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UU ATECTBO TT UU Mcepco opaoa Poccco eepa TAMOBC OCAPCTBEHH TEXHEC HBEPCTET MATEMATA B OHOME Meoece yaa o oe yaoo aa cyeo eoo oee ceaoce 060400, 060500, 060800 Tao aeco TT 2001 . B673-5 epeo Peaoo-aec coeo yepcea Peee:

oop o-aeaecx ay, poeccop T . epaa C. M. a, aa execx ay, oe.. Cepepeuo Cocae C. M. Apxuneo Maeaa ooe. Meo. ya. / Coc.: C. M. Apxeo. Tao: -o Ta. oc. ex. y-a, 20 c.

a eoece yaa o oe yaoo aa cyeo eoo oee ceaoce 060400, 060500, 060800.

. B673-5 Taoc ocyapce exec yepce (TT), 2001 BBEEHE Bc c pae pox ooe xocey eeoc ae cpae pxoc ec ycox apacae eopeeeoc cya eoc ooeco cpee [1]. o oaae, o oae ecoc oye oaeoo oeoo peyaa, ceoaeo, opacae pc, oacoc eya, epeex oep ..

B eeoc pep oo e eco p a pco: pooce, oepec aco.

pooce pc oycoe pooco poy (oapo, ycy), ocyecee x o pooceo eeoc. ce cee poocex pco a pep apoa pooceo eeoc pep eecoopao cooae coxacecx ooo-aeaecx oee, acoc peee coxacecx oee oa oooo aa pooca a pep, ooax c pc eoe oooo aa.

OHOMO-MATEMATECE MOE OPMPOBAH OOBO POBOCTBEHHO POPAMM POMEHHOO PEPT eeppoaa oe cocae oooo aa pooca a pepx c cpe o poocex poecco ocaoo oe e oe acaa cey opao [2].

Moe I Ha ae eecx e X1, X2, , X, p oopx pepaa aeaeca y ocae acya:

n c c = X max j j j=p ycox:

n c X Fi ; i = 1,m; (1) tij j j=, 1,2...,o ; (2) = = V X V, j = 1, 2, , n, (3) j j j e n co o poy, oope peoaaec oo a ao pep c apyeo oy; t apa pya cao-ac., pxoec a ey poy ij j-o a p ooe ee a cex oepax, oope oc a oopyoa i- py (i = 1,m; j = 1,n); (p cooa x oee aae xoceo eeoc aece x apa yy cooac aece apa aapyeo epoe pee; p cooa e x cocae ao aece x apa yy cya opae aoe apa); m co py aoaeeoo exooecoo oopyoa ocox exax pep, oope eecoopao ya peaeo aae; Fi ooo (pace) ece o paoeo pee ceo oopyoa i- py, ce c yeo aox oeo oe op pao pao ce pyoeoc poy a ce opexepop, oope yy pooc apyeo oy. e eoxoo oc opoee.

p pacee ae x e peyec oa ya eoxoe peep pee pao oopyoa, acpoae ocoe pooca oo poy apyeo oy.

p pacee x e x cooa oex peoaaec ae, o ce oopyoae, yacyee oe, apyeo epoe ye ooc oeceeo pyo aepa pecypca. B poo e cyae cooecye e Fi o cooeceo yee; ec e ocox exax pep apyeo oy yy cyapoac ooe peeo-aye yac pooca, o aece oeo py oopyoa oe oa yacoa ooa peeo-ay yaco eo, a e oee py oopyoa, paeae ).

t apa poocex pecypco -o a, cae c ooee ooo j e j-o a ocox exax pep;

0 co cex opaex pecypco pooca, yaex o aae;

R epx paa pacxoo -o a pecypca a pooco ce poy a ao pep apyeo oy;

c coocaa ooa ea ooo e j-o a;

j Vj,V cooeceo epx pa pooca e j-o a j apyeo oy a ao pep;

Xj oe pooca e j-o a a ao pep apyeo oy (epeea ea).

peoo, aee, o a aaa ee xo oo oycoe peee ( poo e cyae eoxoo ye ye eoope e Fi R, a o j p ox aex a aaa ye ea oyce pee).

Oe, o ccea eeppoax oaox oee apoa oaae eocao. A eo: c x oo oo oppoa oo eaee aoe pee c epooc oe x aae cpo o y. To ec pc eoe x ye eca o -a cyax ooe aecx pacxoo poocex pecypco o x opax ae cy pyx cyax oye.



pee aoo poa aa acoee pe ec ee oecee eo ( acoc coxacece oopepae oopepae aeaece oe) [2].

p ocpoe eaao oe I oaaoc. o ce cxoe e c ecya ocoep ea. Oao a pae o ae eca peo. ooy, aee oo, o aece apa paoeo pee cao-ac, yy cya ea, oope oy aeo oac o x opax c ae ( x aaax oo x cpex ae). To ec oaae, o tij c cya ea p cex aex eco i, j.

c c c yc ij cepc cyao e tij [3]. B cy oo, o tij c cya, o p peaa oe oaoo aa (oyeoo c oo peeo e oe I) oe opeoac oo o paoeo pee a ao i pye oopyoa, e ec, xapaepye cooecye eo Fi.

B ax cyax pec o cepxypoe pao, o e peepoe oopyoae (oeceeoe pyo, aepa aco pecypca), o pe pye epop, o a coepeeo e oc.

oppoa e oo oaoo, o ocaoo aeoo aa pooca oo cooa coxacece oe [2, 4]. B acoc coxaceca oe aa apoa pooca, pecaea e coxaceco oe co cea yco ye ao:

Moe II Ha X1, X2, Xn, p oopx c c = 1 X1 + c X ++ c X max 2 2 n n p ycox:

n c P( x Fi ) Pi, i = 1,m ; (1) tij j j=n x R, = 1, 2, , 0; (2) tj j j=Vj Xj Vj, j = 1,n, (3) e Pi epooc oe yco (I) p ao i. Be Pi o aa. ae x ae ceo yy paea epay (0,8; 0,95), oop cooecye paec ocoep co.

coe (I) oaae, o p o i epooc oe epaeca c X Fi oa a ee e Pi. To ec oe II oo ycoe (I) tij j j aao epooco ope. Ocae e epaeca pecae oo eco ope. y oe II co cea yco oo peopaoa ceyy paoey e eeppoay oe III.

Pee oe III yy oopeeo oyc pee oe II.

Moe III Ha ae e X1, X2, Xn, p oopx pepaa y c c c c = 1 X1+ X2 ++ Xn max 2 n p ycox:

n n c 2 Fi - 2-1(Pi ) X ;i = 1, m ; (1) ij t X j ij j j=1 j=n X R, = 1,0 ; (2) tj j j=Vj X V, j = 1,n, (3) j j x c c -te t cpeee aee cyao e tij (i =1,m; j = 1,n ); (X) = ij e dt eoppoaa y aaca [3]; -1(Pi) opaa o o y.

c p pee ax oee, a pao, aece opax ae tij yy cooac ao-o epe x cpee ae. Toa co, o e oe aece apa paoeo pee cao-ac. yy p oe oooo aa pep peocxo co cpee ae, e oeo paepa opeyec ooo o paoeo pee a ao i- pye oopyoa, oop oe aeo peocxo cooecyy ey Fi.

Ceoaeo, o apaee ao peycope eoxoo e peep oa paoeo pee a ao pye oopyoa pe pyoe aoe-o epope o a aae cpo e ye oe ae ooe e ye oe oa.

B e ocao oe III ae peep oa paoeo pee cooecyx py oopyoa e o peycapac c oo ee pay ac epaeca (I) ceyeo pae 2 2 2 2 2 2-1(Pi ) i1X1 + i2 X +... + in X ; i = 1,m.

2 n C oo pee o oe III oo coppoa ay poocey popay pep, oopa oece oee yco (I) c aa epooc. Bepooc e oe ce py yco (I) oopeeo opeeec poeee: P1P2Pm.

aee, a eco, eoxo peep o paoeo pee a o i- c pye oopyoa ye opeec ooe e tij o coeo cpeeo c ae tij oo oy copoy. ooy aece aeoo pao ac yco (I) ao eco pae 2 2 2 2 2 -1(Pi ) 2 i1X1 + i2 X +... + in X, 2 n pyoe paee n 2 2 2 2-1(Pi ) ( X ) / 2 = -1(Pi ) X.

ij j ij j j j=Cyeo eoeoo ycoe (I) oe III eecoopao aca a n n c 2 Fi - -1(Pi ) X, i = 1,m.

ij t X j ij j j=1 j=y aaca (x) p pax aex coeo apyea x pae ceye ae [3]:

(0,1) = 0,11; (0,8) = 0,74; (1) = 0,84; (2) = 0,99; (3) = 1.

oo, aee, o ce Pi = 1, i =1,m. Toa -1(Pi) = 3 p cex i.

Ta opao, ycoe (I) ye e opyy n c 2 Fi 2 2 2 2 2 n ij - 3 i1X1 + i2 X +... + in X ; i = 1,m.

t X j j=eco ae, o oc ceye yco:

n c 2 2 Fi ij - 3 V Fi - 3 X ; i = 1,m.

j t X j ij ij j j=1 j j C yeo eoeoo oe III oo peopaoa paoey (p opeeex ycox) e oe IV.

Moe IV Ha ae e X1, X2, , Xn, p oopx c c c c = 1 X1 + X2 + + Xn max 2 n p ycox:

n c 2 2 2 2 Fi - 3 i1V + i2V +... + inV ; i = 1,m ; (1) ij 1 2 n t X j j=n X R, = 1,2,...,0 ; (2) tj j j=V X V, j =1,n ; (3) j j j peae. C oo oee III IV oo pe ceyeo a aa apoa pooca a pepx. A eo: yc a-o cocoo coppoa ao-o apa ooo pooceo popa pep, 0 0 oeae oe paccapaeo apyeo oy. yc X1, X,..., X 2 n oe yca e oo apaa pooceo popa. Toa oe III ( IV) oo ye yceo cooa oe aeoc oe oo apaa oooo aa pooca. B o cyae peyec oo X = X ( j =1,n) j j oe III ( oe IV) poep ooc yco cooecye oe p aax cex aex e Pi (i = 1,m).





oo eep, o ce Pi = 0,97 (i = 1, 2, , m).

Toa ycoe (I) oe III ye a n c 2 2 2 Fi -1,5 i1X1 +... + in X ; i = 1,m.

ij t X j n j=oo, eep, o ce Pi = 0,74 (i = 1, 2, , m).

Toa ycoe (I) oe III ye a n c 2 2 2 Fi - 0,8 i1X +... + in X ; i = 1,m.

ij t X j j n j=Beocae oe III IV c oopepa. Oao peee aa apoa o ooy aoy-o ae oe aoy oaae (pep) aco oe oca coe pyoe ooee, a a p o ocae aoe oaae oy aeo yxyc. ooy ax cyax eecoopao ecoo apao aox pee, a oopx ec ay o ooy aoy-o pep. Tae apa aox pee aa cyoa o cooecy pep.

ae e eoxoo ye coppoa oo ayee opoccoe peee, oopo ocaoc aeee oooe yxyee cyoax ae cex pepe peaeo aa apoa [4 8].

Moe III oopepao ope oo peca cey opao (oe A).

Moe A Ha X1, X2, , Xn, p oopx ceye pepae y:

c c 1) c = 1 X1 + c X +... + X max;

2 2 n n 2) = 1 X1 + X +... + X max;

2 2 n n 3) = 1X1 + 2 X +... + n X min.

2 n oca cox ayx opoccx ae p ycox:

n c 2 2 2 Fi - -1(Pi ) i1X1 +... + in X ; i = 1,m ; (1) ij t X j n j=n X R, = 1,0 ; (2) tj j j=V X V, j =1,n ; (3) j j j e pa ae ooa ea e j-o a; j apa eoopoo eca j eoo pecypca a ey e j-o a.

CEHH PMEP yc cxoe ae pepa pa ceye ae: n = 3; m = 2; 0 = 2;

c c c t11 = 2;t12 = 3;t13 = 1;

c Be t :

ij c c c t 21 = 22 = 23 = 4;t 1;t 3.

t11 = 5;t12 = 4;t13 = 3;

Be tj :

t = 2;t22 = 4;t23 = 5.

Be Fi: F1= 41; F2= 49;

2 2 11 = 0,1;12 = 0,2;13 = 0,15;

Be ij :

2 = 0,05;2 = 0,15;2 = 0,15;

21 22 Be R : R1 = 60; R2 = 55;

Be Vj: V1 = 1; V2 = 0; V3 = 1;

Be V : V1 = 10;V2 = 10;V3 = 10;

j c Be c : 1 = 10; c = 15; c = 5;

j 2 Be : 1 = 15; = 18;3 = 6;

j Be j: 1 = 50; 2 = 20; 3 = 15.

aee, c cxo ea ocpo coy oe a oe A. Oa ye e cey .

Ha ae e X1, X2, X3, p oopx ceye pepae y:

c = 10X1 + 15X2 + 5X3 max;

= 15X1 + 18X2 + 6X3 max;

= 50X1 + 20X2 + 15X3 min oca cox ayx opoccx ae p ycox:

2 2 2X1 + 3X + X 41 - 3 0,1X1 + 0,2X + 0,15X ;

2 3 2 2 2 4X1 + X + 3X 49 - 3 0,05X1 + 0,15X + 0,15X3 ;

2 3 5X1 + 4X2 +3X3 60;

2X1 + 4X2 +5X3 55;

1 X1 10; 0 X 10; 1 X 10.

2 coe (I) oo pepa acao oo cya, oa ce Pi =1 oa e ce Pi.

=0,74, o ycoe (I) ye e :

2 2 2X1 + 3X + X 41 - 0,8 0,1X1 + 0,2X + 0,15X3 ;

2 3 2 2 4X1 + X + 3X 49 - 0,8 0,05X1 + 0,15X + 0,15X.

2 3 2 yc, aee, eec ecoo apao aox pee o ooe cex pex o e apyeo oy:

1) X1 = 5; X2 = 5; X3 = 5;

2) X1 = 5; X2 = 0; X3 = 2;

3) X1 = 2; X2 = 10; X3 = 1;

4) X1 = 3; X2 = 3; X3 = 3.

Bo, aee, ceyee.

1) poep oycoc x pee p aax aex epooce Pi(i =1,2):

a) cya oa ce Pi = 1 (i =1,2);

) cya oa ce Pi = 0,97 (i = 1,2);

) cya oa ce Pi = 0,74 (i =1,2).

B epo cyae ycoe (1) ye e :

2 2 2X1 + 3X + X 41 - 3 0,1X1 + 0,2X + 0,15X3 ;

2 3 2 2 4X1 + X + 3X 49 - 3 0,05X1 + 0,15X + 0,15X3.

2 3 poepa oycoc y ccey epaec cex epex apao aox pee:

I-o apaa ee:

2 5 + 3 5 + 5 41- 3 + 0,2 25 + 0,15 25 = 31;

30 < 31 (oc).

4 5 + 5 + 3 5 49 - 3 0,05 25 + 0,15 25 + 0,15 25 = 40,1 ;

40 < 40,1 (oc).

Ceoaeo, o apa aa ec oyc I-o yco oe c epooc oe eo P = 1.

2-o apaa aa ee:

2 5 + 0 + 2 41 - 3 0,1 25 + 0,15 4 = 35,7;

12< 35,7 (oc).

4 5 + 0 + 3 2 49 - 3 0,05 25 + 0,15 4 = 44,9;

26< 44,9 (oc).

Bopo apa aa oe ec oyc I-o yco oe c epooc oe oo yco P = 1.

3-o apaa aa ee 2 2 + 310 + 1 41 - 3 0,1 4 + 0,2 100 + 0,15 = 27,4;

35 27,4 (e oc).

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