Given a Project with the following information: Find: Critical Path Number of We

Question

Given a Project with the following information:

Find:

Critical Path

Number of Weeks project duration

The probability of completing this project in 11 weeks (or less)

The probability of completing this project in 14 weeks (or less)

The number of weeks required to assure a 96.5% chance of completion

If you will receive a bonus of $100,000 if this project is completed within 13 weeks and be fined a penalty of $50,000 if the project takes longer than 17 weeks should you bid the job? Please show quantitative support for your answer.

Standard Activity Deviation Path? Critical Duration 2 2 yes yes 2 ves 6 yes yes 2

Explanation / Answer

PLEASE FIND BELOW ANSWERS TO FIRST 5 QUESTIONS :

The   Critical path is A-C-E-G-H

Expected duration of the project

= Sum of durations of activities on critical path

= 2 + 4 + 1 + 4 + 2 weeks

= 13 weeks

CRITICAL PATH = A-C-E-G-H

EXPECTED DURATION OF THE PROJECT = 13 WEEKS

Variance of critical path

= Sum of Squares of Standard Deviations of activities on critical path

= 2^2 + 1^2 + 1^2 + 2^2 + 1^1

= 4 + 1 + 1 + 4 + 1 weeks

= 11 weeks

Therefore standard deviation of duration of critical path = Square root ( 11 weeks ) = 3.316

Let Z value corresponding to the probability of completing the project in 11 weeks or less is Z1

Therefore.

Expected duration of project + Z1 x Standard deviation of activities on critical path = 11

Or, 13 + 3.316.Z1 = 11

Or, 3.315.Z1 = - 2

Or, Z1 = - 2 / 3.315

Or, Z1 = - 0.60 ( rounded to 2 decimal places )

Corresponding probability for Z1 = - 0.60 as derived from standard normal distribution table = 0.27425

PROBABILITY OF COMPLETING THE PROJECT IN 11 WEEKS OR LESS = 0.27425

Let Z value corresponding to the probability of completing the project in 14 weeks or less is Z2

Therefore.

Expected duration of project + Z2 x Standard deviation of activities on critical path = 14

Or, 13 + 3.316.Z2 = 14

Or, 3.315.Z2 = 1

Or, Z2 = 1/3.315

Or, Z2 = 0.30( rounded to 2 decimal places )

Corresponding probability for Z2 = 0.30 as derived from standard normal distribution table = 0.61791

PROBABILITY OF COMPLETING THE PROJECT IN 14 WEEKS OR LESS = 0.61791

Let Z value corresponding to 96.5% chance of completion

= Z value for probability 0.965

= NORMSINV ( 0.965 )

= 1.812

Number of weeks required to assure a 96.5% chance of completion

= Expected duration of project + 1.812 x Standard deviation of duration of critical path

= 13 + 1.812 x 3.316

= 13 + 6.008

= 19.008

NUMBER OF WEEKS REQUIRED TO ASSURE A 96.5% CHANCE OF COMPLETION = 19.008 WEEKS

CRITICAL PATH = A-C-E-G-H

EXPECTED DURATION OF THE PROJECT = 13 WEEKS

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