The table below provides the activities and the three time estimates (optimistic
ID: 375872 • Letter: T
Question
The table below provides the activities and the three time estimates (optimistic, most likely, and pessimistic) for a project. The times are in weeks. Making the usual assumptions necessary to use PERT, perform the calculations and answer the questions below. Fill in the expected time and variance for each activity in the table on the next page. Then perform the necessary calculations to fill in the rest of that table.
Activity
Predecessor
a
m
b
A
---
5
8
17
B
--
2
5
8
C
A,B
6
6
6
D
C
15
18
27
E
C
7
10
13
F
E
4
7
10
G
C
5
8
17
H
D, F, G
3
6
9
I
D,F
4
7
16
J
H
4
4
4
K
I
5
8
17
a) (14 points) Fill in the table with the expected time, variance, earliest start, earliest finish, latest start, latest finish, and slack time for each activity. Do not round off to fewer than 3 decimals.
Activity
t
2
ES
EF
LS
LF
Slack
A
B
C
D
E
F
G
H
I
J
K
b) ______________________________ Which activities are on the critical path? (2 points)
c) ______________________ If each activity is finished in the expected time, what is the minimum possible time required for completing this project? (2 points)
d) ______________________ Calculate the project variance. (2 points)
e) _________________ What is the probability that the project is finished in 51 weeks or less? (2 points)
2. (8 points) A project was analyzed using the standard PERT procedure. The expected completion time for the project was found to be 45 weeks, and the project variance was calculated to be 16. The project completion time is normally distributed, and the activity times are independent.
a) _________________ What is the probability that the project is finished in 47 weeks or less?
b) _________________ What is the probability that the project will take longer than 47 weeks?
c) _________________ What is the probability that the project is finished in 40 weeks or less?
d) _________________ If management wishes to schedule the due-date for finishing the project to be such that there is only a 10% chance on being late, what due-date should be set?
BONUS QUESTION
Customers of a hotel can call the toll-free (800) number to make or modify reservations. If all operators are busy, the caller is placed on hold until an operator becomes available. The calls are routed to the next available operator on a first-in-first-out basis. During normal business hours, the average number of calls per hour is 48, and the average service time for each call is 2 minutes. The phone call arrival rate is a Poisson distribution, while service times are described by an exponential distribution.
a. ______ With 2 operators working, how many minutes is the average customer placed on hold? (1 point)
b. The company is considering using either 2, 3, or 4 people to answer the phones. In the table below, identify the type of system using Kendall notation, specify and µ, and give the operating characteristics specified.
Number of agents
2
3
4
Type of system (Kendall notation)
µ
W
Wq
L
Lq
c. The company has determined that there could be a problem if the number of callers on hold is more than 2. If there are two telephone operators working, then having 4 calls in the system would mean there are two customers receiving service and two others on hold. If there are three telephone operators working, then having 5 calls in the system would meant there are three customers receiving service and two others on hold. Etc.
________ Find the probability that more than 2 callers are on hold if 4 operators are working.
Activity
Predecessor
a
m
b
A
---
5
8
17
B
--
2
5
8
C
A,B
6
6
6
D
C
15
18
27
E
C
7
10
13
F
E
4
7
10
G
C
5
8
17
H
D, F, G
3
6
9
I
D,F
4
7
16
J
H
4
4
4
K
I
5
8
17
Explanation / Answer
In the PERT network, expected time for an activity is weghted mean of Optimistic, Most likely, and Pessimistic times with weights 1, 4, and 1 respectively. Standard deviation is = (Pessimistic - Optimistic) / 6, variance is square of S.D.
d) Sum of critical activities variances is the project variance = 4+0+4+4+4=16
Answer to first four parts only at a time please.
Activity Predecessor a m b t Variance ES EF LS LF Slack S.D. A --- 5 8 17 9 4 0 9 0 9 0 2 B -- 2 5 8 5 1 0 5 4 9 4 1 C A,B 6 6 6 6 0 9 15 9 15 0 0 D C 15 18 27 19 4 15 34 15 34 0 2 E C 7 10 13 10 1 15 25 17 27 2 1 F E 4 7 10 7 1 25 32 27 34 2 1 G C 5 8 17 9 4 15 24 25 34 10 2 H D, F, G 3 6 9 6 1 34 40 41 47 7 1 I D,F 4 7 16 8 4 34 42 34 42 0 2 J H 4 4 4 4 0 40 44 47 51 7 0 K I 5 8 17 9 4 42 51 42 51 0 2 Critical path is A--C--D--I--K with expected duration 51 and S.D. 4, variance 16Related Questions
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