Question

Kelle Carpet and Trim installs carpet in commercial offices. Peter Kelle has been very concerned with the amount of time it took to complete several recent jobs. Some of his workers are very unreliable. A list of activities and their optimistic completion​ time, the most likely completion​ time, and the pessimistic completion time​ (all in​ days) for a new contract are given in the following​ table:

Activity: a,b.c.d.e.f.g.h.i.j,k

Time.(Days ) A, M, B, predecessors

A= 2, 5, 9, zero

B= 10, 11, 12 zero

C= 1, 2, 3, Zero

D= 7, 8, 9, C

E= 1, 3, 5, BD

F= 7, 9, 14, AE

G= 2, 3, 4, AE

H= 3, 5, 7 F

I= 10, 11, 12 G

J= 15, 17, 19 C

K= 4, 8, 12 H,I

b)

1.Activities on the critical path for the project are B - E - F - H - K

.

2.The total project completion time is ....... days. ​(Round your response to two decimal​ places.)

​c) For the given​ project, the earliest start​ (ES) and earliest finish​ (EF) are:

​(Round your responses to two decimal​ places.)

ACTIVITY A TO J

Earliest Start.(ES) . from a-j

Earliest Finish (EF). from a-j

Answer 1

We will use below approach:

Expected time = (Optimistic + 4*Most Likely + Pessimistic)/ 6

Variance = ((Pessimistic - Optimistic)/ 6)2

Earliest Start Time (ES) = the earliest time that an activity can begin

Earliest Finish Time (EF) = the earliest time that an activity can be completed

EF = ES + duration of activity        

Latest Start Time (LS) = the latest time that an activity can begin without lengthening the minimum project duration

Latest Finish Time (LF) = the earliest time than an activity can be completed without lengthening the minimum project duration

LF = LS + duration of activity         

Duration of the project = the difference between the maximum value of the "latest finish time" of projects and the minimum value of the "earliest start time" of projects

Project duration = max(LF) - min(ES)     

Slack = the amount of time that a project can be delayed without increasing the duration of the project

Slack = LF- LS or EF - ES

Critical path is the path with Total Slack = 0

			Expected time = (Optimistic + 4*Most Likely + Pessimistic)/ 6
			Variance = ((Pessimistic - Optimistic)/ 6)2
Activity	Predecessors	Duration			Exp. Duration	Variance	Early Start (ES)	Early Finish (EF)	Late Start (LS)	Late Finish (LF)	Slack	Critical Path
		Optimistic, a	Most Likely, m	Pessimistic, b	Te	σ2
A		2	5	9	5.2	1.36	0	5.2	8.8	14.0	9
B		10	11	12	11.0	0.11	0.0	11.0	0.0	11.0	0	Y
C		1	2	3	2.0	0.11	0.0	2.0	1.0	3.0	1
D	C	7	8	9	8.0	0.11	2.0	10.0	3.0	11.0	1
E	B, D	1	3	5	3.0	0.44	11.0	14.0	11.0	14.0	0	Y
F	A, E	7	9	14	9.5	1.36	14.0	23.5	14.0	23.5	0	Y
G	A, E	2	3	4	3.0	0.11	14.0	17.0	14.0	17.0	0
H	F	3	5	7	5.0	0.44	23.5	28.5	23.5	28.5	0	Y
I	G	10	11	12	11.0	0.11	17.0	28.0	17.0	28.5	1
J	C	15	17	19	17.0	0.44	2.0	19.0	28.5	36.5	18
K	H, I	4	8	12	8.0	1.78	28.5	36.5	28.5	36.5	0	Y
		Activities on Critical path (Slack = 0 ) is B-E-F-H-K
		Project expected duration is 36.5 days (same as critical path completion time)

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