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		3		0.29
		4		0.38
		5		0.29
		6		0.04
B		7		0.22
		9		0.53
		11		0.25
C		9		0.05
		11		0.24
		13		0.36
		15		0.19
		17		0.16
D		10		0.59
		12		0.41

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 0.7584, 0.7279, 0.4741 and 0.9526 to simulate the completion time of the project in weeks.
   

   Activity	Random Number	Completion Time
   A	0.7584	____weeks
   B	0.7279	weeks
   C	0.4741	weeks
   D	0.9526	weeks
   Total		weeks

Answer 1

		T	p	A=T*p
	ACTIVITY	Activity Time (weeks)	Probability	Activity Time*Probability
	A	3	0.29	0.87
		4	0.38	1.52
		5	0.29	1.45
		6	0.04	0.24
			SUM	4.08
	Base Case Time for Activity A			4.08
	B	7	0.22	1.54
		9	0.53	4.77
		11	0.25	2.75
			SUM	9.06
	Base Case Time for Activity B			9.06
	C	9	0.05	0.45
		11	0.24	2.64
		13	0.36	4.68
		15	0.19	2.85
		17	0.16	2.72
			SUM	13.34
	Base Case Time for Activity C			13.34
	D	10	0.59	5.9
		12	0.41	4.92
			SUM	10.82
	Base Case Time for Activity D			10.82
		Time in Weeks
	Activity	Base case	Worst case	Best case
	A	4.08	6	3
	B	9.06	11	7
	C	13.34	17	9
	D	10.82	12	10
	Total	37.30	46.00	29.00
	SIMULATION
	ACTIVITY A
	Mapping of Random Number
	Activity Time	Probability	Cumulative Probability	Mapped Random Number
	3	0.29	0.29	00-28
	4	0.38	0.67	29-66
	5	0.29	0.96	67-95
	6	0.04	1	96-99
	Activity	Random Number	First two Digits	Activity Time	Mapped Numbers
	A	0.7584	75	5	67-95
	ACTIVITY B
	Mapping of Random Number
	Activity Time	Probability	Cumulative Probability	Mapped Random Number
	7	0.22	0.22	00-21
	9	0.53	0.75	22-74
	11	0.25	1	75-99
	Activity	Random Number	First two Digits	Activity Time	Mapped Numbers
	B	0.7279	72	9	22-74
	ACTIVITY C
	Mapping of Random Number
	Activity Time	Probability	Cumulative Probability	Mapped Random Number
	9	0.05	0.05	00-04
	11	0.24	0.29	.05-28
	13	0.36	0.65	29-64
	15	0.19	0.84	65-83
	17	0.16	1	84-99
	Activity	Random Number	First two Digits	Activity Time	Mapped Numbers
	C	0.4741	47	13	29-64