Модели распределения ресурсов в иерархических системах управления качеством речной воды

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  • . 26

    64

    519.86 .6.3.1.0

    . .1, . .2 ( , --)

    . , . - -, . - : , . . - , . : , - , - .

    1 , (gorbaneva@mail.ru) 2 , - , (ougoln@mail.ru)

    mailto:(gorbaneva@mail.ru)mailto:(ougoln@mail.ru)

  • -

    65

    1.

    - . , - . - . - -, : , ; , , - ; , - , - , , ( , ..).

    - [7]. - , , , , .

    2.

    , -, , - , , - . ( , - ) .

    -, - (), -

  • . 26

    66

    . , - .

    - , - . - . , , , - .

    (, ), - -, , , - . - . , ( , - ) , - .

    , : : o ; o ;

    N - , ;

    (). ,

    . -, , - , - .

    .

  • -

    67

    1) , - . , - , , , . , , , , - . - , . :

    ) ; ) ; )

    , .

    - , -.

    2) - , - . , , - . :

    ) , - , , , ;

  • . 26

    68

    ) , . -, , , ;

    ) , - , : , , .

    3) . - . : -, , , , . , -, . -, , , , , .

    4) , .

    : - , - . 3 - , 4 .

  • -

    69

    3. .

    3.1. -

    [12, 13, 18], n . - R, . , , , , - , . - - [16, 17]. , - J0 Ji, i = 1, , n . R = 1.

    , - , , , - .

    , , -, . - , , .. , .

    , -:

    :

    (1) max)()()(1111

    0 ++

    =

    ===

    n

    iiii

    n

    iiii

    n

    iii brbrugbrHJ

    (2) 1)(0 ii bq ,

  • . 26

    70

    (3) 1)(0 ii br ,

    (4) 1)(1

    =

    n

    iii br .

    : (5) ( )( ) ( ) max1 += iiiiiiii rugrubhJ (6) 1)( iii ubq , (7) 1+ ii ub , (8) 0 1, 1, ..., ib i n = , bi , i- - ( ri); ri(bi) , - i- ( R); ui - , i- ; qi(bi) ui, ( ri); gi(uiri) i- ; hi((1 ui bi)ri) i-

    ; ( )

    =

    n

    iii brH

    11 -

    . gi(x), hi(x) H(x) - .

    (1)-(4) (5)-(8) 2- - [5, 6]. - ri qi. : ui, , , bi, . . [3, 4].

    , :

    1) ri = ri(bi) ; 2) qi = qi(bi) -

    ,

  • -

    71

    : .

    : 1) i-

    qi(bi): 0)( iii qbq ( -

    ); )1()( 0 iiii bqbq = ( , qi0

    , - ); iiii bqbq )1(1)( 0= ( , qi0 -

    , 100%, );

    2) , i- , ri(bi); 0)( iii rbr ( -

    );

    nbkrbr iiii

    )1()( 0

    += ( , ri0

    , , - );

    nbbr iii =)( ( , -

    , , )

    [2]: (9) 1=iu , (10) 0=ib , (11) qi = 1,

  • . 26

    72

    (12) ( )

    =

    +=

    11

    1

    1*

    )(

    )(

    xHxg

    xgr n

    ii

    ii

    ,

    (13) ( )

    =

    +=

    11

    1

    1*

    0

    )(

    )(

    xHxg

    xHr n

    ii

    ,

    (14)

    +

    =

    =

    )1()1(

    )1()(1

    1

    11

    1

    11

    *

    Hg

    grJn

    ii

    iii

    ,

    (15)

    =

    +=

    1

    11

    11

    1*

    0 )1()1()( HgrJn

    ii

    .

    - :

    (16) ( )( ) ( )( )

    +=

    11

    1

    2 xhxgxg

    uii

    ii ,

    (17) bi = 1/2. qi0 = 1,

    (18) n

    ri 21

    = .

    - , , , - .

    - :

    (19) )1(22

    1 0

    =knrb ii ,

    (20) ( )( ) ( )

    ++

    =

    )1(221 0

    11

    1

    knr

    xhxgxg

    u iii

    ii

    ,

  • -

    73

    x (0; 1], , bi 1/2.

    , qi -, ri .

    , , , , . . . - . ( , - ) , - .

    3.2. . N = {0, 1, 2, , n}

    , {0} . , . . K N, {i} N.

    - :

    1) -;

    2) -;

    3) - .

    , ( , -) . [1], ..

    =

    KiK ivKv )()( , K

    .

  • . 26

    74

    -

    (21) ( )

    =

    +

    +=

    1

    11

    1

    11

    11

    )1()1()1(2)( HhgNvn

    iii

    ,

    - [1].

    :

    (22) ( )

    ( )

    11 1 1

    01

    11 1

    1

    11 1 1 1

    2| | 1

    1 (1) 2 (1) (1)1

    1 (1) (1)2( 1)

    ( ) (1) (1) 2 (1) (1) ,

    n

    i ii

    n

    ii

    n

    i i is K i K i K

    K s

    H g hn

    n H hn

    s H g g h

    =

    =

    = =

    = + + +

    + + +

    + + + +

    (23) ( )

    ( )

    1

    1 1

    1

    1

    1 1 1 1

    2| | 1

    1

    1 1 1 1

    \{ } \{ }

    (1)12

    (1) (1)

    ( ) (1) (1) 2 (1) (1)

    (1) (1) 2 (1) (1) .

    ll n

    ii

    n

    i i is K i K i K

    K sl K

    i i ii K l i K l

    g

    H g

    s H g g h

    H g g h

    =

    = =

    = + +

    + + + +

    + + +

    ,

    :

    (24) ( )11

    11 11 1

    011 1

    1

    (1) (1)(1) 2 (1) (1) ,

    2 (1) (1)

    n

    ini

    i i ni

    ii

    g Hx H g h

    g H

    =

    =

    =

    +

    = + + +

    (25) ( )11

    1 1 1

    1 11

    1

    (1)(1) 2 (1) (1) .

    2 (1) (1)

    nl

    l i ini

    ii

    gx H g h

    g H

    =

    =

    = + + +

  • -

    75

    4.

    - , . - , .

    - . - , , . - , - . , - - .

    - ( ). , , , -. - , . - .

    [14, 15]: 1:

    ( pi - 1~)1(0 wpw ii ), (26) )(0 ycJ a= (27)

    ipiiipii pwspCwy max)1()1()(

    )0( =

    (28) 10 ip -.

  • . 26

    76

    2: , ( - pi 21 ~)1(~ wpww ii ),

    (29) ( )( )Kch

    n

    jiiicha wpwsKycJ max~1)(

    110 +=

    =

    (30) ( )ip

    iiichipii wpwsKwspCwy max~)1(~)1()( 11)1( =

    0 pi 1 , 0 Kch Kchmax .

    . . , .

    3: ( pi - 2~)1( wpw ii ),

    (31) ( ) ( )( )cach KK

    n

    jiiica

    n

    jicha wpwsKwwsKycJ ,1

    21

    120 max~1~~)( ++= ==

    (32) ( )( )

    (2)1 2 1

    2

    ( ) (1 )

    (1 ) maxi

    i i p i ch i

    ca i i i p

    y w C p s w K s w w

    K s w p w

    =

    % % %

    %

    10 ip , max0 chch KK , max0 caca KK

    . . , , , .

    : - (); J0 ; yi(0), yi(1), yi(2) 1, 2 3; a(y) ; p(p) ; si (); wi ; wi(1 pi) ; 1~w , 2~w , w ( -).

    : - a(y) : ycyca 1)( = ,

  • -

    77

    =

    =n

    iii pwy

    1)1( ,

    p(p) : p

    Dppcp =

    1)( .

    (26)-(28),

    (26)

    21

    1

    22

    1

    2

    max 1 , 0 , *max ,1 ,(1 )

    1 , *max ,1 ,(1 ) (1 ) (1 )

    1 , .(1 )

    ii

    i

    ii i

    i

    i

    ww Dsw w

    wD D Dp ss w

    Ds

    %

    %

    %

    (29)-(30), , -

    (27)

    22

    2

    22

    2

    2

    max 1 , 0 , *max ,1 ,

    1 , *max ,1 ,

    1 , .

    ich

    i i

    ii ch

    ch i i i

    chi

    ww DKw s w

    wD D Dp KK s s w s

    DKs

    %

    %

    %

    Kch . Kch, .

    (31)-(32), ,

    (28)

    2 2

    2 2

    0, ,

    1 , ,max ,

    1 , .max ,

    cai

    i caca i i

    ii

    ca

    ii

    DKs

    D D Dp KK s s ws

    wDK

    wsw

    %

    %

  • . 26

    78

    . : maxchch KK = . - , , - pi 2~)1( wpw ii , -, , . Kca .

    5.

    - , - , . - . - , . . - .

    1. . ., . ., . . -. --: , 2003. 208 .

    2. . . // . , 26.01.2006, 812006.

    3. . ., . . - - -. .: , 1992. 132 .

  • -

    79

    4. . . -. . . . .: , 1981. 488 .

    5. . . - . .: , 1999. 150 .

    6. . . -. .: , 2003. 312 .

    7. . ., . . - // - . . 2. / . . . .: , 2004. . 46-65.

    8. . . - // . 2002. 3. .133-140.

    9. . . . .: , 1996.

    10. . . // - . . 2 // . . .. .: , 2004. . 101-125.

    11. . . - - - // . . 2005. 4.

    12. . . - - // . . 2002. 1.

    13. . . - . .: , 1999. 132 .

    14. . . // . . 2. / . . . : , 2004. . 136-158.

  • . 26

    80

    15. . ., . . // -. 2005. . 32, 4. .504-511.

    16. BARDHAN P. Corruption and Development: a Review of Issues // J. Political Economy. 1996. Vol. 31.

    17. CHANDER P., WILDE L. Corruption in tax administration / Journal of Public Economic