Project Management - Operations research and Operations management - Production & Industrial Engineering Previous Year Questions

1

2007 · Production & Industrial Engineering · Operations research and Operations management · Project Management

Production & Industrial Engineering (PI) 2007

The length of the critical path in weeks is

A

29

B

31

C

38

D

66

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2

2007 · Production & Industrial Engineering · Operations research and Operations management · Project Management

Production & Industrial Engineering (PI) 2007

If \(U_\alpha\) is the earliest start time of event \(\alpha\), then the recurrence equation defining \(U_\alpha\) is

A

\(U_6 = \text{Max}\{U_8, 8\}\)

B

\(U_6 = U_8 - 8\)

C

\(U_6 = \text{Max}\{U_5, U_8, 7, 5\}\)

D

\(U_6 = \text{Max}\{U_5 + 7, U_3 + 5\}\)

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3

2007 · Production & Industrial Engineering · Operations research and Operations management · Project Management

Production & Industrial Engineering (PI) 2007

If activity B has uncertain duration and is uniformly distributed over the interval [8, 12], and T is the earliest start time of event 3 (assume that event 1 starts at time 0), then the mean and variance of T are

A

10 and 0.4

B

10 and 1.33

C

16 and 0.4

D

16 and 1.33

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4

2008 · Production & Industrial Engineering · Operations research and Operations management · Project Management

Production & Industrial Engineering (PI) 2008

The figure illustrates a PERT network describing the precedence relationship among different activities. The optimistic time, most likely time and pessimistic time of the activities are given in the table below.

Activity	Optimistic time (hour)	Most likely time (hour)	Pessimistic time(hour)
1-2	7	9	11
1-3	5	7	9
1-4	4	7	10
2-5	8	10	12
3-5	6	9	12
3-7	8	10	12
4-6	4	6	8
5-7	5	8	11
6-7	3	5	7

The length of the critical path (in hours) is

A

17

B

18

C

24

D

27

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5

2008 · Production & Industrial Engineering · Operations research and Operations management · Project Management

Production & Industrial Engineering (PI) 2008

The standard deviation of the critical path (in hours) is

A

0.66

B

0.94

C

1.37

D

1.56

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6

2008 · Production & Industrial Engineering · Operations research and Operations management · Project Management

Production & Industrial Engineering (PI) 2008

The slack at event number 3 (in hours) is

A

0

B

3

C

6

D

10

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7

2008 · Production & Industrial Engineering · Operations research and Operations management · Project Management

Production & Industrial Engineering (PI) 2008

The length of the critical path (in hours) is

A

17

B

18

C

24

D

27

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8

2013 · Production & Industrial Engineering · Operations research and Operations management · Project Management

Production & Industrial Engineering (PI) 2013 [Session 1]

The critical path of the project, based on the mean activity duration, is

A

1–2–3–4–5

B

1–2–3–5

C

1–3–5

D

1–3–4–5

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9

2013 · Production & Industrial Engineering · Operations research and Operations management · Project Management

Production & Industrial Engineering (PI) 2013 [Session 1]

Let Φ denote the cumulative distribution function of the standard normal random variable. The probability that all activities on the critical path, based on the mean activity duration, are completed in 22 days is

A

Φ⁻¹(0.333)

B

Φ⁻¹(0.816)

C

Φ⁻¹(1.664)

D

Φ⁻¹(2.235)

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10

2014 · Production & Industrial Engineering · Operations research and Operations management · Project Management

Production & Industrial Engineering (PI) 2014

A project consisting of five activities needs crashing. The details of crashing that was carried out are given in the table.

Activity	Normal Time (days)	Shortest Time (days)	Cost in Rs. for Reduction/day	Actually Crashed by (days)
1-2	6	4	100	1 day
1-3	7	5	100	2 days
1-4	10	7	100	1 day
2-4	4	3	200	Not Crashed
3-4	5	4	200	1 day

If the overhead cost of the project is Rs. 200 per day, then the net change in project cost (in Rs.) because of crashing is ______

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11

2017 · Production & Industrial Engineering · Operations research and Operations management · Project Management

Production & Industrial Engineering (PI) 2017

In a project, tasks A, B, C, D, E, F, G, H, I and J are to be performed. The precedence relationships and the time required (in days) to complete the tasks are given in the Table.

Tasks	A	B	C	D	E	F	G	H	I	J
Time (days)	8	10	8	10	16	17	18	14	9	4
Preceding tasks	-	-	-	A	A	B, D	C	C	F, G	E, I, H

The time required (in days) to complete the project along the critical path is __________

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12

2018 · Production & Industrial Engineering · Operations research and Operations management · Project Management

Production & Industrial Engineering (PI) 2018

A project consists of three activities P, Q and R. The durations of activities follow Beta distribution. The predecessors and durations of activities are as per the following table:

Activity	Predecessors	Optimistic time (month)	Most likely time (month)	Pessimistic time (month)
P	—	2	3	10
Q	P	3	5	13
R	Q	3	4	5

The expected project completion time (in month) is ______

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13

2020 · Production & Industrial Engineering · Operations research and Operations management · Project Management

Production & Industrial Engineering (PI) 2020

A project consists of seven activities as listed in the table. The time required for each activity and its immediate predecessor(s) are also given.

Activity	Time required (in weeks)	Immediate Predecessor(s)
P	7	-
Q	4	-
R	2	Q
S	11	P
T	9	P, R
U	9	Q
V	4	T, U

The project completion time using Critical Path Method (CPM) in weeks is ______.

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14

2021 · Production & Industrial Engineering · Operations research and Operations management · Project Management

Production & Industrial Engineering (PI) 2021

A project consists of eight activities. The time required for each activity and its immediate predecessor(s) are given in the table below.

Activity	Activity time (in days)	Immediate predecessor(s)
A	2	-
B	3	-
C	2	A
D	4	A,B
E	4	C
F	3	C
G	X	D,E
H	2	F,G

If the project completion time using critical path method (CPM) is 15 days, then the value of X (in days) is __________. [in integer]

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15

2022 · Production & Industrial Engineering · Operations research and Operations management · Project Management

Production & Industrial Engineering (PI) 2022

A project comprises of seven activities. The expected durations of activities and their variances are as follows:

Activity	Expected duration (minute)	Variance (minute)
A	4	1
B	5	1
C	4	1
D	1	0
E	7	4
F	6	1
G	8	4

The critical path consists of activities B, E and G. The standard deviation (in minute) of the project duration is __________. [round off to two decimal places]

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16

2023 · Production & Industrial Engineering · Operations research and Operations management · Project Management

Production & Industrial Engineering (PI) 2023

Details of activities of a project are given as

Activity	A	B	C	D	E	F	G	H	I	J
Time (days)	8	10	8	7	16	15	18	14	9	4
Predecessors	-	-	-	A	A	B, D	C	C	F, G	E, I, H

The time required, in days, to complete the project along the critical path is _____ (in integer).

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17

2024 · Production & Industrial Engineering · Operations research and Operations management · Project Management

Production & Industrial Engineering (PI) 2024

A project has six activities and the precedence relationship among them is shown in the table.

Activity	Precedent activities
A	None
B	None
C	None
D	A, B
E	B, C
F	A, B

The minimum number of dummy activities needed to draw an activity-on-arrow (AOA) representation of the project network is

A

0

B

1

C

2

D

3

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18

2025 · Production & Industrial Engineering · Operations research and Operations management · Project Management

Production & Industrial Engineering (PI) 2025

The network diagram of eight activities (A to H) along with their time durations (in days, given in bracket) of a project is shown in the figure. The critical path of the project is

A

1–2–3–6

B

1–4–3–6

C

1–5–6

D

1–4–5–6

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19

2026 · Production & Industrial Engineering · Operations research and Operations management · Project Management

Production and Industrial Engineering (PI) 2026

Painting is one of the activities in a construction project. For the painting activity that takes 6 days, both the total float and the free float are zero.
Which ONE of the following is TRUE for the painting activity?

A

Painting is a dummy activity.

B

Painting is a non-critical activity.

C

The start of painting activity can be delayed without causing delay in completion of the construction project.

D

The start of painting activity cannot be delayed without causing delay in completion of the construction project.

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