What is the exam pattern and passing mark for GTU Operation Research (BE04000201)?

The GTU theory examination carries 70 total marks with a duration of 2.5 Hours. Minimum passing criteria is 23 marks (33%). The paper consists of 5 main questions with official marking breakdown and internal choices.

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The official GTU question paper PDF is linked directly from Gujarat Technological University's official examination archive. You can view the full paper online or download the original file.

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Gujarat Technological UniversitySummer 2026 examination

GTU BE04000201 Operation Research Summer 2026 Question Paper & PDF

B.E. · Mechanical Engineering · Semester 4 · Subject code BE04000201

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Total: 70 marks
To pass: 23 marks (33%)
Duration: 2.5 Hours 10:30 AM – 1:00 PM
Questions: 5 with internal choice

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Q.1

14 Marks

(a)

3 marks

Discuss the scope of Operation Research in Medical and Health sector.

(b)

4 marks

Explain the characteristics of Operation Research.

(c)

7 marks

An advertising firm has decided to advertise in magazines. Magazine I have reach of 2000 customers and magazine II has reach of 3000 customers per advertisement. The cost per advertisement is Rs. 400 and Rs. 600 in magazines I and II respectively. The firm has monthly budget of Rs. 60000. The other requirement is that advertisement must reach at least 40000 customers having yearly income Rs. 2.5 Lakhs. In that respect magazine I and magazine II has 400 and 200 reach of such customers. Formulate the LP such that advertisement maximizes the reach to the customers. Solve LPP Graphically.

Q.2

14 Marks

(a)

3 marks

Transportation and Assignment Problems are special case of Linear Programming. Justify this statement.

(b)

4 marks

What do you mean by degeneracy for LPP? How it can be solved?

(c)

7 marks

Solve the following LPP by Big M method:

Maximize $Z = 3x_1 - x_2$ Subject to $2x_1 + x_2 \le 2$ $x_1 + 3x_2 \ge 3$ $x_2 \le 4$ and $x_1 , x_2 \ge 0$ .

(c)

7 marks

Construct the dual of the following primal problem. Solve the problem by generated dual LPP.

Maximize $Z = 3x_1 + 2x_2$ Subject to $2x_1 + x_2 \le 5$ $x_1 + x_2 \le 3$ and $x_1, x_2 \ge 0$

Q.3

14 Marks

(a)

3 marks

Discuss Transshipment Problem. Explain solving procedure.

(b)

4 marks

Discuss the significance of Saddle point in terms of Game theory.

(c)

7 marks

Find an optimal solution to an assignment problem with following cost matrix. Also find the alternate optimal solution if possible.

	$J_1$	$J_2$	$J_3$	$J_4$
$M_1$	10	9	7	8
$M_2$	5	8	7	7
$M_3$	5	4	6	5
$M_4$	2	3	4	5

(a)

3 marks

Disucss the step by step procedure fo Stepping stone method.

(b)

4 marks

Explain decision tree diagram by taking suitable example related to Engineering Problem's solution.

(c)

7 marks

A transportation company has 5, 10, 7 and 3 trucks available at four different sites A, B, C and D. Its customers have requirement of 5, 8 and 10 trucks at the three different destinations X, Y and Z respectively. The distance (in kms.) from an origin to destination is summarized in the following table. Formulate above problem as transportation problem and determine strategy for a company using VAM. Test the optimality of VAM solution and determine optimum strategy for the transport company.

	X	Y	Z
A	70	30	60
B	40	60	80
C	50	80	40
D	80	40	30

Q.4

14 Marks

(a)

3 marks

What do you understand by EOQ? Derive formula when demand is constant, lead times are known and fixed, and that all inventory arrives at once.

(b)

4 marks

For queuing theory, explain Kendall’s Notations.

(c)

7 marks

A copy maker has one copy making machine and he operates as the order comes. The order arrival is poison distribution having interval time of 0.5 min. The average time to serve a copy is distributed with mean of 0.3 min. Determine the following:

1Utilization factor of the machine

2Idle time for machine in a day having working hours of 10 hours

3No. of persons waiting in the system

4No. of persons waiting in the queue

5Average waiting time in the queue

(a)

3 marks

Discuss the applicability of Group Replacement theory with proper applications in the industry.

(b)

4 marks

For Inventory control, justify the synchronization of ABC analysis and VED analysis.

(c)

7 marks

Following percentage failure (at the month end)have been observed for certain type of light bulbs:

There are total 1000 bulbs in use and it costs Rs. 10 to replace an individual bulb which has fused out. If all bulbs are replaced simultaneously, it would cost Rs. 4 per bulb. Two policies are being considered for replacement of bulbs; First, replace all bulbs simultaneously at fixed interval whether failed or not and do individual replacement in intermediate periods. Secondly, individual replacement of bulbs as and when it fails. Determine the optimum policy for replacement of bulbs based on above failure data and costs.

Month	1	2	3	4	5
% Failure	10	25	50	80	100

Q.5

14 Marks

(a)

3 marks

Explain different types of floats with formulas.

(b)

4 marks

Which factors are considered in decision making process under high level of uncertainity? Explain through flow chart.

(c)

7 marks

Solve the following pay-off matrix for player A and B. Also find out the optimal strategies and value of the game using algebraic method.

Player A \ Player B	$B_1$	$B_2$
$A_1$	-5	5
$A_2$	-6	4
$A_3$	8	4

(a)

3 marks

What is crashing in terms of Project management? Disucss its importance in Project Managment.

(b)

4 marks

Discuss at least four applications of Minimax Strategy and Maximin Strategy each.

(c)

7 marks

The details of activity in project management is as below. Find:

ICritical Path and project duration.

IIOptimum project cost with considering indirect cost is Rs. 100 per day.

Activities	Normal Time	Normal Cost	Crash Time	Crash Cost
1-2	3	300	2	400
2-3	6	480	4	520
2-4	7	2100	5	2500
2-5	8	400	6	600
3-4	4	320	3	360
4-5	5	500	4	520

Other Semester 4 subjects

BE Mechanical

2141905

Complex Variables and Numerical Methods

3141901

Mechanical Measurement and Metrology

3141906

Fluid Mechanics and Hydraulics Machines

3141907

Fundamentals of Machine Design

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About this paper

Official Gujarat Technological University (GTU) examination paper for Operation Research (Summer 2026, B.E. · Mechanical Engineering, Sem 4). Features complete 70-mark regular & remedial examination pattern, official marking distribution across all 5 questions, and direct 1-click official PDF download.

Transcribed for student exam preparation from Gujarat Technological University official examination archives. Questions, syllabus guidelines, and curriculum marking schemes remain the intellectual property of Gujarat Technological University.

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