Приложение 1 Расчёт временных параметров событий проекта

1. Ранний срок свершения событий определим по формуле:

t_p ( j ) = max {t_p( i ) + t ( i, j )}

Этап I

Примем, что ранний срок наступления исходного (1-го) события равен нулю, т.е. t_p ( 1 ) = 0. Тогда t_p ( 2 ) = t_p( 1 ) + t ( 1, 2 ) = 0 + 3 = 3;

t_p ( 3 ) = t_p( 1 ) + t ( 1, 3 ) = 0 + 4 = 4;

t_p ( 4 ) = t_p( 3 ) + t ( 3, 4 ) = 4 + 8 = 12;

t_p ( 5 ) = t_p( 1 ) + t ( 1, 5 ) = 0 + 2 = 2;

Т.к. к событию 6 ведут два пути: от события 2 и от события 4, получим:

t_p ( 6 ) = max = max {3 + 7; 12 + 9} = 21;

t_p ( 7 ) = max = max {2 + 15; 21 + 14} = 35;

t_p ( 8 ) = t_p( 7 ) + t ( 7, 8 ) = 35 + 12 = 47;

t_p ( 9 ) = t_p( 8 ) + t ( 8, 9 ) = 47 + 2 = 49;

t_p ( 10 ) = t_p( 8 ) + t ( 8, 10 ) = 47 + 3 = 50;

t_p ( 11 ) = max = max {49 + 6; 50 + 9} = 59.

Этап II

t_p ( 1 ) = 59;

t_p ( 2 ) = t_p( 1 ) + t ( 1, 2 ) = 59 + 5 = 64;

t_p ( 3 ) = max = max {59 + 4; 64 + 9} = 73;

t_p ( 4 ) = max = max {59 + 7; 73 + 11} = 84;

t_p ( 5 ) = t_p( 4 ) + t ( 4, 5 ) = 84 + 2 = 86;

t_p ( 6 ) = max = max {73 + 8; 86 + 11} = 97;

t_p ( 7 ) = t_p( 6 ) + t ( 6, 7 ) = 97 + 2 = 99;

t_p ( 8 ) = t_p( 3 ) + t ( 3, 8 ) = 73 + 5 = 78;

t_p ( 9 ) = max = max {99 + 9; 78 + 5} = 108.

Этап III

t_p ( 1 ) = 59;

t_p ( 2 ) = t_p( 1 ) + t ( 1, 2 ) = 59 + 4 = 63;

t_p ( 3 ) = t_p( 2 ) + t ( 2, 3 ) = 63 + 4 = 67;

t_p ( 4 ) = max = max {59 + 12; 67 + 5} = 72;

t_p ( 5 ) = max = max {59 + 3; 63 + 15} = 78;

t_p ( 6 ) = t_p( 3 ) + t ( 3, 6 ) = 67 + 3 = 70;

t_p ( 7 ) = max = max {67 + 6; 72 + 3} = 75;

t_p ( 8 )

Этап IV

t_p ( 1 ) = 108;

t_p ( 2 ) = t_p( 1 ) + t ( 1, 2 ) = 108 + 3 = 111;

t_p ( 3 ) = t_p( 1 ) + t ( 1, 3 ) = 108 + 10 = 118;

t_p ( 4 ) = max = max {111 + 2; 118 + 8} = 126;

t_p ( 5 ) = t_p( 4 ) + t ( 4, 5 ) = 126 + 9 = 135;

t_p ( 6 ) = t_p( 4 ) + t ( 4, 6 ) = 126 + 7 = 133;

t_p ( 7 ) = max = max {135 + 3; 133 + 11} = 144;

t_p ( 8 ) = max = max {133 + 15; 144 + 4} = 148;

t_p ( 9 ) = max = max {144 + 9; 148 + 5} = 153.

2. Поздний срок наступления событий Этап IV

t_n( 9 ) = Т _{кр. Проекта} = 153;

t_n( 8 ) = min{t_n(9) – t_n(8,9)} = 153 – 5 = 148;

t_n ( 7 ) = min = min {148 – 4; 153 – 9} = 144;

t_n ( 6 ) = min = min {148 – 15; 144 – 11} = 133;

t_n( 5 ) = min{t_n(7) – t_n(5,7)} = 144 – 3 = 141;

t_n ( 4 ) = min = min {133 – 7; 141 – 9} = 126;

t_n( 3 ) = min{t_n(4) – t_n(3,4)} = 126 – 8 = 118;

t_n( 2 ) = min{t_n(4) – t_n(2,4)} = 126 – 2 = 124;

t_n ( 1 ) = min = min {118 – 10; 124 – 3} = 108.

Этап III

t_n( 8 ) = 108;

t_n( 7 ) = min{t_n(8) – t_n(7,8)} = 108 – 5 = 103;

t_n( 6 ) = min{t_n(8) – t_n(6,8)} = 108 – 4 = 104;

t_n( 5 ) = min{t_n(8) – t_n(5,8)} = 108 – 7 = 101;

t_n( 4 ) = min{t_n(7) – t_n(4,7)} = 103 – 3 = 100;

t_n ( 3 )

t_n ( 2 ) = min = min {101 – 15; 95 – 4} = 86;

t_n ( 1 )

Этап II

t_n( 9 ) = 108;

t_n( 8 ) = min{t_n(9) – t_n(8,9)} = 108 – 5 = 103;

t_n( 7 ) = min{t_n(9) – t_n(7,9)} = 108 – 9 = 99;

t_n( 6 ) = min{t_n(7) – t_n(6,7)} = 99 – 2 = 97;

t_n( 5 ) = min{t_n(6) – t_n(5,6)} = 97 – 11 = 86;

t_n( 4 ) = min{t_n(5) – t_n(4,5)} = 86 – 2 = 84;

t_n ( 3 )

t_n( 2 ) = min{t_n(3) – t_n(2,3)} = 73 – 9 = 64;

t_n ( 1 )

Этап I

t_n(11) = 59

t_n(10) = min{t_n(11) – t_n(10;11)} = 59 – 9 = 50;

t_n( 9 ) = min{t_n(11) – t_n(9,11)} = 59 – 6 = 53;

t_n ( 8 ) = min = min {50 – 3; 53 – 2} = 47;

t_n( 7 ) = min{t_n(8) – t_n(7,8)} = 47 – 12 = 35;

t_n( 6 ) = min{t_n(7) – t_n(6,7)} = 35 – 14 = 21;

t_n( 5 ) = min{t_n(7) – t_n(5,7)} = 35 – 15 = 20;

t_n( 4 ) = min{t_n(6) – t_n(4,6)} = 21 – 9 = 12;

t_n( 3 ) = min{t_n(4) – t_n(3,4)} = 12 – 8 = 4;

t_n( 2 ) = min{t_n(6) – t_n(2,6)} = 21 – 7 = 14;

t_n ( 1 )