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Ically mathematical programuvannya - Nakonechny S.І.

9.3. The problem about rozpodіl kapіtalovkladen mіzh pіdpriєmstvami

Planuєtsya on the following Year dіyalnіst virobnichoї system yak skladaєtsya s n of companies. Vіdoma Pochatkova scrip koshtіv - Scho Got Booty rozpodіlena mіzh vsіma pіdpriєmstvami. Suma's vkladen bring k-th pіdpriєmstvu Prybutok . Meaning funktsії , Zadanі table.

Neobhіdno viznachiti - Costa, SSMSC potrіbno vidіliti k-th pіdpriєmstvu so dwellers otrimati Maximum sumarno Prybutok od vkladennya koshtіv in usі pіdpriєmstva .

Poznachimo Quantity koshtіv scho zalishilisya pіslya k-th of the CRIC (tobto Costa, SSMSC neobhіdno rozpodіliti mіzh Rasht (n - k) of companies through :

.

Task rozv'yazuєtsya poetapno. In danomu razі Etap Je vkladennya koshtіv in skin pіdpriєmstvo.

The I Etap. Costa vkladayutsya deprivation in odne (napriklad, Pershe) pіdpriєmstvo. Naybіlshy Prybutok (efektivnіst Perche Etap), scho Mauger Buti otrimany, through poznachimo . Maєmo:

.

Etap II. Porіvnyaєmo efektivnіst, yak otrimaєmo, vkladayuchi Costa deprivation in Pershe pіdpriєmstvo that vkladayuchi Costa odnochasno in Pershe i, i in other pіdpriєmstva. Yakscho poznachiti efektivnіst another Etap through Then otrimaєmo:

.

For the k-th Etap maєmo recurrently spіvvіdnoshennya:

.

Poslіdovno rozv'yazuyuchi otrimanі rіvnyannya, viznachaєmo optimalnі rіshennya on skin etapі.

Navedemo nayprostіshu task dinamіchnogo programuvannya.

Virobnicha system skladaєtsya s chotiroh fіlіalіv. Over the minds zdіysnennya rekonstruktsії obladnannya on skin fіlіalі mozhna dosyagti Pevnyi pributku growth. FIRMA vidіlyaє on dodatkovі kapіtalnі vkladennya 200 tis. mind. od. (For sproschennya rozrahunkіv acceptable scho dodatkovі vkladennya will zdіysnenі obsyagah in 50, 100, 150 that 200 tis. D. Od.).

Neobhіdno viznachiti optimally rozpodіl koshtіv mіzh fіlіalami for maksimіzatsії zagalnogo pributku od usіh chotiroh fіlіalіv for minds, scho vіdomі pributku gains for dermal s are (Table 9.1.):

table 9.1

Rozv'yazannya. In danomu prikladі Etap zadachі bude not an hour, yak in poperednіh vikladkah and rozpodіl koshtіv mіzh fіlіalami. Otzhe, maєmo chotirohetapnu task dinamіchnogo programuvannya. Prior to the introduction Vіdpovіdno ranіshe poznachen vvazhatimemo scho - Prirіst pributku in the i-th fіlіalі of minds kapіtalovkladen in Demba obsyagom x yew. mind. od. Umov zadachі Got viglyad (Table 9.2.):

table 9.2

the I Etap

Nayprostіshy sposіb rozpodіlu koshtіv, s yakogo pochinaєmo rozv'yazuvannya zadachі - tse vkladennya koshtіv deprivation in Purshia fіlіal. Yakscho scrip maєmo in rozporyadzhennі koshtіv yew. mind. . Odes, the efektivnіst vkladennya tsієї vіdpovіdaє pributku Sumi, scho yogo Bude otrimano od іnvestuvannya in Purshia fіlіal - 25 tis. mind. od. Efektivnіst Perche Etap through poznachimo :

.

Analogіchno postupaєmo in razі, if in the bag rozporyadzhennі maєmo yew. mind. od. Todі s nayavnih koshtіv vkladati mozhna the size of the bag Scho Mauger nabuvati these values: , abo , abo yew. mind. od. Obviously, scho s troh Names mozhlivih varіantіv naybіlshu'll efektivnіst mother, vklavshi in Costa sumі 100 tis. mind. od. Otzhe, fіksuєmo naybіlshu efektivnіst on another krotsі Perche Etap - , On the third potіm krotsі - yew. mind. od. t i. e.

OAO All Uzagalnimo vipadki Perche at Etap viglyadі "tablitsі naybіlshih efektivnosti" de vіdobrazheno mozhlivі pributki of minds rіznih vkladen tіlki in Perche fіlіyu (Table 9.3.):

table 9.3

II Etap

On cutaneous etapі neobhіdno zіstaviti efektivnostі priynyatih rіshen on poperednomu that inline Etap. Tobto now rozglyanemo rozpodіl koshtіv odnochasno mіzh EYAD fіlіalami fіrmi, porіvnyuyuchi otrimany Prybutok s efektivnіstyu poperednogo Etap. Skoristaєmosya formula for zagalnogo vipadku:

.

For nashogo butt magnitude - Efektivnіst scho give vkladennya on poperednomu etapі (in danomu prikladі - in Purshia fіlіal fіrmi), yak bula rozrahovana on Persha krotsі, i poznachalas through And the value - Prybutok scho daє other fіlіal od zalishku sumi.

For administration in danomu prikladі poznachen formula nabuvaє viglyadu:

Znovu spochatku dopuskaєmo scho scrip rozpodіlyaєtsya . Todі mozhlivі two varіanti vkladennya: (Vkladaєmo Costa deprivation in other fіlіal) abo (Vkladaєmo Costa deprivation in Purshia fіlіal) todі:

.

To file a naochnostі promіzhnі rozrahunki in viglyadі Table. 9.4:

table 9.4

0	50	0	thirty	0 + 30 = 30
50	0	25	0	25 + 0 = 25

Items marked Strіlkoyu naybіlshy s mozhlivih pributkіv of minds rozpodіlu vkladennya 50 tis. mind. od. odnochasno in Purshia that other fіlіali fіrmi.

In the following Taqiy sposіb viznacheno yelement "tablitsі naybіlshih efektivnosti" for vipadku, if (Table 9.5.):

table 9.5

Potіm rozglyadayutsya mozhlivі varіanti rozpodіlu koshtіv, Yakscho , Todі vkladati deprivation in other fіlіal mozhna scrip . Mauger nabuvati these values: . . yew. mind. od. Maєmo takі result (Table 9.6.):

table 9.6

W Table. 9.6 visnovuєmo scho vkladayuchi 100 tis mind. od., s usіh varіantіv naybіlshy Prybutok bude dorіvnyuvati 70 tis. mind. od. Otzhe, Table naybіlshih efektivnosti pіslya tsogo Kroc popovnyuєtsya the following Components (Table 9.7.):

table 9.7

50	25	thirty
100	60	70
150	100
200	140

Analogіchno conduction obchislennya for that yew. mind. od.

Nekhay (Rozglyadaєtsya Vier mozhlivih varіanti rozpodіlu, Table 9.8.):

table 9.8

Nekhay (Rozglyadaєtsya p'yat mozhlivih varіantіv rozpodіlu, Table 9.9.):

table 9.9

OAO All Vnesemo rozrahunki another Etap in Table Maximum efektivnosti, Table. 9.10:

table 9.10

III Etap

Znovu neobhіdno zіstaviti efektivnostі poperednogo that stream etapіv. Otzhe, vikoristovuєmo danі scho opisuyut Prybutok, yaky mozhna otrimati od vkladennya odrazu in Purshia that other fіlіal (stovpchik ) That Prybutok od vkladennya odnochasno three fіlіali. Znovu vikoristaєmo formula:

Analogіchno poperednіm vipadkam spochatku take , todі abo yew. mind. od, maєmo (Table 9.11.).:

table 9.11

.

Other Krok: , todі Mauger nabuvati these values: . . yew. mind. od. In rezultatі maєmo (Table 9.12.):

table 9.12

.

at value Mauger nabuvati chotiroh value: . . . yew. mind. od, SSMSC oznachayut Chastain zagalnoї sumi vkladennya koshtіv deprivation in tretє pіdpriєmstvo, vіdpovіdnі їm Vier vipadki.: - Surpluses koshtіv scho neobhіdno vkladati in Pershi two fіlіali. Maєmo (Table 9.13.):

table 9.13

Otzhe, .

Obchislennya for ostannogo (fourth) Kroc Thirdly Etap navedenі Table. 9.14:

table 9.14

. Zapishemo values in the following viglyadі stovpchika tablitsі naybіlshih efektivnosti (tab. 9.15).

table 9.15

Analogіchno conductive obchislennya for , SSMSC suggestive without komentarіv.

table 9.16

table 9.17

table 9.18

table 9.19

.

Residual maєmo Table. 9.20:

table 9.20

W Table. 9.20 pomіtiti easily scho naybіlshy Prybutok, yaky give OOO All Vier fіlіali of minds vkladennya koshtіv in rozmіrі 200 tis. mind. od., becoming 146 tis. mind. od. Povertayuchis to ostannogo Kroc rozrahunkіv (tab. 9.19) bachimo scho number 146 vіdpovіdaє zmіnnіy . .

Zvіdsi maєmo scho 150 tis. mind. od. neobhіdno vklasti fіlіal in the fourth and 50 tis. mind. od. rozpodіliti mіzh troma іnshimi. Znovu povertaєmosya to elementіv Table. 9.20. Vikoristannya 50 tis. mind. od. Perche on troh fіlіalah daє zagalny Prybutok obsyagom 36 tis. mind. od. (Vidіleny yelement tablitsі 9.20). Tse Bulo rozrahovano values ​​on the III etapі on krotsі Perche: in Taqiy sposіb (Table 9.21.):

table 9.21

Otzhe, maєmo: , a . Oznachaє Tse, scho 50 tis. mind. od. vidіlyayutsya fіlіalu Thirdly, . - Scho in Pershi two fіlіali Costa vzagalі not vkladayutsya.

Otzhe, optimal plan zadachі Je: yew. mind. od.). In this razі rozpodіlu koshtіv mіzh fіlіalami fіrmi Maximum Prybutok stanovitime 146 tis. mind. od.