Page 251 - DCOM303_DMGT504_OPERATION_RESEARCH

Operations Research

Notes Taking all these time estimates into consideration, the expected time of an activity is arrived at.
The average or mean (t ) value of the activity duration is given by,
a
 
 (5)

The variance of the activity time is calculated using the formula,

 
    (6)
 

Probability for Project Duration

The probability of completing the project within the scheduled time (T ) or contracted time may
s
be obtained by using the standard normal deviate where T is the expected time of project
e
completion.

 (7)


Probability of completing the project within the scheduled time is,
P (T< T ) = P ( Z< Z ) (from normal tables) (8)
s 0

Example: An R&D project has a list of tasks to be performed whose time estimates are
given in the Table 12.8, as follows.

Time expected for each activity is calculated using the formula (5):
 
T =
a

   
= = = 6 days for activity A

Similarly, the expected time is calculated for all the activities.
The variance of activity time is calculated using the formula (6).

 
 =  
 

 
=   = 0.444
 
Similarly, variances of all the activities are calculated. Construct a network diagram and calculate
the time earliest, T and time Latest T for all the activities.
E L

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