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Ically mathematical programuvannya - Nakonechny S.І.
9.6. Butt rozv'yazuvannya tasks dinamіchnogo programuvannya
FIRMA planuє naroschuvati virobnichі potuzhnostі on chotiroh pіdpriєmstvah, mayuchi for tsogo 4 million USD. For skin pіdpriєmstva rozrobleno іnvestitsіynі projects SSMSC vіdobrazhayut prognozovanі zagalnі vitrati C (obsyagi kapіtalovkladen) that the D revenues, pov'yazanі s realіzatsієyu skin project. Tsі pokazniki navedenі Table. 9.22:
table 9.22
Project | Pіdpriєmstvo |
|||||||
1 |
2 |
3 |
4 |
|||||
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
2 |
1 |
3 |
1 |
4 |
2 |
4 |
1 |
2 |
3 |
2 |
5 |
2 |
6 |
3 |
9 |
2 |
8 |
4 |
3 |
7 |
3 |
8 |
4 |
12 |
3 |
5 |
Purshia project is not peredbachaє rozshirennya virobnitstva and what i Got nulovі vitrati income. Neobhіdno rozrobiti plan іnvestuvannya vidіlenih koshtіv in zaznachenі pіdpriєmstva so dwellers will win the maximum Prybutok.
Rozv'yazannya. Yak vzhe nagoloshuvalos, sproschenim, ale i naymensh efektivnosti way rozv'yazuvannya podіbnih tasks Je perebіr usіh mozhlivih varіantіv. Prote on praktitsі їh so bagato scho proanalіzuvati їh OAO All i vibrato Sered them nayefektivnіshy nemozhlivo. HEAD nedolіkami such a method rozv'yazuvannya Je great obsyag obchislen, vіdsutnіst aprіornoї information The nedopustimі rozv'yazki and takozh nemozhlivіst skoristatisya promіzhnimi results for analіzu vіdkidannya suboptimal kombіnatsіy proektіv.
Rozv'yazhemo qiu problem pochinayuchi Poshuk umovno-optimal upravlіnnya s ostannogo CRIC. Krok zadachі vvazhatimemo dermal s chotiroh of companies, oskіlki for dermal s are maєmo vibrato optimally іnvestitsіyny project for obmezhenih resursіv penny.
Zauvazhimo, scho in tsomu razі nedinamіchny processes rozglyadaєmo yak dinamіchny, Abi skoristatisya dinamіchnogo programuvannya methods for optimal znahodzhennya rozv'yazku. Zvyazok mіzh zaznachenimi Croke zabezpechuєtsya obmezhennyam on zagalny obsyag vidіlenih koshtіv - 4 million USD.
Zmіnnі zadachі vіzmemo so Bulo dwellers mozhna poslіdovno keruvati processes rozpodіlu koshtіv:
x 1 - obsyag kapіtalovkladen, vidіlenih CRIC 1-4;
x 2 - obsyag kapіtalovkladen, vidіlenih CRIC 2-4;
x 3 - obsyag kapіtalovkladen, vidіlenih at CRIC 3 i 4;
x 4 - obsyag kapіtalovkladen, vidіlenih 4 krotsі.
- Obsyag іnvestitsіy in i-those pіdpriєmstvo .
- Optimal obsyag іnvestitsіy in i-those pіdpriєmstvo.
Recurrently spіvvіdnoshennya scho opisuє phone reception mіzh efektivnosti upravlіnnya od the 4th to the 1st of the CRIC (od fourth to Perche pіdpriєmstva) podaєtsya in viglyadі:
.
. .
de - Sumarno efektivnіst іnvestitsіy h i th Step to ostannogo.
here , Oskіlki p'yatogo pіdpriєmstva not іsnuє.
Vikonaєmo poetapnі rozrahunki for tsієyu Modell.
Etap IV.
.
Result rozrahunkіv file a table:
table 9.23
x 4 |
Dohіd |
optimally rozv'yazok |
|||||
0 |
0 |
0 |
0 |
0 |
|||
1 |
0 |
2 |
2 |
1 |
|||
2 |
0 |
2 |
8 |
8 |
2 |
||
3 |
0 |
2 |
8 |
5 |
8 |
2 |
|
4 |
0 |
2 |
8 |
5 |
8 |
2 |
of minds
.
Result rozrahunkіv navedenі Table. 9.24:
table 9.24
3 x |
Dohіd |
optimally rozv'yazok |
||||
0 |
0 |
0 |
||||
1 |
2 |
0 |
||||
2 |
8 |
0 |
||||
3 |
9 |
3 |
||||
4 |
12 |
2 4 abo |
Rozrahunki vikonuyut so. Let him know potrіbno . Obchislyuєmo of the formula:
.
Otzhe,
.
.
.
Zauvazhimo scho , For the third oskіlki pіdpriєmstva not іsnuє project іnvestitsіyami s 1 million UAH. meaning Take h poperednoї tablitsі. Potіm maєmo:
.
Etap 2
of minds:
. .
Result rozrahunkіv podanі Table. 9.25:
table 9.25
x 2 |
Dohіd |
optimally rіshennya |
|||||
k 2 = 0 |
k 2 = 1 |
k 2 = 2 |
k 2 = 3 |
k 2 = 4 |
|||
0 |
0 |
0 |
0 |
||||
1 |
4 |
4 |
4 |
1 |
|||
2 |
8 |
6 |
6 |
8 |
0 |
||
3 |
9 |
12 |
8 |
8 |
12 |
1 |
|
4 |
12 |
13 |
14 |
10 |
14 |
2 |
Etap 1.
of minds:
. .
Vikonuєmo rozrahunki deprivation for x 1 = 4, podayuchi їh in Table. 9.26:
table 9.26
x 1 |
Dohіd |
optimally rozv'yazok |
||||
4 |
15 |
1 |
Znaydemo optimal plan. Іz tablitsі Kroc viplivaє Perche, scho , Tobto for Perche pіdpriєmstva realіzuєtsya other projects, Yakima peredbacheno 1 million UAH іnvestitsіy s income scho dorіvnyuє 3 million UAH. Otzhe, for two, three fourth of companies i zalishaєtsya 4 - 1 = 3 mln іnvestitsіy. Іz tablitsі another Kroc maєmo, scho minds for 2 x 3 = Maximum efekt mozhna otrimati in razі realіzatsії for another project pіdpriєmstva Perche (k 2 = 1). Dohіd in such razі stanovitime 4 million USD. Otzhe, x 3 = 3 - 1 = 2, i tobto for the third fourth of companies slіd vikoristati іnvestitsіy 2 million USD. Іz tablitsі the Third Step by brain x 3 = 2 maєmo scho k 3 = 0. Otzhe x 4 = 2, and Yomou vіdpovіdayut kapіtalnі vkladennya 4 k = 2, SSMSC zabezpechuyut dohіd obsyagom 8 million USD. Residual maєmo: dohіd od 4 million USD іnvestitsіy becoming 3 + 4 + 8 = 15 (million USD).
Pіdpriєmstvo rozroblyaє strategіyu popovnennya zapasіv deyakoї produktsії for jobs perіodu, yaky skladaєtsya h N etapіv (pіdperіodіv). For dermal s are vіdomy obsyag popitu, and not vіn Je odnakovim for vsіh etapіv. Dwellers zadovolniti popit, pіdpriєmstvo Mauger pridbati neobhіdnu Quantity produktsії, deputies have її virobnika, abo vigotoviti її samostіyno. Peredbachaєtsya scho reserves popovnyuyutsya mittєvo, zapіznennya delivery that defіtsit nedopustimі. Fallow od rinkovoї kon'yunkturi pіdpriєmstvu Mauger Buti vigіdno stvoryuvati reserves produktsії for zadovolennya popitu in maybutnomu scho pov'yazano against, s dodatkovimi vitratami on zberіgannya zapasіv.
Potrіbno rozrobiti programa upravlіnnya reserves pіdpriєmstva, tobto viznachiti obsyagi of order yogo th perіod rozmіschennya, dwellers zagalnі vitrati on postachannya that zberіgannya produktsії boule mіnіmalnimi and popit zadovolnyavsya povnіstyu th svoєchasno.
Danі zadachі submitted in tab. 9.27:
table 9.27
Perіod (quarter rock) |
Obsyag popitu on produktsіyu, yew. od. |
Vitrati on rozmіschennya of order, yew. UAH |
Vitrati on zberіgannya, yew. UAH |
1 |
4 |
7 |
2 |
2 |
5 |
8 |
3 |
3 |
3 |
6 |
1 |
4 |
2 |
9 |
0 |
Vіdomo, scho on the cob planned perіodu stock becomes 2 yew. od., and pid hour kupіvlі produktsії dіє Wholesale znizhok system. Vitrati on pridbannya 1 yew. od. produktsії stanovlyat 15 tis. UAH, and if rozmіr of order perevischuє 3 yew. od., then vitrati znizhuyutsya 12% i stanovlyat 12 tis. UAH.
Nekhay - Quantity etapіv planned perіodu. Todі for the i-th Etap vvedemo takі poznachennya: xi - stock produktsії Etap on the cob; yi - obsyag zamovlenoї produktsії (obsyag of order); hi - vitrati on zberіgannya 1 yew. od. stock produktsії; KI - vitrati on rozmіschennya of order; - Obsyag popitu on produktsіyu; Ciyi - vitrati scho pov'yazanі s kupіvleyu (virobnitstvom) produktsії yi.
Viznachimo f (xi, yi) yak mіnіmalnі vitrati on Etap , Yakscho obsyagi zapasіv dorіvnyuyut xі.
Rekurentnі zalezhnostі scho vіdpovіdayut skhemі zvorotnogo runs, carols viglyadu:
of minds:
. . .
For the N-th Etap maєmo:
of minds:
. .
Rozglyanemo pokrokovy rozrahunok optimalnoї strategії upravlіnnya reserves.
Etap 4. Maєmo: .
of minds:
.
Mozhlivі varіanti rozv'yazkіv navedenі Table. 9.28:
table 9.28
x 4 |
optimally rozv'yazok |
||||
0 |
39 |
2 |
|||
1 |
24 |
1 |
|||
2 |
0 |
0 |
Etap 3. Maєmo: .
of minds:
.
Result rozrahunkіv will file at the Table. 9.29:
table 9.29
3 x |
Salary: |
optimally rozv'yazok |
||||||
y 3 = 0 |
y 3 = 1 |
y = 2 3 |
y = 3 3 |
y 3 = 4 |
3 y = 5 |
|||
0 |
3 • 6 + 15 + 39 = 90 |
• 6 + 4 + 12 + 24 = 78 |
6 + 5 • 12 + 0 = 66 |
66 |
5 |
|||
1 |
6 + 2 • 15 + 1 • 1 + 39 = 76 |
6 + 3 • 15 • 1 + 1 + 39 = 76 |
6 + 3 • 12 • 1 + 1 + 0 = 55 |
55 |
4 |
|||
2 |
6 + 1 + 15 • 2 • 1 + 39 = 62 |
6 + 2 • 15 + 2 • 1 + 24 = 62 |
6 + 3 • 15 • 2 + 1 + 0 = 53 |
53 |
3 |
|||
3 |
3 • 1 + 39 = 42 |
6 + 1 • 15 • 3 + 1 + 24 = 48 |
6 + 2 • 15 • 3 + 1 + 0 = 39 |
39 |
2 |
|||
4 |
4 • 1 + 24 = 48 |
6 + 1 • 15 • 4 + 1 + 0 = 25 |
25 |
1 |
||||
5 |
5 • 1 + 0 = 5 |
5 |
0 |
Rozrahunki vikonuєmo so. Napriklad, obchislimo i . Oskіlki of minds then Mauger nabuvati values 0, 1, 2, 3, 4, 5, and - Takozh values 0, 1, 2, 3, 4, 5. Now znaydemo i for i . For i maєmo:
Analogіchno:
.
.
Dali obchislyuєmo:
Otzhe,
at .
So needless vikonuєmo rozrahunki for x = 1, 2, 3, 4, 5, and the results have zapisuєmo vіdpovіdnu table.
2. Etap Maєmo: β2 = 5.
of minds:
.
A table zapisuєmo deprivation ostatochnі result obchislen (Table 9.30.):
table 9.30
x 2 |
Optimalnі rozv'yazki |
|||||||||||||||||||||||
y 2 = 0 |
y 2 = 1 |
y 2 = 2 |
y 2 = 3 |
y 2 = 4 |
2 y = 5 |
y 2 = 6 |
y 2 = 7 |
y 2 = 8 |
y 2 = 9 |
y 2 = 10 |
||||||||||||||
x 2 = 0 |
134 |
135 |
145 |
143 |
141 |
133 |
133 |
10 |
||||||||||||||||
x = 1 2 |
125 |
126 |
136 |
134 |
132 |
124 |
124 |
9 |
||||||||||||||||
x 2 = 2 |
125 |
117 |
127 |
125 |
123 |
115 |
115 |
8 |
||||||||||||||||
2 x = 3 |
113 |
117 |
118 |
116 |
114 |
106 |
106 |
7 |
||||||||||||||||
x 2 = 4 |
101 |
105 |
118 |
107 |
105 |
97 |
97 |
6 |
||||||||||||||||
x 2 = 5 |
81 |
93 |
106 |
107 |
96 |
88 |
81 |
0 |
||||||||||||||||
x 2 = 6 |
73 |
94 |
95 |
96 |
79 |
73 |
0 |
|||||||||||||||||
x 2 = 7 |
74 |
83 |
74 |
79 |
74 |
0 2 abo |
||||||||||||||||||
x 2 = 8 |
63 |
72 |
67 |
63 |
0 |
|||||||||||||||||||
9 x 2 = |
52 |
55 |
52 |
0 |
||||||||||||||||||||
= 2 x 10 |
35 |
35 |
0 |
Etap 1.
Maєmo: β1 = 4.
of minds:
.
Dієmo so i yak on etapі 2 skladayuchi rezultatіv table (Table 9.31.):
table 9.31
1 x |
Optimalnі rozv'yazki |
||||||||||||
y = 1 2 |
y 1 = 3 |
y = 1 4 |
y 1 = 5 |
y 1 = 6 |
y = 1 7 |
y 1 = 8 |
y 1 = 9 |
y 1 = 10 |
y 1 = 11 |
y 1 = 12 |
|||
2 |
174 |
180 |
174 |
177 |
180 |
176 |
180 |
193 |
194 |
195 |
180 |
174 |
2 4 abo |
Otzhe, dіstali two varіanti upravlіnnya optimal inventory plan pіdpriєmstva Yakimov vіdpovіdayut odnakovі mіnіmalnі zagalnі vitrati on postachannya that zberіgannya produktsії.
Іnformatsіyu about Purshia varіant optimal plan mіstit Table. 9.32:
table 9.32
Etap |
stock |
Obsyag of order |
Popit |
Zalishok produktsії on kіnets Etap |
Vitrati on pridbannya produktsії that її zberіgannya |
1 |
|||||
2 |
|||||
3 |
|||||
4 |
|||||
at once |
174 |
Other varіant optimal plan imposed in the Table. 9.33:
table 9.33
Etap |
stock |
Obsyag of order |
Popit |
Zalishok produktsії on kіnets Etap |
Vitrati on pridbannya produktsії that її zberіgannya |
1 |
|||||
2 |
|||||
3 |
|||||
4 |
|||||
at once |
174 |
Zіstavlyayuchi tsі two varіanti, bachimo, vіdrіznyayutsya scho stink deprivation Persha EYAD Etap i give zmogu manevruvati fіnansovimi resources pіdpriєmstva, yak slit vodnochase virіshuє low іnshih problems.
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