(2a). In a project network, the project completion time has been determined to b
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Question
(2a). In a project network, the project completion time has been determined to be a random variable with a mean of 52 days and a standard deviation of 5 days (and can be assumed to be Normally distributed). How many days should we allow for this project to have approximately 99% probability of completion? (b). A process has a cycle time of 10 minutes. The throughput time is 10 hours. If the throughput time is reduced to 5 hours without changing the cycle time, what is the increase in inventory (as a percentage)? (Note: if there is a decrease, then the 'increase is negative) (Provide two significant digits after the decimal point).Explanation / Answer
(2a).
The z-score for the probability of 99% could be found out using the z-score table.
By looking at the z-score table we find the value of z to be 2.33 for probability of 99%.
Mean, mu = 52 days
Standard Deviation, sd = 5 days
Let, d be the number of days that we should allow for the project to have completed with approximately 99% probability.
Therefore,
z = (d-mu)/sd
Hence, the number of days that we should allow for the project to have completed with approximately 99% probability is 63.65 days.
(b).
Work in progress = Cycle time * throughput
Case 1:
Cycle time = 10 minutes
Throughput time = 10 hours = 600 minutes
Therefore, Work in progress = 10*600 = 6000 units
Case 2:
Cycle time = 10 minutes
Throughput time = 5 hours = 300 minutes
Therefore, Work in progress = 10*300 = 3000
Now, Increase in inventory = 3000-6000 units = -3000 units
Hence, Increase in inventory as a percentage = (-3000/6000)*100% = -50.00%
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