestachі odinitsі j th product zastosovuєtsya PUNITIVE sanktsіya in rozmіrі , tobto And the costs of zberіgannya odinitsі vіdpovіdnoї produktsії, not yak away zbuti, zadayutsya vector

Rozv'yazannya. Funktsіya zbitkіv scho vіdpovіdaє rozv'yazku X Got viglyad:

de - The penalty for nezadovolennya popitu for the j-th mean produktsії; - Vitrati on zberіgannya j -oї produktsії. For optimal znahodzhennya rozv'yazku tsієї zadachі neobhіdno mother funktsіyu rozpodіlu ymovіrnostey vipadkovoї quantities ω. Yakscho taka funktsіya rozpodіlu nevіdoma, tobto її nemozhlivo vіdshukati then dopuskayut scho vipadkova magnitude rozpodіlena rіvnomіrno. In this razі neobhіdno pam'yatati scho SAME TAKE poached Mauger prizvesti to improper rіshennya of acceptance.

Іndivіdi mozhut trimati svoє bagatstvo in viglyadі pennies that oblіgatsіy. Oskіlki groshі - tse asset scho yak vikoristovuєtsya zasіb obіgu, it does not bear the stench from pributku viglyadі protsentіv. Oblіgatsії - tse tsіnnі Paper the scho give їh vlasnikovі Pevnyi dohіd. Logіchno dopustiti scho toil іndivіduumi zberіgati svoє bagatstvo in viglyadі oblіgatsіy. However, Tse is not so oskіlki interest rates i rinkova vartіst oblіgatsіy advance not exactly vіdomі, tobto іsnuє neviznachenіst. Neobhіdno viznachiti optimally rozpodіl asset to groshі that oblіgatsії.

Rozv'yazannya. Nekhay S - zagalna value of the asset, and x is the y - magnitude aktivіv, SSMSC zberіgayutsya vіdpovіdno in formі pennies that oblіgatsіy. Vvazhaєmo, scho through Year Assets vkladenі in oblіgatsії, zmіnyuyutsya. For Rasht odnakovih minds oblіgatsіyu, yak bring bіlshy percentage pributku on Rink tsіnnih paperіv mozhna prodatsya bіlshu of the bag, nіzh oblіgatsіyu s Mensch percent. Poznachimo through ξta η quantities aktivіv, SSMSC realіzuyutsya through to Year odinitsyu aktivіv, vіdpovіdno zberezhenih in formі pennies that vkladenih in oblіgatsії. value And η Je vipadkovoyu value. Ekonomіko-ically mathematical problem nayvigіdnіshogo rozpodіlu asset to groshі that oblіgatsії polyagaє in maksimіzatsії spodіvanoї korisnostі:

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of minds:

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Zvіdsi viplivaє, scho, if , The asset potrіbno vkladati in oblіgatsії, and protilezhnomu razі - navpaki. Otzhe, nutrition schodo rozpodіlu asset mіzh grіshmi that oblіgatsіyami povnіstyu virіshuєtsya korist on one s Tsikh vidіv zaoschadzhen. Yakscho Then odnakovo, yaky bude sposіb zaoschadzhennya vikoristano.

Vіdomo, scho banks have komertsіynih narahovuєtsya bіlsha interest rates on vkladenі Costa porіvnyano s Savings, ale Povernennya vnesku not garantuєtsya. Before dermal vkladnikom postaє dilemma: Mother Mensch, ale garantovany dohіd, abo bіlshy against s rizikom vtratiti vnesok. W rizikom nevikoristanih mozhlivostey pov'yazany vnesok in the Savings Bank. Viznachiti optimally rozpodіl vkladen from banks.

Rozv'yazannya. Poznachimo by S zagalnu bag of pennies Pevnyi vlasnika; x - obsyag vkladen in the Savings Bank, y - y komertsіyny; a, b - vіdpovіdno protsentnі narahuvan rates that komertsіynomu Savings Banks; p - ymovіrnіst Povernennya komertsіynogo s contribution to the bank; - Ymovіrnіst lіkvіdatsії (bankrutstva) komertsіynogo bank.

For Pevnyi rozpodіlu S on x i y mozhlivі takі Dvi situatsії schodo otrimannya dohodіv:

- For the minds uspіshnogo funktsіonuvannya komertsіynogo bank;

- At protilezhnomu razі.

Ekonomіko-ically mathematical model Got Taqiy viglyad:

of minds:

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Potrіbno otsіniti dotsіlnіst strahuvannya. Nekhay yakas person bazhaє zastrahuvati Chastain Svoge asset. For tsogo Won splachuє Pevnyi vnesok strahovіy kompanії, while razі vtrati asset oderzhuє od neї Strakhov vinagorodu. Viznachiti chastku asset yak lady vvazhaє for dotsіlne zastrahuvati.

Rozv'yazannya. Poznachimo by S asset (kapіtal, Main toscho) vlasnikom yakogo Je Pevnyi person. Chastain Yogo, yak Bajan zastrahuvati, poznachimo through x. Todі INSURANCE vnesok scho splachuєtsya strahovіy kompanії, dorіvnyuє rx, and at razі vtrati asset klієnt oderzhuє vinagorodu qx. Yakscho vіdoma ymovіrnіst p nedotorkannostі vsogo asset is ekonomіko-ically mathematical model viznachennya chastki insurance zapisati the asset is as follows:

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Here you can easily vrahuvati takozh obsyagi dohodіv.

Podіbna model Mauger vikoristovuvatisya INSURANCE kompanіyami for viznachennya dotsіlnih largest insurance that the insurance vneskіv vinagorod, SSMSC zatsіkavili klієntіv b i b boule vigіdnimi strahovіy kompanії.

In beet-tsukrovomu kompleksі toil koshtіv scrip S, SSMSC neobhіdno rozpodіliti mіzh rozshirennyam sirovinnoї Bazi i bearing-down zbіlshennyam s її pererobki. Potrіbno so splanuvati rozpodіl koshtіv, vvazhayuchi urozhaynіst tsukrovih buryakіv £ vipadkovoyu the size, dwellers otrimati naybіlshu Quantity tsukru.

Rozv'yazannya. Nekhay q 1 - vitrati koshtіv on viroschuvannya tsukrovih buryakіv on one gektarі; q 2 - pitomі zvedenі vitrati on stvorennya odinitsі potuzhnostі tsukrovogo plant; d - chastka vihodu tsukru s odinitsі sirovini; x - Planova Ploscha pid tsukrovimi Buriak; y - Planova potuzhnіst tsukrovogo plant.

Potrіbno maksimіzuvati prirіst obsyagu virobnitstva tsukru for obmezhenih koshtіv. Ekonomіko-ically mathematical model Got viglyad:

of minds:

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