Question

Problem 12-09 (Algorithmic)

A project has four activities (A, B, C, and D) that must be performed sequentially. The probability distributions for the time required to complete each of the activities are as follows:

Activity		Activity Time (weeks)		Probability
A		4		0.28
		5		0.37
		6		0.29
		7		0.06
B		6		0.24
		8		0.57
		10		0.19
C		10		0.13
		12		0.25
		14		0.41
		16		0.16
		18		0.05
D		11		0.72
		13		0.28

1. Provide the base-case, worst-case, and best-case calculations for the time to complete the project.

   Activity	Base case	Worst case	Best case
   A	weeks	weeks	weeks
   B	weeks	weeks	weeks
   C	weeks	weeks	weeks
   D	weeks	weeks	weeks
   Total	weeks	weeks	weeks

2. Use the random numbers 0.5162, 0.4437, 0.7361 and 0.2603 to simulate the completion time of the project in weeks.

   Activity	Random Number	Completion Time
   A	0.5162	weeks
   B	0.4437	weeks
   C	0.7361	weeks
   D	0.2603	weeks
   Total		weeks

3. Discuss how simulation could be used to estimate the probability that the project can be completed in weeks or less.
   
   Simulation provides a distribution of project completion times. The____ of times weeks and under can be used to estimate the probability that the project will be completed within weeks.

Answer 1

a)

Activity	Base case		Worst Case		Best case
A	5	Weeks	7	Weeks	4
B	8	Weeks	10	Weeks	6
C	14	Weeks	18	Weeks	10
D	11	Weeks	13	Weeks	11
Total	38	Weeks	48	Weeks	31

b)

Activity	Random number	Completion time
A	0.5162	5	Weeks
B	0.4437	8	Weeks
C	0.7361	14	Weeks
D	0.2603	11	Weeks
Total		38	Weeks

c)

Simulation provides a distribution of project completion times. The percentage of simulation trials with completion of times weeks and under can be used to estimate the probability that the project will be completed within weeks