Network Analysis

• 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)







Learning Curve

Learning is the process of acquiring skill, Knowledge, and ability by an individual. According to learning curve theory the productivity of the worker increases with increase in experience due to learning effect. The learning theory suggests that the best way to master a task is to “learn by doing”. In other words, as people gain experience with a particular job or project they can produce each unit more efficiently than the preceding one.

The speeding up of a job with repeated performance is known as the learning effect or learning curve effect.

The cumulative average time per unit produced is assumed to fall by a constant percentage every time the total output is doubled. So generally learning effect is found in the multiples of 2. If learning curve effect is asked between two even numbers then Learning curve equation is formed ie. Learning curve effect is expressed mathematically as follows:

Learning curve equation =
Y = a(x) -b Where Y = Average time per unit
a = Total time for first unit
x = Cumulative number of units manufactured
b = the learning curve index

Learning curve index (b) = log (1- % decrease)
Log 2

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