11 The following precedence diagram reflects three time esti

11. The following precedence diagram reflects three time estimates in weeks for each activity. Determine: a. The expected completion time for each path and its variance. b. The probability that the project will require more than 49 weeks. c. The probability that the project can be completed in 46 weeks or less. 12. A project manager has compiled a list of major activities that will be required to install a computer information system in her firm. The list includes estimated completion times for activities and precedence relationships

Solution

a. Let,

te = Expected Time, to = Optimal Time, tm = Most Likely Time, tp = Pessimistic time.

The expected completion time is calculated as te = ( to + 4tm + tp ) / 6 and the variance is calculated as var = ( tp - to )² / 36. They are

b. The probability that the project will require more than 49 weeks is

c. The probability that the project will complete in 46 weeks or less

Path	Activity		Times		te=	Expected	var =	var
		to	tm	tp	(to+4tm+tp)/6	Completion Time	(tp-to)2/36
	1	8	8	8	8		0
1-2-3-8	2	11	12	13	12	37.34	0.11	1.06
	3	9	10	12	10.17		0.25
	8	5	7	10	7.17		0.69
	1	8	8	8	8		0
1-2-4-6	2	5	6	7	6	43	0.11	5.11
	4	14	18	26	18.67		4
	6	8	10	14	10.33		1
	1	8	8	8	8		0
1-2-4-7	2	5	6	7	6	40	0.11	0.81
	4	13	13	13	13		0
	7	10.5	13	15.5	13		0.69
	1	8	8	8	8		0
	2	10	12	14	12		0.44
1-2-5-9-10	5	7	10	12	9.83	46.83	0.69	1.25
	9	10	11	12	11		0.11
	10	6	6	6	6		0