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Tuesday 12 April 2011

Network Analysis

CPM
• Total float = LS – ES (or) LF – EF

• Free float = Total float – Head event slack

• Independent float = Free float – Tail event slack

• In the diagram Es = Lf in the critical path

• Critical path is the longest duration

• To find the minimum time associated cost (i.e. Additional cost incurred per unit of time saved) following formula is used :-
Crash cost per day (or) Activity cost supply
= Crash cost – Normal cost
Normal time – Crash time

• Interfacing float = It is the part of the total float which causes reduction in the float of the succession activities. In other words it is the portion of activity float which cannot be continued without affecting adversely the float of the subsequent activity or activities.

• Steps in proceeding the problem : -

2. First find and fill the ES and LF column from the diagram.

3. Then find LS and EF as follows :-
Ls = Lf – Duration
Ef = Es + Duration

4. Find total float

5. Find free float. Wherever total float column has zero free float column is also taken has zero and remaining elements is filled as said above

6. Find Independent float. Wherever free float column has zero Independent float column is also taken has zero and remaining elements is filled as said above



Notes: -
1. ES = Earliest Start. Indicates earliest time that the given activity can be scheduled
2. EF = Earliest Finish. Time by which the activity can be completed at the earliest.

3. LF = Latest Finish. Latest allowable occurrence time of the head event of the activity.

4. LS = Latest Start.

5. Total duration of the critical path is the maximum time/amount consumed for the activity. This should be crashed with respect to crashing days and crashing cost. This crashing should not change the critical path.

PERT : -

• Expected (or) Average time is found by assigning weights as follows : -
1 for optimistic
4 for Most likely
1 for pessimistic
Average time = 1 optimistic + 4 most likely + 1 pessimistic
6
• Standard Deviation = (Pessimistic time – Optimistic time)
6
• Variance = (Standard Deviation)2

• Probability of completing the project in N days
= Required time(N) (-) Expected time (critical path duration)
Standard Deviation
[Nothing but Z = (X - Mean) / Standard deviation]
= Y (say)
= Find Z(y)
= Probability %
- If required time > Expected time then = 0.5 + Z(Y)
- If required time < Expected time then = 0.5 – Z(Y)

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