Ciencia

PROBLEMA 1.
En el sgte. Diagrama de flechas, determine:
a) Los tiempos optimistas para comenzar y terminar cada actividad.
b) Los tiempos pesimistas para comenzar y terminar cada actividad.
c) El camino crítico.

ACTIVIDAD | DURACIÓN | TIEMPO OPTIMISTA | TIEMPO PESIMISTA | FT | FL | FI | COND. |
CÓDIGO | DESC. | SIMB. | | | | | | | |
i | j | | | tij | t°i | t°j | t*i| t*j | | | | |
5 | 10 | | | 4 | 0 | 4 | 0 | 6 | 2 | 0 | 0 | NC |
5 | 15 | | | 14 | 0 | 14 | 0 | 14 | 0 | 0 | 0 | CRI |
10 | 15 | | | 8 | 4 | 14 | 6 | 14 | 2 | 2 | 0 | NC |
10 | 25 | | | 20 | 4 | 51 | 6 | 51 | 27 | 27 | 25 | NC |
15 | 20 | | | 7 | 14 | 21 | 14 | 21 | 0 | 0 | 0 | CRI |
15 | 25 | | | 16 | 14 | 51 | 14 | 51 | 21 | 21 | 21 | NC |
20 | 25 | | | 30 | 21 |51 | 21 | 51 | 0 | 0 | 0 | CRI |
20 | 30 | | | 12 | 21 | 66 | 21 | 66 | 33 | 33 | 33 | NC |
25 | 30 | | | 15 | 51 | 66 | 51 | 66 | 0 | 0 | 0 | CRI |
30 | 35 | | | 4 | 66 | 70 | 66 | 70 | 0 | 0 | 0 | CRI |

PROBLEMA 2.
Conociendo la duración de las actividades de n proyecto, determine la ruta crítica correspondiente.

Código | Duración |
i | j | |
0 | 1 | 0  |
1 | 2 |  5 |1 | 3 |  10 |
1 | 4 |  3 |
2 | 3 |  5 |
2 | 5 |  14 |
3 | 6 |  6 |
4 | 5 |  4 |
4 | 7 |  11 |
5 | 6 |  7 |
5 | 9 |  13 |
6 | 9 |  9 |
6 | 10 |  1 |
7 | 8 |  6 |
7 | 9 | 6  |
8 | 9 |  4 |
8 | 10 |  6 |
 9 | 10  |  4 |

Solución:

ACTIVIDAD | DURACIÓN | TIEMPO OPTIMISTA | TIEMPO PESIMISTA | FT | FL | FI | COND. |
CÓDIGO | DESC. | SIMB. | | | | | | | |i | j | | | tij | t°i | t°j | t*i | t*j | | | | |
0 | 1 | | TP | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | CRI |
1 | 2 | | | 5 | 0 | 0 | 0 | 5 | 0 | 0 | 0 | CRI |
1 | 3 | | | 10 | 0 | 0 | 0 | 20 | 10 | 0 | 0 | NC |
1 | 4 | | | 3 | 0 | 0 | 0 | 14 | 11 | 0 | 0 | NC |
2 | 3 | | | 5 | 5 | 5 | 5 | 20 | 10 | 0 | 0 | NC |
2 | 5 | | | 14 | 5 | 5 | 5 | 19 | 0 | 0 | 0 | CRI |
3 | 6 || | 6 | 10 | 20 | 20 | 26 | 10 | 10 | 0 | NC |
4 | 5 | | | 4 | 3 | 14 | 14 | 19 | 12 | 12 | 1 | NC |
4 | 7 | | | 11 | 3 | 14 | 14 | 25 | 11 | 0 | -11 | NC |
5 | 6 | | | 7 | 19 | 19 | 19 | 26 | 0 | 0 | 0 | CRI |
5 | 9 | | | 13 | 19 | 19 | 19 | 35 | 3 | 3 | 3 | NC |
6 | 9 | | | 9 | 26 | 26 | 26 | 35 | 0 | 0 | 0 | CRI |
6 | 10 | | | 1 | 26 | 26 | 26 | 39 | 12 | 12 | 12 | NC |7 | 8 | | | 6 | 14 | 25 | 25 | 31 | 11 | 0 | -11 | NC |
7 | 9 | | | 6 | 14 | 25 | 25 | 35 | 15 | 15 | 4 | NC |
8 | 9 | | | 4 | 20 | 31 | 31 | 35 | 11 | 11 | 0 | NC |
8 | 10 | | | 6 | 20 | 31 | 31 | 39 | 13 | 13 | 2 | NC |
9 | 10 | | | 4 | 35 | 35 | 35 | 39 | 0 | 0 | 0 | CRI |

PROBLEMA 3.
Usando los datos de la sgte. Red, calcule la duración del proyecto, los tiemposoptimistas y pesimistas para comenzar y terminar cada actividad, las holguras de actividad, los flotantes totales, los flotantes libres, los flotantes independientes y la ruta crítica.

SOLUCION:
Actividades | Duración (Hr.) | Tiempo Optimista | Tiempo Pesimista | Holgura Act. | FT | FL | FI | Condición |
Código | Descrip. | Símb. | tij | t°i | t°j | t*i | t*j | | | | | |
i | j | | | || | | | | | | | |
0 | 5 | | | 11 | 0 | 11 | 0 | 11 | 0 | 0 | 0 | 0 | C |
0 | 10 | | | 8 | 0 | 20 | 0 | 20 | 12 | 12 | 12 | 12 | NC |
5 | 10 | | | 9 | 11 | 20 | 15 | 20 | 0 | 0 | 0 | -4 | C |
5 | 15 | | | 4 | 11 | 15 | 11 | 19 | 4 | 4 | 0 | 0 | NC |
5 | 25 | | | 15 | 11 | 36 | 15 | 39 | 13 | 13 | 10 | 6 | NC |
10 | 20 | | | 16 | 20 | 36 | 20 | 36 | 0 | 0 | 0 | 0 | C|
10 | 30 | | | 6 | 20 | 44 | 20 | 44 | 18 | 18 | 18 | 18 | NC |
10 | 35 | | | 20 | 20 | 40 | 20 | 46 | 6 | 6 | 0 | 0 | NC |
15 | 20 | | | 17 | 15 | 36 | 19 | 36 | 4 | 4 | 4 | 0 | NC |
20 | 25 | | | 0 | 36 | 36 | 36 | 39 | 3 | 3 | 0 | 0 | NC |
20 | 30 | | | 8 | 36 | 44 | 36 | 44 | 0 | 0 | 0 | 0 | C |
20 | 45 | | | 15 | 36 | 56 | 36 | 56 | 5 | 5 | 5 | 5 | NC |
25 | 40 |...