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Разработка метода формирования маршрутных матриц однородной замкнутой экспоненциальной сети массового обслуживания

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Niaea?aeaiea

Aaaaeaiea no?. 3

Iinoaiiaea caaea/e 5

Ae?ooaeueiua NaII 6

Ia?o?ooiua iao?eoeu ae?ooaeueiuo NaII 9

Iaoiaeu iino?iaiey ia?o?ooiuo iao?eoe ae?ooaeueiuo NaII 14

Iauaa ?aoaiea 14

I?eia? iaoiaeaeaiey iauaai ?aoaiey 16

Iaoiae oi?ie?iaaiey ia?o?ooiie iao?eoeu 20

Iiene ii noaoenoe/aneiio a?aaeeaioo 22

Iaoiae “oyaeaeiai oa?eea” 22

Oi?ie?iaaiea iao?eoeu. Iienaiea iaoiaea 23

Aeai?eoi i?ia?aiiu, ?aaeecothuae iaoiae 25

Iacia/aiea e iienaiea i?ia?aiiu OPTIM 29

Caeeth/aiea 31

Nienie eeoa?aoo?u 32

I?eeiaeaiea 1. Nienie eaeaioeoeeaoi?ia 33

I?eeiaeaiea 2. Oaeno i?ia?aiiu 34

Aaaaeaiea

Oe?ieia ?acoeueoaoeaiia i?eiaiaiea naoae ianniaiai ianeoaeeaaiey (NaII)
?acee/iuo eeannia [1-2] a ea/anoaa iaoaiaoe/aneeo iiaeaeae aeene?aoiuo
nenoai n naoaaie no?oeoo?ie e noioanoe/aneei oa?aeoa?ii
ooieoeeiie?iaaiey iaoneaaeeaaao aeaeueiaeoaa eioaineaiia ?acaeoea oai?ee
naoae ianniaiai ianeoaeeaaiey, iaoiaeia ?aoaiey caaea/ eo aiaeeca,
neioaca e iioeiecaoeee, a eae aea iaoiaeieiaee iiaeaee?iaaiey
aeene?aoiuo nenoai naoyie ianniaiai ianeoaeeaaiey. Naoe ianeoaeeaaiey,
yaeythueany iiaeaeyie niioaaonoaothueo aeene?aoiuo nenoai aoaeai
n/eoaoue iauaeoiuie.

I?e ?aoaiee caaea/ aiaeeca, neioaca e iioeiecaoeee iauaeoiuo /anoi
eniieuecoaony iiiyoea iaeioi?ie “iioeiaeueiie” NaII. Niaea?aeaiea
oa?ieia “iioeiaeueiay” a cia/eoaeueiie noaiaie ii?aaeaeyaony
niaea?aeaieai ?aoaaiuo caaea/. Iai?eia?, iiiaea caaea/e aiaeeca NaII
naycaiu n iieneii “oceeo” iano a NaII, o.a. nenoai ianniaiai
ianeoaeeaaiey, i.i. /enea i?aauaathueo o?aaiaaiee a eioi?uo i?aauoatho
iaeioi?ua aeiionoeiua cia/aiey. Iinea iaoiaeaeaiey oceeo iano eo
ono?aiytho, iai?eia?, oaaee/eaaaony eioaineaiinoue ianeoaeeaaiey a
niioaaonoaothueo NaII, eee eciaiyy ia?o?ooiua iao?eoeu NaII. Oaeei
ia?acii a ea/anoaa iioeiaeueiie iiaeao ?anniao?eaaoueny, iai?eia?, NaII,
ai anao nenoaiao eioi?ie iaoaiaoe/aneea iaeeaeaiey aeeeoaeueiinoae
ianeoaeeaaiey iaeeiaeiau. *anoi oeaeueth ?aoaiey caaea/ neioaca e
iioeiecaoeee yaeyaony oi?ie?iaaiey NaII aiciiaeii aieueoae i?iioneiie
niiniaiinoe.

I?e yoii iniaue eioa?an i?aaenoaaeyao eeann caaea/ oaeiai oeia, eiaaea
?aoaiea aeinoeaaaony ca n/ao eciaiaiey ia?o?ooiie iao?eoeu naoe,
inoaaeyy iaeciaiiuie caaeaiiua eioaineaiinoe ianeoaeeaaiey a nenoaiao
ianniaiai ianeoaeeaaiey.

Oeaeueth ianoiyuae aeeieiiiie ?aaiou yaeyaony ?ac?aaioea iaoiaea
oi?ie?iaaiey ia?o?ooiuo iao?eoe iaeii?iaeiie caieiooie
yeniiiaioeeaeueiie naoe ianniaiai ianeoaeeaaiey.

1. Iinoaiiaea caaea/e

Ionoue caaeaia iauaeoiay NaII, ii?aaeaeyaiay iaai?ii [1]

Ionoue oae aea caaeaiu – eiioeaiooaeueiue aaeoi?,
iino?iaiiue ia iniiaaiee oai?ai, i?eaaaeaiiuo a [1] e S – iao?eoea
niaaeiinoae, ii?aaeaeyaiay neaaeothuei ia?acii:

– ianoi?ie?iaaiiay iao?eoea .

Iaiaoiaeeii iino?ieoue ae?ooaeueioth NaII yoaeiiiiai oeia, a anee yoi
iaaiciiaeii, oi naoue noaiaea?oiiai eee neiiao?e/iiai aeaeia [1]. Aeey
yoiai iaiaoiaeeii caaeaoue iaai?
[1-2], eioi?ui ii?aaeaeyaony iaeii?iaeiay caieiooay
yeniiiaioeeaeueiay naoue. Yoio iaai? ioee/aaony io iaai?a
oieueei oai, /oi aeey iaai noi?ie?iaaia ia?o?ooiay iao?eoea . O.i.
caaea/a ninoieo a oii, /oiau iaeoe iaecaanoiua ia?o?ooiua aa?iyoiinoe
, yoa caaea/a iacuaaaony caaea/ae neioaca [1].

2. Ae?ooaeueiua NaII

Iiaeii iaeeaeaoue aunieie i?iioneiie niiniaiinoe io NaII n ia?aiao?aie,
iaania/eaathueie a noaoeeiia?iii ?aaeeia ooieoeeiie?iaaiea NaII cia/aiey
iaoaiaoe/aneeo iaeeaeaiee /enea i?aauaathueo a nenoaiao o?aaiaaiee,
i?iii?oeeiiaeueiua eioaineaiinoe ianeoaeeaaiey a aeaiiuo NaII.

I?e ?aoaiee caaea/ aiaeeca, neioaca e iioeiecaoeee iauaeoiuo NaII
eniieuecotho NaII, eioi?ua aoaeai iacuaaoue ae?ooaeueiuie. Ia?aiao?u
ae?ooaeueiuo NaII oi?ie?othony ia iniiaa ia?aiao?ia, niioaaonoaothueo
iauaeoiuo NaII. A /anoiinoe, ae?ooaeueiua NaII iiaoo ioee/aoueny io
niioaaonoaothueo iauaeoiuo NaII oieueei naieie ia?o?ooiuie iao?eoeaie.
?anniao?eaathony ae?ooaeueiua NaII o?ao aeaeia: yoaeiiiua, noaiaea?oiua
e neiiao?e/iua [1].

Ae?ooaeueiua NaII ?acee/iuo aeaeia, niioaaonoaothuea iaeioi?ie iauaeoiie
NaII ioee/athony oiiieiaeyie, ii?aaeaeyaiuie eo ia?o?ooiuie iao?eoeaie.

Ae?ooaeueiua NaII eaaeaeiai aeaea iiaoo auoue iaeiiai ec neaaeothueo
oeiia: eiina?aaoeaiiai, ?aaoey?iiai, ?aaiiia?iiai [1]. Oei ii?aaeaeyaony
o?aaiaaieyie, i?aaeuyaeyaiuie i?e oi?ie?iaaiee naoe e iaeioi?ui aa
oa?aeoa?enoeeai.

Enoiaey ec niia?aaeaiee, i?eaaaeaiiuo a [1], i?e enneaaeiaaiee
aeene?aoiuo nenoai ai iiiaeo neo/ayo a ea/anoaa eo iiaeaeae (iauaeoiuo
NaII) iiaoo aanueia yooaeoeaii eniieueciaaoueny yeniiiaioeeaeueiua NaII.

A ea/anoaa ae?ooaeueiuo NaII ?anniao?eaathony yeniiiaioeeaeueiua,
iaeii?iaeiua, caieiooua NaII, ii?aaeaeyaiua iaai?ii

(1)

Iniiaiua noaoeeiia?iua oa?aeoa?enoeee ?anniio?aiu a [1], [2].

N/eoay ecaanoiuie aaeoi? aa?iyoiinoae ia?aoiaea
o?aaiaaiee a nenoaiu naoe ianeoaeeaaiey i?e eo i/a?aaeiuo ia?aoiaeao
(aaeoi? yaeyaony ?aoaieai o?aaiaiey n oneiaeai
ii?ie?iaee ) e iiiaeanoaa aaee/ei

e ( –
iiiaeanoai iiia?ia NaII). Ia?o?ooiua iao?eoeu ae?ooaeueiuo NaII,
, ii?aaeaeythony ?aoaieai nenoaiu o?aaiaiee
(2)-(4) n aiciiaeiui eniieueciaaieai oneiaee (5)-(6).

(2)

(3)

(4)

(5)

(6)

?aoaiea nenoaiu (2)-(4) a neo/aa, eiaaea ana ?aaiu 1, a
oneiaey (5)-(6) ia eniieuecothony ii?aaeaeyao iao?eoeo aeey
ae?ooaeueiuo NaII neiiao?e/iiai aeaea, eiathueo iieiinaycioth oiiieiaeth
n iaoeyie.

Eniieueciaaiea i?e ?aoaiee (2)-(4) oieueei oneiaee (5) aeaao
iieiinaycioth oiiieiaeth aac iaoaeue noaiaea?oiiai aeaea.

I?e ii?aaeaeaiee ia?o?ooiuo iao?eoe yoaeiiiuo ae?ooaeueiuo NaII
eniieuecothony oneiaey (5)-(6). I/aaeaeii, eniieueciaaiea aeaiiuo
oneiaee iicaieyao a iauai neo/aa caaeaoue i?iecaieueioth oiiieiaeth
yoaeiiiie naoe, a eioi?ie ia aeiioneathony iaoee. O.a. ia?o?ooiay
iao?eoea yoaeiiiie naoe iiaeao eiaoue no?oeoo?o, oiaeaeanoaaiioth (a
ioiioaiee /enea e ?aniieiaeaiey ioeaauo yeaiaioia) no?oeoo?a ia?o?ooiie
iao?eoeu, niioaaonoaothuae iauaeoiie NaII. Yoe iao?eoeu iiaoo
ioee/aoueny oieueei cia/aieyie iaioeaauo yeaiaioia. Caiaoei, /oi
iiaenenoaia (4) ii?aaeaeyao ioiioaiey ioiineoaeueiuo eioaineaiinoae
ano?a/iuo iioieia o?aaiaaiee ec ni a nj e ia?aoii.

Ii?aaeaeaiea 1. Ia?o?ooiua iao?eoeu e iaeii?iaeiuo,
caieioouo NaII e n iaeiii?eai?iuie NII,
ii?aaeaeyaiuie iaai?aie

iacuaathony iiaeiaiuie, anee iie eiatho iaeeiaeiaia /enei e
?aniieiaeaiea ioeaauo yeaiaioia e ioee/athony oieueei cia/aieyie
iaioeaauo yeaiaioia.

Ii?aaeaeaiea 2. NaII e , ii?aaeaeaiiua iaai?aie

iacuaathony iiaeiaiuie, anee eo ia?o?ooiua iao?eoeu e
iiaeiaiu, a inoaeueiua yeaiaiou iaai?ia ?aaiu niioaaonoaaiii.

Ii?aaeaeaiea 3. Iaeii?iaeiay caieiooay yeniiiaioeeaeueiay NaII n
iaeiii?eai?iuie NII, ii?aaeaeyaiay iaai?ii

e oaeiaeaoai?ythuay oneiaeyi:

iacuaaaony ae?ooaeueiie NaII eiina?aaoeaiiai oeia.

Ii?aaeaeaiea 4. Iaeii?iaeiay caieiooay NaII n iaeiii?eai?iuie
NII, ii?aaeaeyaiay iaai?ii

e oaeiaeaoai?ythuay oneiaeth
iacuaaaony ae?ooaeueiie NaII ?aaoey?iiai oeia.

Ii?aaeaeaiea 5. NaII , ii?aaeaeyaiay iaai?ii

e oaeiaeaoai?ythuay oneiaeth

( – i. i. aeeeoaeueiinoe i?aauaaiey o?aaiaaiey a ni )
iacuaaaony ae?ooaeueiie NaII ?aaiiia?iiai oeia.

A [1] ?anniio?aiu iniiaiua oa?aeoa?enoeee ae?ooaeueiuo NaII ?acee/iuo
oeiia e aeieacai ?yae oai?ai, ia iniiaaiee eioi?uo iiaoo auoue iino?iaiu
yoe oa?aeoa?enoeee. (A oii /enea aaeoi? .)

2.1 Ia?o?ooiua iao?eoeu ae?ooaeueiuo NaII.

?aoaiea aii?ina i nouanoaiaaiee ae?ooaeueiuo NaII niioaaonoaothueo
aeaeia e oeiia caaeneo io cia/aiee ia?aiao?ia L, N, aaeoi?a
. I?e yoii aeey eneeth/aiey o?eaeaeueiuo neo/aaa
aeinoaoi/ii iio?aaiaaoue, /oiau cia/aiey ia?aiao?ia L e N oaeiaeaoai?yee
i/aaeaeiui niioiioaieyi
(7), a cia/aiey eiiiiiaio aaeoi?a
oaeiaeaoai?yee ia?aaainoao (8).

Aeey ae?ooaeueiie NaII ?aaiiia?iiai oeia ia cia/aiey

iaeeaaeuaaaony aeiiieieoaeueiia ia?aie/aiea

(9),aaea

(10)

A [1] iieacaii, /oi aa?iyoiinoe nouanoaotho e
oaeiaeaoai?ytho o?aaiaaieyi:

(11)

aeey ae?ooaeueiuo NaII eiina?aaoeaiiai e ?aaoey?iiai oeiia i?e
auiieiaiee ia?aie/aiee (7), (8), a aeey ae?ooaeueiuo NaII ?aaiiia?iiai
oeia (7),(8),(9). Iiyoiio aoaeai n/eoaoue, /oi aeey i?aaenoaaeythueo
oai?aoe/aneee eioa?an ae?ooaeueiuo NaII ia?aiao?u L, N, e oaeiau,
/oi (7),(8),(9) auiieiythony e nouanoaoao aaeoi?
iino?iaiiue ia iniiaaiee oai?ai, i?eaaaeaiiuo a [1].

Ii?aaeaeaiea 6. Ae?ooaeueiua NaII, ia?aiao?u L, N, eioi?uo
oaeiaeaoai?ytho ia?aie/aieyi (7),(8), (9), a aaeoi? ii?aaeaeyaony
ia iniiaaiee oai?ai [1] e oaeiaeaoai?yao oneiaeyi (11) iacuaathony
eiioeaiooaeueiuie ae?ooaeueiuie NaII, a aaeoi? – eiioeaiooaeueiui
aaeoi?ii.

Oaeei ia?acii, eiioeaiooaeueiuie yaeythony ana ae?ooaeueiua NaII aeey
eioi?uo aua ia noi?ioee?iaaia eee ia iiaeao auoue noi?ioee?iaaia
ia?o?ooiay iao?eoea , oaeay, /oi eiioeaiooaeueiue aaeoi?
yaeyaony ?aoaieai o?aaiaiey (12) n oneiaeai
ii?ie?iaee

(13).

Ae?oaeie neiaaie ae?ooaeueiay NaII ia nouanoaoao iiea ia
ii?aaeaeaiu ana yeaiaiou iaai?a , a oii /enea e . Iiyoiio
eioa?an i?aaenoaaeyao oneiaea nouanoaiaaiey ia?o?ooiuo iao?eoe aeey
eioeaiooaeueiuo NaII.

Ia?o?ooiua iao?eoeu eiioeaiooaeueiuo ae?ooaeueiuo NaII nouanoaaiii
caaenyo io eo oiiieiaee. Iaicia/ei eiioeaiooaeueioth ae?ooaeueioth NaII
/a?ac , aaea niioaaonoaaiii aeey naoe neiiao?e/iiai,
noaiaea?oiiai e yoaeiiiiai aeaeia.

Aaaaeai a ?anniio?aiea i?a?ao , ioia?aaeathuee oiiieiaeth NaII .
Aa?oeiu niioaaonoaotho NII, a aeoae – o?aaeoi?eyi ia?aoiaeia
o?aaiaaiee iaaeaeo nenoaiaie.

I – oth aa?oeio i?a?aoa iaicia/ei /a?ac , a aeoao
niaaeeiythuoth n /a?ac .I/aaeaeii, –
neeueiinayciue. Eniieuecoy iaicia/aiey e , niioaaonoaaiii
aeey iieonoaiaiae enoiaea e caoiaea , iaicia/ei iao?eoeo
niaaeiinoe i?a?aoa e, o/eouaay, /oi noiia yeaiaioia i – ie no?iee
iao?eoeu ?aaia , a noiia yeaiaioia i – iai noieaoea –
. A i?a?aoa

Ii ii?aaeaeaieth eiaao iieiinaycioth oiiieiaeth n iaoeyie. O. i.
a i?a?aoa ( – eiioeaiooaeueiay neiiao?e/iay NaII).
Eaaeaeay aa?oeia niaaeeiaia aeoaie ni anaie ae?oaeie e eiaao iaoeth
. Ana yeaiaiou ?aaiu 1.

Eiioeaiooaeueiay noaiaea?oiay NaII eiaao iieiinaycioth oiiieiaeth
aac iaoaeue. Ana yeaiaiou iao?eoeu niaaeiinoe ?aaiu aaeeieoea,
e?iia yeaiaioia aeaaiie aeeaaiiaee.

Oiiieiaey eiioeaiooaeueiie yoaeiiiie NaII iiaeao auoue
i?iecaieueiie e aeieaeia oaeiaeaoai?youe eeoue iaeiiio o?aaiaaieth –
auoue oiaeaeanoaaiiie oiiieiaee niioaaonoaothuae iauaeoiie NaII. Iiyoiio
oiaeaeanoaaiai i?a?aoo iauaeoiie NaII, iao?eoeu e
oiaeaeanoaaiiu. Ec nayce n neaaeoao:

anee ia niaaeia n , oi .

anee niaaeia n , oi anee , .

/enei iaecaanoiuo naoe

(14).

Aaaaeai a ?anniio?aiea iiiaeanoai eiinoaio

anee ia niaaeia n e , anee niaaeia n
e iiuiinoue
Eiiaaea aeey iiaeao auoue caaeaii iiiaeanoai eiinoaio
, , iiuiinoe , eniieuecoaiia i?e
oi?ie?iaaiee ia?o?ooiie iao?eoeu . A yoii neo/aa, anee niaaeia
n e , oi i?e iaee/ee a iiiaeanoaa yeaiaioa

, niioaaonoaothuaai iieaaaaony, /oi .

Iauaaeeiaiea iiiaeanoaa e aeaao iiiaeanoai

, yeaiaiou eioi?iai ii?aaeaeytho cia/aiea niioaaonoaothueo ia?o?ooiuo
aa?iyoiinoae .

Aeey ii?aaeaeaiey ia?o?ooiuo aa?iyoiinoae naoe cia/eoaeueiue
eioa?an i?aaenoaaeytho aiciiaeii eiathueany aeaiiua i n?aaieoaeueiie
aaee/eia ano?a/iuo iioieia iaaeaeo e . Ioiineoaeueiua
eioaineaiinoe iioieia o?aaiaaiee ec a ?aaiu
.Iaicia/ei ioiioaiea eioaineaiinoae /a?ac , o. a.
. Aaee/eia iacuaaaony eiyooeoeeaioii
iaiaia, a o?aaiaiea
– o?aaiaieai iaiaia.

Iaicia/ei /a?ac iiiaeanoai eiyooeoeeaioia iaiaia.
Caaeaiea yoiai iiiaeanoaa ii?aaeaeyao o?aaiaiee
iaiaia, eioi?ua iiaoo auoue eniieueciaaiu i?e ii?aaeaeaiee
.

Neaaeiaaoaeueii aeey ?aoaiey iaecaanoiuo ia?o?ooiuo aa?iyoiinoae iiaeao
auoue eniieueciaaia nenoaia A eeiaeiuo aeaaa?ae/aneeo o?aaiaiee,
aeeth/athuay o?e iiaenenoaiu:

iiaenenoaia o?aaiaiee iioieia (L o?aaiaiee):

iiaenenoaia o?aaiaiee ii?ie?iaee (L o?aaiaiee):

iiaenenoaia o?aaiaiee iaiaia ( o?aaiaiee):

*enei o?aaiaiee iaiaia caaeneo io oiiieiaee naoe e cia/aiee , e
iiaeao auoue iaiueoa [1].

Oai?aia 1. Aeey eiioeaiooaeueiie neiiao?e/iie ae?ooaeueiie NaII
eiina?aaoeaiiai, ?aaoey?iiai eee ?aaiiia?iiai oeia n eiioeaiooaeueiui
aaeoi?ii ia?o?ooiay iao?eoea anaaaea nouanoaoao e aa
yeaiaiou ii?aaeaeythony niioiioaieyie
. Aeieacaoaeuenoai i?eaaaeaii a [1].

Oai?aia 2. Aeey eiioeaiooaeueiie noaiaea?oiie ae?ooaeueiie NaII
eiina?aaoeaiiai, ?aaoey?iiai eee ?aaiiia?iiai oeiia ia?o?ooiay iao?eoea
nouanoaoao, anee niaianoia nenoaia o?aaiaiee:

(15)

(16)

(17)

Cia/aiey yeaiaioia iao?eoeu ii?aaeaeythony ?aoaieai yoie nenoaiu.
Oai?aia aeieacaia a [1].

Caia/aiea Iauaa ?aoaiea nenoaiu (15) – (17) ii?aaeaeyao aaneiia/iia
/enei iiaeiaiuo iao?eoe . Aeey eiie?aoecaoeee iao?eoeu
caaeatho eiie?aoiua cia/aiey naiaiaeiuo iaecaanoiuo.

Oai?aia 3. Aeey eiioeaiooaeueiie yoaeiiiie ae?ooaeueiie naoe
ethaiai oeia n eiioeaiooaeueiui aaeoi?ii , caaeaiiie oiiieiaeae,
ii?aaeaeyaiie i?a?aoii , iao?eoeu niaaeiinoe ,
caaeaiiui iiiaeanoaii eiyooeoeeaioia iaiaia , ia?o?ooiay
iao?eoea nouanoaoao, anee niaianoia nenoaia o?aaiaiee

(18)

(19)

(20)

(21)

(22)

i?e ia?aie/aieyo (23)

Aeieacaoaeuenoai ni. a [1].

I?eia?u ae?ooaeueiuo NaII ?acee/iuo aeaeia ?anniio?aiu a [1].

3. Iaoiaeu iino?iaiey ia?o?ooiuo iao?eoe NaII.

3.1. Iauaa ?aoaiea.

Caaea/a iino?iaiey ia?o?ooiie iao?eoeu ae?ooaeueiie NaII iiaeao auoue
?aoaia neaaeothuei ia?acii:

Ionoue aeaia eiioeaiooaeueiay yoaeiiiay ae?ooaeueiay NaII , ninoiyuay
ec L NII. Aeey eioi?ie ii?aaeaeaiu aaeoi? , i?a?ao , iao?eoea
niaaeiinoe , iiiaeanoai , iiiaeanoai eiyooeoeeaioia
iaiaia.

Iaiaoiaeeii noi?ioee?iaaoue ia?o?ooioth iao?eoeo ,o.a. iaeoe L2
iaecaanoiuo , .

Ec o?aaiaiee (22) – (23) iieo/eee cia/aiey iaecaanoiuo ,aaea
O ii?aaeaeyaony (14).

A ?acoeueoaoa iieo/eee nenoaio eeiaeiuo aeaaa?ae/aneeo o?aaiaiee (18) –
(20) io O iaecaanoiuo (eiaeaen naa?oo – ii?yaeeiaue iiia?
iaecaanoiie).

?aoay nenoaio iaoiaeii Aaonna, iieo/ei iaeei ec o?ao aiciiaeiuo
aa?eaioia:

Nenoaia ia?ac?aoeia. A yoii neo/aa noi?ie?iaaoue ia?o?ooioth iao?eoeo
, a neaaeiaaoaeueii e ae?ooaeueioth yoaeiiioth NaII iaaiciiaeii.

Nenoaia ?ac?aoeia iaeiicia/ii. A yoii neo/aa iaiaoiaeeii i?iaa?eoue,
oaeiaeaoai?ytho ee iieo/aiiua cia/aiey ia?aaainoaai
(23). Anee ia?aaainoaa auiieiythony, oi iieo/aiiia ?aoaiea aeaao
cia/aiey inoaaoeony O iaecaanoiuo , o. i. caeai/eaaaony
oi?ie?iaaiea ia?o?ooiie iao?eoeu . Anee (23) ia auiieiyaony, oi
noi?ie?iaaoue

iaaiciiaeii.

Nenoaia ?ac?aoeia iaiaeiicia/ii. Iauaa ?aoaiea nenoaiu (18) – – (20)
oaeoe/anee ii?aaeaeyao aaneiia/iia iiiaeanoai iiaeiaiuo iao?eoe
aeey eiie?aoiie eiioeaiooaeueiie NaII. Caaeaiea eiie?aoiuo cia/aiee
naiaiaeiuo ia?aiaiiuo ii?aaeaeyao eiie?aoioth ia?o?ooioth iao?eoeo aeey
oaeie NaII. I/aaeaeii, /oi yoi eiie?aoiia ?aoaiea aeieaeii
oaeiaeaoai?youe ia?aie/aieyi (23).

Ionoue ia?aua m ia?aiaiiuo – naiaiaeiua, oiaaea anee
, oi inoaeueiua , iiaeii caienaoue eae
. O. a. inoaeueiua (O-m) ia?aiaiiuo iiaoo auoue eeiaeii
au?aaeaiu /a?ac . Iiaenoaaeyy iieo/aiiua au?aaeaiey a
ia?aaainoaa

(24)

iieo/ei nenoaio ia?aaainoa:

(25)

Yoa nenoaia ia?aaainoa ia?acoao oae iacuaaaiia iiiaia?aiiia iiiaeanoai a
m – ia?iii i?ino?ainoaa. Anee yoi iiiaeanoai ia ionoi, oi, oae eae iii
ia?aie/aii, iii yaeyaony auioeeui iiiaia?aiieeii. Oi/ea iacuaaaony
aa?oeiie auioeeiai iiiaia?aiieea a , anee iia yaeyaony aeiionoeiie
e i?aaenoaaeyao niaie oi/eo ia?ana/aiey m eeiaeii iacaaeneiuo
aeia?ieineinoae. (Eaaeaeia eeiaeiia o?aaiaiea caaeaao aeia?ieineinoue,
eaaeaeiio eeiaeiiio ia?aaainoao ec (25) niiinoaaeyaony ia?aie/aiiia
aeia?ieineinoueth iieoi?ino?ainoai; aeia?ieineinoue iieo/atho, caiaiyy
ciae ia?aaainoaa ia ciae ?aaainoaa.) Aa?oeia au?iaeaeaiiay, anee iia
yaeyaony oi/eie ia?ana/aiey aieaa /ai m aeia?ieineinoae.

Aa?oeio iaeuecy i?aaenoaaeoue a aeaea auioeeie
eeiaeiie eiiaeiaoeee aeaoo ae?oaeo oi/ae aeiionoeiie iaeanoe
aeey anao aeiionoeiuo oi/ae ( ).
Anyeia iiiaia?aiiia iiiaeanoai eiaao eiia/iia /enei aa?oei. Anee
aeiionoeiay iaeanoue ia?aciaaia n ia?aaainoaaie e m
o?aaiaieyie, oi iia iiaeao eiaoue naiia aieueoaa aa?oei. O. e.
aeiionoeiay iaeanoue a aeaiiii neo/aa yaeyaony auioeeui iiiaia?aiieeii,
oi eaaeaeay aeiionoeiay oi/ea eiaao ii iaiueoae ia?a iaeii
i?aaenoaaeaiea:

(26),

aaea – aa?oeiu iiiaia?aiieea;
.

Oaeei ia?acii, anee iu iaeaeai ana aa?oeiu iiiaia?aiieea (anee iie
nouanoaotho. A i?ioeaiii neo/aa ?aoaiey ia nouanoaoao), oi iu iieo/ei
iauaa ?aoaiea caaea/e oi?ie?iaaiey iao?eoeu .

aaea – aeiionoeiay oi/ea, iaeaeaiiay ii oi?ioea
(26). Iieo/ei inoaaoeany O iaecaanoiuo e caaa?oei iino?iaiea ia?o?ooiie
iao?eoeu.

3.2. I?eia? iaoiaeaeaiey iauaai ?aoaiey.

Aeaia eiioeaiooaeueiay yoaeiiiay ae?ooaeueiay NaII , n L=5, aeey
eioi?ie ii?aaeaeaiu eiioeaiooaeueiue aaeoi? , i?a?ao , iao?eoea
niaaeiinoae .

Iiiaeanoai .

Ec o?aaiaiee (21), (22) iieo/ei cia/aiey 15 iaecaanoiuo ia?o?ooiuo
aa?iyoiinoae ec 25. Inoaaoeany iaecaanoiua caioia?oai
,

iieo/ei:

?anniio?ei nenoaio eeiaeiuo o?aaiaiee (18), (19), (17). I?eiaiyy e iae
aeai?eoi Aaonna iieo/ei:

nenoaia niaianoia.

?aoaiea iaiaeiicia/ii 10-8=2 iaecaanoiuo iiaoo auoue aua?aiu
i?iecaieueii.

?aoaai nenoaio e iieo/aai:

(()

Iiaenoaaei ?acoeueoaou a (25). Iieo/ei nenoaio oeia (26):

(27)

Yoa nenoaia ia?aaainoa ia?acoao iiiaia?aiiia iiiaeanoai, ecia?aaeaiiia
ia ?en. 1.

Ethaay ia?a i?eiaaeeaaeauay aeiionoeiie iaeanoe
oaeiaeaoai?yao nenoaia (27).

Iiiaia?aiieeo eiaao 5 aa?oei:

Ethaay oi/ea aeiionoeiiai iiiaeanoaa eiaao i?aaenoaaeaiea
, aaea – aa?oeiu, , , . Ionoue,
iai?eia?, , oiaaea

. Iiaenoaaei cia/aiey e a ((),
iieo/ei

?enoiie 1.

3.3. Iaoiae oi?ie?iaaiey ia?o?ooiie iao?eoeu ae?ooaeueiie NaII.

Caaea/a iino?iaiey ae?ooaeueiie NaII iiaeao auoue naaaeaia e caaea/a
iaeeiaeiiai i?ia?aiie?iaaiey.

Ionoue caaeaia eiioeaiooaeueiay ae?ooaeueiay NaII , aeey eioi?ie
caaeai eiioeaiooaeueiue aaeoi? , i?a?ao , iao?eoea
niaaeiinoae , iiiaeanoai .

Caaea/ae iaeeiaeiiai i?ia?aiie?iaaiey iauaai aeaea iacuaaaony caaea/a:
Iaeoe

(2.1)

i?e ia?aie/aieyo

(2.2)

Aaaaeai a ?anniio?aiea ooieoeeth ;
i/aaeaeii, /oi anee iouuaony oaeay, /oi ,oi
anoue eneiiay ia?o?ooiay iao?eoea. O. i. iu iieo/eee caaea/o:

(2.3)

i?e ia?aie/aieyo

(2.4)

Caaea/a (2.3) – (2.4) yaeyaony caaea/ae iaeeiaeiiai i?ia?aiie?iaaiey. Aa
iiaeii ioianoe e caaea/ai eaaae?aoe/iiai i?ia?aiie?iaaiey – eeann caaea/
aeey eioi?uo oeaeaaay ooieoeey eaaae?aoe/ia, a ana ia?aie/aiey eeiaeiu.

?aoay caaea/o (2.3) – (2.4) iaeiei ec iaoiaeia, ?anniio?aiiuo a [3-5]
iiaeii iieo/eoue iaeei ec ?acoeueoaoia:

, aaea . A yoii
neo/aa noi?ie?iaaoue ia?o?ooioth iao?eoeo iaaiciiaeii.

. A yoii neo/aa anoue eneiiay
ia?o?ooiay iao?eoea ae?ooaeueiie NaII.

Aeey ?aoaiey CII ?ac?aaioai ?yae iaoiaeia, iicaieythueo, ioi?aaeyynue io
iaeioi?iai ia/aeueiiai ?aoaiey, iieo/aoue iineaaeiaaoaeueii cia/aiey,
eioi?ua iaoiaeyony ana aeeaea e eneiiie oi/ea iaeneioia (ieieioia).
A?oiia iaoiaeia, iniiaaiiuo ia au/eneaiee e n?aaiaiee cia/aiee oeaeaaie
ooieoeee a ?yaea oi/ae ia?aae neaaeothuei oaaii, iacuaaaony iieneiauie
iaoiaeaie iioeiecaoeee.

A caaea/a iiaeii i?aaenoaaeoue oeaeaaoth ooieoeeth eae
aeia?iiaa?oiinoue. Iaeneiaeueiia cia/aiea aeinoeaaaony a aa?oeia naiiai
aunieiai oieia. Iiene yeno?aioia ia/eiatho n ethaie oaeiaiie oi/ee,
i?e/ai aeaeaathony a iai?aaeaiee iaenei?aeoaai iiaeuaia, iiea ia
aeinoeaatho eeai aa?oeiu, eeai a?aieoeu. I?e aeinoeaeaiee a?aieoeu
iaiaoiaeeii eneeth/eoue ia?aiauaiea ca i?aaeaeu ia?aie/aiee. I?e
aeinoeaeaiee aa?oeiu, eioi?ay ano?aoeeanue a iai?aaeaiee iaenei?aeoaai
iiaeuaia iiai?a/eaatho ai aiiaue aua?aiiii iai?aaeaiee iaenei?aeoaai
iiaeuaia. Oaeei ia?acii aeinoeaatho oi/ee, aaea aeaeaeaiea a ethaii
iai?aaeaiee i?eaiaeeo e nioneo. A yoii neo/aa ooaa?aeaeatho, /oi iaeaeai
ii e?aeiae ia?a eieaeueiue yeno?aioi.

Ia i?aeoeea, i?e ?aaeecaoeee yoiai iaoiaea aicieeatho aeaa o?oaeiinoe.
Ai-ia?auo, yoi ioiineoaeueiay iaeay nei?inoue noiaeeiinoe. Aeey
i?aiaeieaiey yoiai neoaeao iaoiaeu iaoiaeaeaiey aieaa yooaeoeaiuo
iai?aaeaiee, /ai iai?aaeaiea iaenei?aeoaai iiaeuaia. Aoi?ay o?oaeiinoue
ninoieo a oii, /oi yoio iaoiae iicaieyao iaia?oaeeoue eieaeueiua
iaeneioiu, ii ia aeaao aa?aioee aeinoeaeaiey aaniethoiiai (aeiaaeueiiai)
yeno?aioia. *oiau i?aiaeieaoue yoo o?oaeiinoue iau/ii ia/eiatho iiene ec
?acee/iuo oi/ae, e, anee au/eneaiey noiaeyony e ?aciui aa?oeiai, oi
auae?atho iaeaieaa aunieoth ec ieo. Oaeaea iiaeii eniieueciaaoue iaoiae,
ecaanoiue iiae iacaaieai “iaoiae oyaeaeiai oa?eea”, i?e eioi?ii
aeaeaeaiea oi/ee iaiiieiaao aeaeaeaiea oyaeaeiai oa?eea ii aoa?enoie
iiaa?oiinoe. ?anniio?ei iaeioi?ua ec iaoiaeia iieneiaie iioeiecaoeee.

3.4. Iiene ii noaoenoe/aneiio a?aaeeaioo.

Ionoue iaaei iaeoe iaeneioi . A oi/ea aeaeaaony m
neo/aeiuo eniuoaiee e au/eneythony i?e?auaiey oeaeaaie ooieoeee

aaea – neo/aeiua aaee/eiu, – neo/aeiue oaa.

Aeaeaa ii?aaeaeytho aaee/eio

On?aaeiaiiia ii anai ?aaeecaoeeyi cia/aiey niaiaaeaao n
enoeiiui iai?aaeaieai iaenei?aeoaai iiaeuaia, o. a.

Aeaeaa ec oi/ee niaa?oaaony i/a?aaeiie ?aai/ee oaa:

3.5. Iaoiae “oyaeaeiai oa?eea”.

?anniio?ei i?inoaeoee aa?eaio neo/aeiiai iienea:

ionoue – i?iecaieueiay oi/ea. Ec niaa?oaaony aeaeaeaiea n
oaaii a neo/aeiii iai?aaeaiee n ?aaiiia?iui ?ani?aaeaeaieai.

Aeaeaeaiea i?aaenoaaeythuae oi/ee iienuaaaony oae:

Yoio aeai?eoi aac iaiyoe iiaeao auoue oniaa?oainoaiaai. Iai?aaeaiea
oaea/iuo i?ia caiiieiaaony e aa?iyoiinoue oaaa a yoeo iai?aaeaieyo
aic?anoaao. Aeey yoiai aaaaeai aaeoi? iaiyoe , i?iaeoeee eioi?iai
ia eii?aeeiaoiua ine ii?aaeaeytho aa?iyoiinoue auai?a
iieiaeeoaeueiiai iai?aaeaiey ii i – ie ine. – iiiioiiiay,
iaoauaathuay ooieoeey, oiaaea , a
eciaiyaony oae:

aaea
– ia?aiao? caiiieiaiey, – oa?aeoa?ecoao nei?inoue iao/aiey,
.

Yoio iaoiae iacuaaaony iaoiaeii “oyaeaeiai oa?eea”.

3.6. Oi?ie?iaaiea ia?o?ooiie iao?eoeu.

Ionoue iinoaaeaia caaea/a (2.3) – (2.4). Aeey iaoiaeaeaiey ?aoaiey
i?eiaiei iaoiae iineaaeiaaoaeueiie iioeiecaoeee.

Iienaiea iaoiaea.

1. Ia/aeueiue oaa e=0.

A ea/anoaa ia/aeueiiai i?eaeeaeaiey auaa?ai iaeioi?oth iao?eoeo .
Iao?eoea aeieaeia oaeiaeaoai?youe oneiaeyi 2.4. Caaeaaeei oi/iinoue
.

Caia/aiea. Auoa auei neacaii, /oi aeey oiai, /oiau iiauneoue
aa?iyoiinoue iaoiaeaeaiey aeiaaeueiiai yeno?aioia auae?atho ianeieueei
ia/aeueiuo i?eaeeaeaiee. iiaeao auoue aua?aia neo/aeii, eeai
iaeanoue ii?aaeaeaiey iiaeao auoue ?acaeoa ia eioa?aaeu e a ea/anoaa
auae?athony oceu iieo/aiiie naoee. Iaoiaeu auai?a /enea neo/aeiuo i?ia
eee ?acia?iinoe naoee iienaiu a [3] – [7].

2. e-ue oaa. Auai? iai?aaeaiey aeaeaeaiey.

Aeey eaaeaeiai yeaiaioa , aaea
au/eneei cia/aiey oeaeaaie ooieoeee , aaea
– iao?eoea, a eioi?ie ana yeaiaiou ?aaiu yeaiaioai iao?eoeu
, e?iia iaeiiai yoiai yeaiaioa , eioi?ue ?aaai
. Cia/aiea aaee/eiu auae?aaony ec niia?aaeaiee i oi/iinoe, n eioi?ie
euaony . Iaoiaeu auai?a aaee/eiu iienaiu a [3] – [7].

Oaeei ia?acii iieo/ei iiiaeanoai cia/aiee oeaeaaie ooieoeee .
( iiaeao auoue iieiaeeoaeueiie e io?eoeaoaeueiie). Aeey anao
yeaiaioia . Auaa?ai oaia?ue .
Niioaaonoaothuee yeaiaio iao?eoeu caiiieiaai. Ionoue yoi aoaeao
.Auaa?ai oaia?ue a no?iea i1 yeaiaio , oaeie, /oi
. Caiiiiei oaeaea
yoio yeaiaio.

?anniio?ei aeaa aiciiaeiuo aa?eaioa:

a) Anee , oi
caiiieiaai eiiiiiaiou , e ia?aoiaeei e 3.

a) Anee ,
oi , ia?aoiaeei e 4.

3. e-ue oaa. Aeaeaeaiea a aua?aiiii iai?aaeaiee.

Ec oi/ee ia?aoiaeei e neaaeothuei ia?acii:

Anee , oi
ii?aaeaeyaony neaaeothuei ia?acii:

e:=e+1, ia?aoiaeei e 3.

Anee , oi , e:=e+1,
ia?aoiaeei e 2.

4. Eiia/iue oaa.

Anee ( – aaee/eia, ii?aaeaeythuay oi/iinoue
au/eneaiey yeno?aioia), oi – eneiiay ia?o?ooiay iao?eoea.

Anee , oi auae?atho ae?oaia ia/aeueiia
i?eaeeaeaiea e ia?aoiaeyo e 2. Anee iiiaeanoai ia/aeueiuo i?eaeeaeaiee
en/a?iaii, oi iieaaatho, /oi noi?ie?iaaoue ia?o?ooioth iao?eoeo
iaaiciiaeii.

4. Aeai?eoi i?ia?aiiu, ?aaeecothuee iaoiae iino?iaiey

ia?o?ooiie iao?eoeu.

Aeai?eoi ninoieo ec 6 ooieoeeiiaeueiuo aeieia, auiieiyaiuo a ii?yaeea,
eioi?ue noaiaoe/ii ecia?aaeai ia ?enoiea 2 “Noaia aeai?eoia”. Ieaea
i?eaaaeaii iacia/aiea e niaea?aeaiea anao 6-oe ooieoeeiiaeueiuo aeieia.
Aeai?eoi ?aaeecoao iienaiiue auoa iaoiae.

Aeie 1.

Iacia/aiea: Aaiae aeaiiuo, iaiaoiaeeiuo aeey iino?iaiey ia?o?ooiie
iao?eoeu.

Niaea?aeaiea: Aaiae aeaiiuo, eiie?aoece?othueo ?aoaaioth caaea/o (o. a.
caaea/o iino?iaiey ia?o?ooiie iao?eoeu ae?ooaeueiie NaII (2.3) – (2.4)).
Yoe aeaiiua aeieaeiu niaea?aeaoue /enei NII a naoe e iao?eoeo niaaeiinoe
enoiaeiie eiioeaiooaeueiie ae?ooaeueiie NaII, a oaeaea eiioeaiooaeueiue
aaeoi? .

Aeie 2.

Iacia/aiea: Caaeaiea ia/aeueiiai i?eaeeaeaiey.

Niaea?aeaiea: Iao?eoea oi?ie?oaony iooai i?enaiaiey neo/aeiuo
cia/aiee yeaiaioai oaeeo, /oi , aaea I – iiiaeanoai
iiia?ia yeaiaioia iao?eoeu niaaeiinoe, oaeeo /oi

I?e yoii iaiaoiaeeii niaethaeaoue noioanoe/iinoue iao?eoeu, o. a.
oneiaey (2.4). Inoaeueiua yeaiaiou iieo/atho neaaeothuei ia?acii:

( – yeaiaiou iao?eoeu niaaeiinoe).

O. i. aeie 2 ?aaeecoao ioieo 1 ?anniio?aiiiai auoa iaoiaea.

Aeie 3. ?aaeecoao ioieo 2 iaoiaea oi?ie?iaaiey ia?o?ooiie iao?eoeu.

Iacia/aiea: Auai? iai?aaeaiey, a eioi?ii aoaeao inouanoaeyoueny iiene
yeno?aioia.

Niaea?aeaiea: 3.1) Au/eneaiea oeaeaaie ooieoeee oaeouae iao?eoeu .

3.2) Auai? oaeeo yeaiaioia e e aaee/eiu ,
(iieiaeeoaeueiie eee io?eoeaoaeueiie), /oi

Iinea oiai eae yoe oneiaey auiieiaiu e yeaiaiou iaeaeaiu ia?aoiaeyo e
oneiaeth 1:

1) Anee , oi
ia?aaeathony a ea/anoaa enoiaeiuo aeaiiuo a Aeie 4 e oi?aaeaiea
ia?aaeaaony Aeieo 4.

2) Anee 1) ia auiieiyaony, oi oaeouay iao?eoea caiiieiaaony eae e
oi?aaeaiea ia?aoiaeeo ia Aeie 5.

Iiae?iaii auai? yeaiaioia e iienai auoa a ioieoa 2 iaoiaea
oi?ie?iaaiey iao?eoeu .

Aeie 4. ?aaeecoao ioieo 3.

Iacia/aiea: Inouanoaeyao aeaeaeaiea a iai?aaeaiee aua?aiiii Aeieii 3 aei
oao ii? iiea ia aoaeao aeinoeaiooa a?aieoea (oneiaey (2.4)), eeai
aa?oeia ia yoii iai?aaeaiee.

Niaea?aeaiea: Iiea ia aoaeao aeinoeaiooa a?aieoea, o. a. ia ia?anoaioo
auiieiyoueny oneiaey:

( – aua?aiu Aeieii 2)

Eeai ia aoaeao aeinoeaiooa aa?oeia aeey oaeouaai iai?aaeaiey, o. a.

(()

( (() – oneiaea aeinoeaeaiey aa?oeiu a oi/ea ). Iiaoi?ytho ?aai/ee
oaa: i?enaaeaatho cia/aiea
.

Eae oieueei aeaeaeaiea i?ae?auaaony oaeouay iao?eoea caiiieiaaony e
oi?aaeaiea ia?aaeaaony a Aeie 3.

Aeie 5.

Iacia/aiea: Ii?aaeaeeoue aeinoeaioo ee aeiaaeueiue yeno?aioi a oi/ea ,
ii?aaeaeaiiie Aeieii 2. O. a. aeinoeaiooi ee ?aoaiea caaea/e (2.3) –
(2.4).

Niaea?aeaiea: I?iaa?ythony oneiaey 2:

Anee ( – aaee/eia, ii?aaeaeythuay oi/iinoue, n eioi?ie
euaony yeno?aioi, niaea?aeeony ai aoiaeiuo aeaiiuo), oi aeaeaaony
auaiae, /oi

– ?aoaiea caaea/e (2.3) – (2.4);

Anee , oi anee ?ac ia aue aeinoeaioo iaeei e oio aea
ieieioi, oi?aaeaiea ia?aaeaaony a Aeie 2 ( iiaeao auoue caaeaia a
enoiaeiuo aeaiiuo).

A i?ioeaiii neo/aa iieaaaaony, /oi ?aoaiey caaea/e (2.3) – (2.4)
aeinoe/ue iaaiciiaeii.

Iinea i?iaa?ee oneiaey 2 oi?aaeaiea ia?aaeaaony a Aeie 6.

Aeie 6.

Iacia/aiea: Oi?ie?iaaiea auoiaeiuo aeaiiuo.

Niaea?aeaiea: Oi?ie?oaony niiauaiea, neaaeothuei ia?acii:

Anee ?aoaiea iaeaeaii, oi auoiaeiuie aeaiiuie yaeyaony .

Anee i?eiyoi ?aoaiea i iaaiciiaeiinoe aeinoe/ue ?aoaiey, oi auoiaeiuie
aeaiiuie aoaeao niiauaiea i oii, /oi ?aoaiea ia nouanoaoao.?enoiie 2.
No?oeoo?iay noaia aeai?eoia ?aaeecothuaai

iaoiae oi?ie?iaaiey ia?o?ooiie iao?eoeu.

5. Iacia/aiea i?ia?aiiu OPTIM e iienaiea i?ia?aiiu.

I?ia?aiia OPTIM iaienaia ia ycuea Turbo Pascal. I?ia?aiia i?aaeiacia/aia
aeey ?aoaiey caaea/e oi?ie?iaaiey ia?o?ooiie iao?eoeu ae?ooaeueiie NaII.
I?ia?aiia i?aaenoaaeyao niaie ?aaeecaoeeth aeai?eoia i?eaaaeaiiiai a
i?aaeuaeouae aeaaa. I?ia?aiia i?inoa a eniieueciaaiee, o?aaoao
iacia/eoaeueiue iauai iia?aoeaiie iaiyoe. Iaaeinoaoeii i?ia?aiiu
yaeyaony iaaeinoaoi/ii aunieia auno?iaeaenoaea, eae e o iiiaeo ae?oaeo
i?ia?aii, ?aaeecothueo iiaeiaiua iaoiaeu iioeiecaoeee.

Ia?o?ooiua iao?eoeu e iao?eoeu niaaeiinoe yaeythony ?ac?yaeaiiuie
iao?eoeaie, o. a. iao?eoeaie, niaea?aeaueie ioiineoaeueii iaeia /enei
iaioeaauo yeaiaioia. Iiyoiio aeey enneaaeiaaiey ae?ooaeueiuo NaII
aieueoie ?acia?iinoe a i?ia?aiia OPTIM i?aaeoniio?aii i?aaenoaaeaiea
iao?eoe niaaeiinoe a aeaea aaeoi?a, niaea?aeauaai iiia?a noieaoeia,
niaea?aeaueo iaioeaaua yeaiaiou caienaiiua a ii?yaeea aic?anoaiey
iiia?ia noieaoeia e no?ie. Iiia? iineaaeiaai iieiaeeoaeueiiai yeaiaioa a
no?iea aa?aony ni ciaeii “-”. Iiaeiaiia i?aaenoaaeaiea iao?eoeu
niaaeiinoe iicaieyao iiauneoue nei?inoue aaiaea enoiaeiuo aeaiiuo.

I?ia?aiio iiaeii oneiaii ?acaeoue ia ooieoeeiiaeueiua aeiee, auiieiaiiua
a aeaea ioaeaeueiuo i?ioeaaeo? e ooieoeee.

1. Aaiae enoiaeiuo aeaiiuo. ?aaeecoao ioieo 1 aeai?eoia. Auiieiai a
aeaea i?ioeaaeo?u InputData.

Niaea?aeaiea: n/eouaaao enoiaeiua aeaiiua ec oaeea OPT.DAT . Enoiaeiua
aeaiiua auae?athony a neaaeothuai ii?yaeea:

e – /enei iaioeaauo yeaiaioia iao?eoeu niaaeiinoe.

L – /enei NII.

Svect – oiaeiaaiiay iao?eoea niaaeiinoe (aaeoi? ?acia?iinoe e).

– eiioeaiooaeueiue aaeoi? (?acia?iinoe L).

2. Caaeaiea ia/aeueiie iao?eoeu ?aaeecoao Aeie 2 aeai?eoia.
Auiieiai a aeaea i?ioeaaeo? MatrSmez e TetaMatr. I?ioeaaeo?a MatrSmez
oi?ie?oao iao?eoeo niaaeiinoe ia iniiaaiee aaeoi?a Svect. I?ioeaaeo?a
TetaMatr i?aia?acoao iao?eoeo niaaeiinoe a iao?eoeo (iiae?iaii
iienaii a aeai?eoia a Aeiea 2).

3. Auai? iai?aaeaiey nionea. ?aaeecoao Aeie 3 aeai?eoia. Auiieiai a
aeaea i?ioeaaeo?u IndLocate. Aeey ?aaiou eniieuecoao ooieoeee target
(teta) e stepish, au/eneythuea cia/aiea oeaeaaie ooieoeee e noaiaiue
iieoenoiaea aa?oeiu niioaaonoaaiii.

4. Inouanoaeyao aeaeaeaiea a aua?aiiii iai?aaeaiee. ?aaeecoao Aeie 4
aeai?eoia, auiieiaia a aeaea i?ioeaaeo?u Move.

5. Ia?aaioea ?acoeueoaoia e oi?ie?iaaiey oaeea auoiaeiuo aeaiiuo.
?aaeecoao Aeiee 5 e 6 aeai?eoia. Auiieiai a aeaea i?ioeaaeo?u
OutputData.

Niaea?aeaiea: Ia?aaaouaaao ?acoeueoaou ?aaiou Aeieia 2, 3, 4. Auoiaeiua
aeaiiua oi?ie?othony a aeaea auoiaeiiai oaeea OPT. REZ

Auoiaeiie oaee niaea?aeeo eeai iieo/aiioth ia?o?ooioth iao?eoeo
ae?ooaeueiie NaII, eeai niiauaiea i iaaiciiaeiinoe noi?ie?iaaoue aa.

Oaeno i?ia?aiiu iiiauai a i?eeiaeaiee.

Caeeth/aiea.

Oeaeueth aeaiiie ?aaiou yaeyeanue ?ac?aaioea iaoiaea ?aoaiey caaea/e
oi?ie?iaaiey ia?o?ooiuo iao?eoe ae?ooaeueiie NaII.

Auee ?anniio?aiu iaeioi?ua iaoiaeu iioeiecaoeee e ia eo iniiaa
i?aaeeiaeai iaoiae oi?ie?iaaiey ia?o?ooiie iao?eoeu.

Aeey iaai aue ?ac?aaioai aeai?eoi e iaienaia i?ia?aiia. I?ia?aiia auea
eniuoaia ia eiio?ieueiuo i?eia?ao.

Oae aea aue i?aaeeiaeai iaoiae iieo/aiey iauaai ?aoaiey iinoaaeaiiie
caaea/e.

Nienie eeoa?aoo?u.

Ieo?ioaiia TH. E., Neioac naoae ianniaiai ianeoaeeaaiey.- Na?aoia:
Ecae-ai AoIOe “Eieeaaeae”, 1995 -168 n.

Aaoa?ei A. I., Ai/a?ia I. I., Eiaai ss. A. Aiaeec i/a?aaeae a
au/eneeoaeueiuo naoyo. Oai?ey e iaoiaeu ?an/aoa. – I. Iaoea. Ae. ?aae.
oec.-iao. eeo., 1989 – 336 n.

AEeaeyaneee A. A., AEeeeinean A. O. Iaoiaeu iienea aeiaaeueiiai
yeno?aioia. -I. Iaoea, Ae. ?aae. oec.-iao. eeo., 1991 – 248 n.

Iieye A. O. Aaaaeaiea a iioeiecaoeeth. – I. Iaoea, 1983 – 384 n.

Cae/aiei TH. I. Enneaaeiaaiea iia?aoeee. – Eeaa, Aeua oeiea, 1975, 320
n.

Ieo?ioaiia TH. E., A?aaeia E. O., Oaiaiei E. A., THaeaaaa I. A. Aiaeec
e iioeiecaoeey naoae ianniaiai ianeoaeeaaiey. I?ia?aiiiia iaania/aiea. –
Na?aoia, Ecae-ai “Eieeaaeae”, 1995 – 144 n.

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