Question

Question 2: Consider the following activities and their durations and requirements for a construction project.

Activity	Predecessors	Activity Duration (days)
		Optimistic	Most likely	Pessimistic
A	-	2	7	9
B	-	3	6	9
C	-	3	5	8
D	A	15	19	20
E	B, C	6	9	10
F	C	2	4	6
G	A, E	4	8	13
H	G	1	2	4

Part a) Draw the project network and determine the critical path in the project network using most likely activity durations. (Show the network, total flow of each activity, and critical path)

Part b) How many days activity F could be delayed its early start date without delaying the start date of other activities? (Explanations and calculations)

Part c) If company’s president wants to have a 95% chance of completing the project before July 30, when should the project began? (Explanations and calculations)

Answer 1

Answer:

Paths	Duration	Variance
AD	25.00	2.58
AGH	16.83
BEGH	25.00	5.00
CEGH	24.17
CF	9.17
Critical Path	Duration (days)	Variance, σ2	Standard Deviation, σ (=sqrt(variance))
BEGH *	25.00	5.00	2.236

* In case of multiple critical paths use the one with the largest variance largest variance

Answer b

Activity	Preceding Activity	Duration, D	Early start, ES=Max of early finish of preceeding activities	Early finish, EF = ES + D	Activity	Late finish, LF= Min of LS of successor activities	Late start, LS= LF - D	Total slack= LF-EF	Critical activity name	Critical activity, activities with 0 slack time
A		7	0.00	6.50	A	6.50	0.00	0.00	A	YES
B		6	0.00	6.00	B	6.00	0.00	0.00	B	YES
C		5	0.00	5.17	C	6.00	0.83	0.83
D		19	6.50	25.00	D	25.00	6.50	0.00	D	YES
E		9	6.00	14.67	E	14.67	6.00	0.00	E	YES
F		4	5.17	9.17	F	25.00	21.00	15.83
G		8	14.67	22.83	G	22.83	14.67	0.00	G	YES
H		2	22.83	25.00	H	25.00	22.83	0.00	H

Activity F has a total slack of 15.83 days. So activity F could be delayed (by 15.83 days) at its early start date without delaying the start date of other activities

Answer c

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