Question

Mubarak textbook Construction Project Scheduling and Control - 3rd edition(Chapter 11) can be used as reference, but problem not from textbook

PROBLEM 2

2. A project team developed a detailed construction plan that includes activities with uncertain durations, including precedence constraints. The plan was simulated 10 times, and using a significance level (α) of 0.05, the expected project duration was found to be: 365 ± 47 days In other words, the true mean duration could be anywhere between 318 days and 412 days. Moreover, this is ONLY the mean duration. Given any particular outcome, actual duration could be quite different. We would like to calculate the expected duration with only 20 total days of error. Please provide the number of simulation replications (n) required to accomplish this. Use both approximations found in the lecture on number of replications.

Answer 1

The plan was initially simulated 10 times and the margin of error that is obtained at 5% significance level is 47 days. Now the margin of error is given by

ie ..............................................(1)

( The z value is obtained from standard normal table). I have used a calculator here which is easy for you understand how this value came)

Click on the below link for online normal calculator

https://surfstat.anu.edu.au/surfstat-home/tables/normal.php

Attached below is a screen shot of getting the value

5% significance level means the current interval with margin of error 47 days is accepted with 95% confidence... that means 95% of the samples of size 10 selected will have its mean value within the current interval

From (1) obtain ,

Inorder to calculate the expected duration with 20 days of margin of error we need to increase the sample size as the standard deviation is large

ie  

ie n shoould be greater than 55.22 to a margin of error o 30. Hence the number of simulations required is 56