Operations Research - Materials, Manufacturing and Industrial Engineering - Mechanical Engineering Previous Year Questions

1

2008 · Mechanical Engineering · Materials, Manufacturing and Industrial Engineering · Operations Research

Mechanical Engineering (ME) 2008

In an M/M/1 queueing system, the number of arrivals in an interval of length \(T\) is a Poisson random variable (i.e. the probability of there being \(n\) arrivals in an interval of length \(T\) is \(\frac{e^{-\lambda T} (\lambda T)^n}{n!}\)). The probability density function \(f(t)\) of the inter-arrival time is given by

A

\(\lambda^2 (e^{-\lambda t})\)

B

\(\frac{e^{-\lambda t}}{\lambda^2}\)

C

\(\lambda e^{-\lambda t}\)

D

\(\frac{e^{-\lambda t}}{\lambda}\)

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2

2008 · Mechanical Engineering · Materials, Manufacturing and Industrial Engineering · Operations Research

Mechanical Engineering (ME) 2008

For the standard transportation linear programme with \( m \) sources and \( n \) destinations and total supply equaling total demand, an optimal solution (lowest cost) with the smallest number of non-zero \( x_{ij} \) values (amounts from source \( i \) to destination \( j \)) is desired. The best upper bound for this number is

A

\(mn \)

B

\(2(m+n) \)

C

\(m+n \)

D

\(m+n-1 \)

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3

2008 · Mechanical Engineering · Materials, Manufacturing and Industrial Engineering · Operations Research

Mechanical Engineering (ME) 2008

For the network below, the objective is to find the length of the shortest path from node P to node G. Let \( d_{ij} \) be the length of directed arc from node \( i \) to node \( j \). Let \( s_j \) be the length of the shortest path from P to node \( j \). Which of the following equations can be used to find \( s_G \)?

A

\(s_G = \text{Min}\{s_Q, s_R\} \)

B

\(s_G = \text{Min}\{s_Q - d_{QG}, s_R - d_{RG}\} \)

C

\(s_G = \text{Min}\{s_Q + d_{QG}, s_R + d_{RG}\} \)

D

\(s_G = \text{Min}\{d_{QG}, d_{RG}\} \)

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4

2008 · Mechanical Engineering · Materials, Manufacturing and Industrial Engineering · Operations Research

Mechanical Engineering (ME) 2008

After introducing slack variables s and t, the initial basic feasible solution is represented by the tableau below (basic variables are s = 6 and t = 6, and the objective function value is 0).
After some simplex iterations, the following tableau is obtained
From this, one can conclude that

A

The LP has a unique optimal solution

B

The LP has an optimal solution that is not unique

C

The LP is infeasible

D

The LP is unbounded

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5

2009 · Mechanical Engineering · Materials, Manufacturing and Industrial Engineering · Operations Research

Mechanical Engineering (ME) 2009

The critical path duration of the network (in days) is

A

11

B

14

C

17

D

18

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6

2010 · Mechanical Engineering · Materials, Manufacturing and Industrial Engineering · Operations Research

Mechanical Engineering (ME) 2010

Little's law is a relationship between

A

stock level and lead time in an inventory system

B

waiting time and length of the queue in a queuing system

C

number of machines and job due dates in a scheduling problem

D

uncertainty in the activity time and project completion time

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7

2010 · Mechanical Engineering · Materials, Manufacturing and Industrial Engineering · Operations Research

Mechanical Engineering (ME) 2010

Simplex method of solving linear programming problem uses

A

all the points in the feasible region

B

only the corner points of the feasible region

C

intermediate points within the infeasible region

D

only the interior points in the feasible region

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8

2010 · Mechanical Engineering · Materials, Manufacturing and Industrial Engineering · Operations Research

Mechanical Engineering (ME) 2010

The project activities, precedence relationships and durations are described in the table. The critical path of the project is

A

P-R-T-V

B

Q-S-T-V

C

P-R-U-W

D

Q-S-U-W

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9

2011 · Mechanical Engineering · Materials, Manufacturing and Industrial Engineering · Operations Research

Mechanical Engineering (ME) 2011

Cars arrive at a service station according to Poisson’s distribution with a mean rate of 5 per hour. The service time per car is exponential with a mean of 10 minutes. At steady state, the average waiting time in the queue is

A

10 minutes

B

20 minutes

C

25 minutes

D

50 minutes

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10

2011 · Mechanical Engineering · Materials, Manufacturing and Industrial Engineering · Operations Research

Mechanical Engineering (ME) 2011

The unit worth of resource R₂, i.e. dual price of resource R₂, in Rs. per kg is

A

0

B

1350

C

1500

D

2000

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11

2011 · Mechanical Engineering · Materials, Manufacturing and Industrial Engineering · Operations Research

Mechanical Engineering (ME) 2011

The manufacturer can make a maximum profit of Rs.

A

60000

B

135000

C

150000

D

200000

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12

2013 · Mechanical Engineering · Materials, Manufacturing and Industrial Engineering · Operations Research

Mechanical Engineering (ME) 2013 [Session 1]

Customers arrive at a ticket counter at a rate of 50 per hr and tickets are issued in the order of their arrival. The average time taken for issuing a ticket is 1 min. Assuming that customer arrivals form a Poisson process and service times are exponentially distributed, the average waiting time in queue in min is

A

3

B

4

C

5

D

6

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13

2013 · Mechanical Engineering · Materials, Manufacturing and Industrial Engineering · Operations Research

Mechanical Engineering (ME) 2013 [Session 2]

A linear programming problem is shown below.
Maximize \( 3x + 7y \)
Subject to \( 3x + 7y \le 10 \)
\( 4x + 6y \le 8 \)
\( x, y \ge 0 \)
It has

A

an unbounded objective function.

B

exactly one optimal solution.

C

exactly two optimal solutions.

D

infinitely many optimal solutions.

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14

2014 · Mechanical Engineering · Materials, Manufacturing and Industrial Engineering · Operations Research

Mechanical Engineering (ME) 2014 [Session 1]

The jobs arrive at a facility, for service, in a random manner. The probability distribution of number of arrivals of jobs in a fixed time interval is

A

Normal

B

Poisson

C

Erlang

D

Beta

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15

2014 · Mechanical Engineering · Materials, Manufacturing and Industrial Engineering · Operations Research

Mechanical Engineering (ME) 2014 [Session 1]

Jobs arrive at a facility at an average rate of 5 in an 8 hour shift. The arrival of the jobs follows Poisson distribution. The average service time of a job on the facility is 40 minutes. The service time follows exponential distribution. Idle time (in hours) at the facility per shift will be

A

\(\frac{5}{7}\)

B

\(\frac{14}{3}\)

C

\(\frac{7}{5}\)

D

\(\frac{10}{3}\)

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16

2014 · Mechanical Engineering · Materials, Manufacturing and Industrial Engineering · Operations Research

Mechanical Engineering (ME) 2014 [Session 2]

If there are m sources and n destinations in a transportation matrix, the total number of basic variables in a basic feasible solution is

A

m + n

B

m + n + 1

C

m + n – 1

D

m

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17

2014 · Mechanical Engineering · Materials, Manufacturing and Industrial Engineering · Operations Research

Mechanical Engineering (ME) 2014 [Session 2]

Consider the following data with reference to elementary deterministic economic order quantity model

Annual demand of an item	100000
Unit price of the item (in Rs.)	10
Inventory carrying cost per unit per year (in Rs.)	1.5
Unit order cost (in Rs.)	30

The total number of economic orders per year to meet the annual demand is ______

Check answer

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18

2014 · Mechanical Engineering · Materials, Manufacturing and Industrial Engineering · Operations Research

Mechanical Engineering (ME) 2014 [Session 3]

A minimal spanning tree in network flow models involves

A

all the nodes with cycle/loop allowed

B

all the nodes with cycle/loop not allowed

C

shortest path between start and end nodes

D

all the nodes with directed arcs

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19

2014 · Mechanical Engineering · Materials, Manufacturing and Industrial Engineering · Operations Research

Mechanical Engineering (ME) 2014 [Session 3]

Consider an objective function \( Z(x_1, x_2) = 3x_1 + 9x_2 \) and the constraints \( x_1 + x_2 \leq 8 \), \( x_1 + 2x_2 \leq 4 \), \( x_1 \geq 0, x_2 \geq 0 \). The maximum value of the objective function is ______

Check answer

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20

2014 · Mechanical Engineering · Materials, Manufacturing and Industrial Engineering · Operations Research

Mechanical Engineering (ME) 2014 [Session 4]

The total number of decision variables in the objective function of an assignment problem of size n × n (n jobs and n machines) is

A

n²

B

2n

C

2n – 1

D

n

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