SPM-UNIT III

RISK MANAGEMENT

Prof. Kanchana Devi

PERT Technique

Used to evaluate the effects of uncertainty

CPM & PERT are similar

CPM requires Single Estimate

PERT requires Three Estimates

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PERT Three Estimates are

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Most Likely Time

The time we would expect the task to take under

normal circumstances. “ m”

Optimistic Time

Shortest time in which we could expect to complete

the activity, barring the miracles. “a”

Pessimistic Time

Worst Possible time. “b”

Expected Duration

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PERT Combines the three estimates to form a

single expected duration, te

Formula for te is

te= a+4m+b

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Calculate the expected duration

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Activity Optimistic(a) Most Likely(m)

Activity Duration

Pessimistic(b)

A 5 6 8

B 3 4 5

C 2 3 3

D 3.5 4 5

E 1 3 4

F 8 10 15

G 2 3 4

H 2 2 2.5

After Calculating Expected

Duration

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PERT Network after the

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Activity Standard Deviation

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S = b-a which gives the degree of uncertainty

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The activity standard deviation is proportional to the difference between the optimistic and pessimistic estimates.

Can be used as a ranking measure of the degree of uncertainty or risk for each activity

Standard Deviation

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PERT With ‘SD’

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Probability of Meeting or Missing

Target Date

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The PERT Technique uses the following three

step method for calculating the probability

of meeting or missing a target date:

Calculate SD of each project event

Calculate the Z value for each event that has a target

value

Convert Z values to a probability

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Note: To add two Standard Deviations we must add their squares and then find the square root of the sum.

The SD for event 3 depends on the activity B. The SD for event 3 is therefore 0.33

For event 5 there are two possible paths, B+E or F. The total SD for path B+E is √(0.332+0.502) = 0.6 and For path F is 1.17

SD for event 5 is therefore the greater of two 1.17

Z- Value Formula

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Te is the Expected Date

T Target Date

S SD

Z = T - te

S

Calculate Z value –Event ‘4’

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(10-9.00)/0.53 = 1.8867

A Z-Value may be converted to the

probability of not meeting the target date by

using the graph given below

Converting Z values to

Probabilities

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A Z-value may be converted to the

probability of not meeting the target date by

using the graph.

Eg:

The Z-Value for the project completion (event 6)

is 1.23. Using graph this equates to a probability

of approximately 11%, that is, there is an 11%

risk of not meeting the target date of the end of

week 15.

Monte Carlo Simulation

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An alternative to PERT Technique

MC Simulation are a class of general analysis techniques that are valuable to solve any problem that is complex, nonlinear or for some uncertain parameters.

It involves repeated random sampling to compute the results.

Advantage:

Repeated computation of random numbers - easier to use this technique when available as a computer program

Steps – MC Simulation

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Step 1: Express the project completion time in terms of the

duration of the n-activities xi,i=1,n and their dependencies

as a precedence graph, d= f(x1,x2,….xn).

Step 2: Generate a set of random inputs, Xi1,Xi2, …Xin using

the specified probability distributions.

Step 3: Evaluate the project completion time expression

and store the result in di.

Step 4: Repeat steps 2 and 3 for the specified number of

times.

Step 5: Analyze the results di, i=1,n; summarize and display

using a histogram.

Histogram

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