Hi Friends,

For the following activieis, We need to

Find the critical path

Draw the network diagram

Find Total, Free and Independent float?         

Activity	1-2	1-3	1-4	2-5	3-6	3-7	4-6	5-8	6-9	7-8	8-9
Duration (Months)	2	2	1	4	8	5	3	1	5	4	3

 

 Below is my working.  But Network diagram is not visible properly even after copying from Word.   From the above table, it can be easily drawn.    I face hurdle while calculating the FREE Float and Total Float of each activity.  Guide me to get them done ASAP.

 

1.       Let’s draw the network diagram

2.       Find all the paths in the diagram. A path is any string of activities goes from the start of the project to the end.  From the diagram and the given information in the problem definition, assuming that the Activity 1 is a starting point and Activity 9 is the ending point.

A6

A4

A9

A5

A2

A3

A7

A8

A1

                                                                                       3

 

                               1

                                                                                         8                                                                          5

                                       2                                              5

                                                                                                                                   4                                       3

                                       2                                                                                                  1

                                                                                     4

 

 

Paths:

A1 à A4 à A6 à A9

A1 à A3 à A7 à A8 à A9

A1 à A3 à A6 à A9

A1 à A2 à A5 à A8 à A9

 

3.       Find the duration of each path by adding up the durations of each of the activities on the path.

A1 à A4 à A6 à A9                      è           1 + 3 + 5 = 9

A1 à A3 à A7 à A8 à A9         è           2 + 5 + 4 + 3 = 14

A1 à A3 à A6 à A9                      è           2 + 8 + 5 = 15                      ç Critical Path

A1 à A2 à A5 à A8 à A9         è           2 + 4 + 1 + 3 = 10

 

The critical path is the one with the longest duration.

 

Finding the Float for each activity

The float for any activity is the amount of time that it can slip before it causes your project to be delayed. You might also see the word “slack” – it’s the same thing.

 

1.       Write down all the paths in the Network diagram.

There are 4 possible paths in the network diagram.

A1 à A4 à A6 à A9

A1 à A3 à A7 à A8 à A9

A1 à A3 à A6 à A9

A1 à A2 à A5 à A8 à A9

2.       Float for each activity in the critical path is ZERO

3.       Find the next longest path. Subtract its duration from the duration of the critical path, and that’s the float for each activity on it.

Next longest path is A1 à A3 à A7 à A8 à A9                è           2 + 5 + 4 + 3 = 14

Duration of this path is 14

Duration of the critical path is 15

So, the float is 15 – 14 = 1

Float for the activity A3 remains same as ZERO as it is already found as per the critical path. It won’t change.

Float for the activities A7 and A8 are 1 and 1 respectively.

 

          4.       Do the same for next longest path in the network diagram.

Next longest path is A1 à A2 à A5 à A8 à A9                è           2 + 4 + 1 + 3 = 10

Duration of this path is 10

Duration of the critical path is 15

So, the float is 5

Float for Activities A8 and A9 are already found in the previous steps.

Float for Activities A2 and A5 are 5 and 5 respectively.

 

5.       Do the same for next longest path in the network diagram.

Next longest path is A1 à A4 à A6 à A9                            è           1 + 3 + 5 = 9

Duration of this path is 9

Duration of the critical path is 15

So, the float is 6

Float for Activities A6 and A9 are already found in the previous steps.

Float for Activity A4 is 6.