Question

In: Operations Management

Consider the following precedence chart: ACTIVITY PRECEDING ACTIVITIES OPTIMISTIC TIME (days) MOST LIKELY TIME (days) PESSIMISTIC...

Consider the following precedence chart:

ACTIVITY PRECEDING ACTIVITIES OPTIMISTIC TIME (days) MOST LIKELY TIME (days) PESSIMISTIC TIME (days)
A - 5 10 15
B - 10 12 14
C - 10 10 10
D B,C 2 4 6
E A 4 8 12
F A 4 8 12
G D,E 10 12 14
I F 4 8 12
J G 2 4 6


The total slack for activity C is __________

a.

0

b.

2

c.

8

d.

4

Solutions

Expert Solution

The expected durations of each activity are presented below :

Task

Optimistic (O)

Most likely ( m)

Pessimistic(P)

Expected duration

A

5

10

15

10.00

B

10

12

14

12.00

C

10

10

10

10.00

D

2

4

6

4.00

E

4

8

12

8.00

F

4

8

12

8.00

G

10

12

14

12.00

I

4

8

12

8.00

J

2

4

6

4.00

Expected duration = ( Optimistic duration + 4 x Most likely duration + Pessimistic duration) / 6

The precedence diagram of activities as follows :

                                    A

B

C

                    F

              E

                             D

                    I

                                                G

                                               J

The possible parallel paths and their expected durations as follows :

A-F-I = 10 + 8 + 8 = 26

A-E-G-J = 10 + 8 + 12 + 4 = 34

B-D-G-J = 12 + 4 + 12 + 4 = 32

C-D-G-J = 10 + 4 + 12 + 4 = 30

Since A-E-G-J has the longest Expected duration, it forms the critical path.

Slack for activities C, D

= Duration A-E-G-J – Duration C-D-G-J

= 34 – 30 DAYS

= 4 days

TOTAL SLACK FOR ACTIVITY C = 4 DAYS


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