Categories: 6th Semester

Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE – SEMESTER ?VI (NEW) – EXAMINATION ? SUMMER 2018

Subject Code: 2163201 Date: 28/04/2018

Subject Name: Operation Research

Time: 10:30 AM to 01:00 PM Total Marks: 70

Instructions:

1. Attempt all questions.

2. Make suitable assumptions wherever necessary.

3. Figures to the right indicate full marks.

MARKS

Q.1 (a) Discuss in brief the areas of application of Operation Research. 03

(b)Use simplex method to solve following LPP

???????????????? ?? = 45?? 1

+ 80?? 2

Subject to the constraints

5?? 1

+ 20?? 2

= 400, 10?? 1

+ 15?? 2

= 450, ?? 1

, ?? 2

= 0

04

(c)Explain the Phases of OR study.

07

Q.2 (a) What is the degeneracy in simplex method? How it can be resolved? 03

(b) Solve the following LPP using graphical method.

???????????????? ?? = 4?? + 5??

Subject to the constraints

?? + ?? = 1, ?? + 2?? = 4, ?? = 4, ?? = 4, ?? , ?? = 0

04

(c) Solve the following LPP using Two phase method.

???????????????? ?? = 60?? 1

+ 48?? 2

Subject to the constraints

4?? 1

+ 2?? 2

= 8, 2?? 1

– 4?? 2

= 6, ?? 1

, ?? 2

= 0

07

OR

(c) Solve the following LPP using BIG ? M method.

???????????????? ?? = 40?? 1

+ 20?? 2

Subject to the constraints

2?? 1

+ 5?? 2

= 48, 8?? 1

+ 5?? 2

= 72, ?? 1

, ?? 2

= 0

07

Q.3 (a) Discuss the Northwest and Least cost method for finding initial basic solution.

Give its advantage and disadvantage.

03

(b) A company has three plants at location A, B and C which produce the same

product. It has to supply this to buyers located at P, Q and R. The weekly plant

capacities for A, B and C are 250, 800 and 350 units respectively, while the

buyer requirements are 700, 200 and 500 for P, Q and R respectively. The unit

shipping costs (in Rs) are given as:

Plant

Buyers

P Q R

A 8 4 10

B 9 7 9

C 6 5 8

Determine the distribution for the company so as to minimize the cost of

transportation using Least Cost Method.

04

Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE – SEMESTER ?VI (NEW) – EXAMINATION ? SUMMER 2018

Subject Code: 2163201 Date: 28/04/2018

Subject Name: Operation Research

Time: 10:30 AM to 01:00 PM Total Marks: 70

Instructions:

1. Attempt all questions.

2. Make suitable assumptions wherever necessary.

3. Figures to the right indicate full marks.

MARKS

Q.1 (a) Discuss in brief the areas of application of Operation Research. 03

(b)Use simplex method to solve following LPP

???????????????? ?? = 45?? 1

+ 80?? 2

Subject to the constraints

5?? 1

+ 20?? 2

= 400, 10?? 1

+ 15?? 2

= 450, ?? 1

, ?? 2

= 0

04

(c)Explain the Phases of OR study.

07

Q.2 (a) What is the degeneracy in simplex method? How it can be resolved? 03

(b) Solve the following LPP using graphical method.

???????????????? ?? = 4?? + 5??

Subject to the constraints

?? + ?? = 1, ?? + 2?? = 4, ?? = 4, ?? = 4, ?? , ?? = 0

04

(c) Solve the following LPP using Two phase method.

???????????????? ?? = 60?? 1

+ 48?? 2

Subject to the constraints

4?? 1

+ 2?? 2

= 8, 2?? 1

– 4?? 2

= 6, ?? 1

, ?? 2

= 0

07

OR

(c) Solve the following LPP using BIG ? M method.

???????????????? ?? = 40?? 1

+ 20?? 2

Subject to the constraints

2?? 1

+ 5?? 2

= 48, 8?? 1

+ 5?? 2

= 72, ?? 1

, ?? 2

= 0

07

Q.3 (a) Discuss the Northwest and Least cost method for finding initial basic solution.

Give its advantage and disadvantage.

03

(b) A company has three plants at location A, B and C which produce the same

product. It has to supply this to buyers located at P, Q and R. The weekly plant

capacities for A, B and C are 250, 800 and 350 units respectively, while the

buyer requirements are 700, 200 and 500 for P, Q and R respectively. The unit

shipping costs (in Rs) are given as:

Plant

Buyers

P Q R

A 8 4 10

B 9 7 9

C 6 5 8

Determine the distribution for the company so as to minimize the cost of

transportation using Least Cost Method.

04

(c) ABC company is engaged in manufacturing 5 brands of packed snacks. It has

five manufacturing setups, each capable of manufacturing any of its brands one

at a time, The costs to make a brand on these setups vary according to

following table.

S1 S2 S3 S4 S5

B1 4 6 7 5 15

B2 7 3 6 9 5

B3 8 5 4 6 9

B4 9 12 7 11 10

B5 7 5 9 8 11

Find the optimum assignment on these setups resulting in the minimum cost?

07

OR

Q.3 (a) Classify the Assignment problem in detail. 03

(b) Solve the following transportation problem using Vogel?s Approximation

Method.

To D1 D2 D3 D4 Available

Units From

F1 10 9 11 10 200

F2 12 10 8 7 60

F3 8 9 11 12 40

Demand 100 50 60 40

[D stands for destination. F stands for factory.]

04

(c) Define the simulation model. Distinguish between deterministic and stochastic

simulation mode.

07

Q.4 (a) Discuss the differences between CPM and PERT. 03

(b) What is critical path? State the necessary and sufficient condition of critical path.

Can a project have multiple critical paths?

04

(c) Determine the critical path for the following network. What is the total time

required for the project. Also find the free float and independent float for each

activity.

Activity 1-2 1-3 2-4 3-4 3-5 4-6 5-6

Duration 2 8 4 1 2 5 6

07

OR

Q.4 (a) Enlist the components of the Queuing System. Define Balking in Queuing

System.

03

(b) What do you mean by Minimum Spanning Tree? Discuss any algorithm for

finding minimum spanning tree.

04

(c) A researcher studying the ?Q? theory at a counter of a railway station has

concluded that the inter-arrival rate at a desk is 3 minutes while the inter-

service, both following Poisson distribution, is 2 minutes. Answer the

following questions using the given facts.

1) What is the average waiting time of a customer in the system?

2) How many customers are there waiting in the queue?

3) The management is ready to start a new counter if the average waiting time

in the system is 8 minutes; find the arrival rate (per hour) of the customers.

07

Q.5 (a) Explain Individual replacement versus group replacement. 03

(b) Determine the age at which the following type of machine be replaced:

Cost price = Rs 8,000

Operating Costs = Rs 1000 for the first Year, increasing by Rs 500 every year

Resale Value = Rs 4000 for first year, decreasing by Rs 500 every year.

04

(c) A company manufactures around 200 mopeds. Depending upon the

availability of raw materials and other conditions, the daily production has

07

Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE – SEMESTER ?VI (NEW) – EXAMINATION ? SUMMER 2018

Subject Code: 2163201 Date: 28/04/2018

Subject Name: Operation Research

Time: 10:30 AM to 01:00 PM Total Marks: 70

Instructions:

1. Attempt all questions.

2. Make suitable assumptions wherever necessary.

3. Figures to the right indicate full marks.

MARKS

Q.1 (a) Discuss in brief the areas of application of Operation Research. 03

(b)Use simplex method to solve following LPP

???????????????? ?? = 45?? 1

+ 80?? 2

Subject to the constraints

5?? 1

+ 20?? 2

= 400, 10?? 1

+ 15?? 2

= 450, ?? 1

, ?? 2

= 0

04

(c)Explain the Phases of OR study.

07

Q.2 (a) What is the degeneracy in simplex method? How it can be resolved? 03

(b) Solve the following LPP using graphical method.

???????????????? ?? = 4?? + 5??

Subject to the constraints

?? + ?? = 1, ?? + 2?? = 4, ?? = 4, ?? = 4, ?? , ?? = 0

04

(c) Solve the following LPP using Two phase method.

???????????????? ?? = 60?? 1

+ 48?? 2

Subject to the constraints

4?? 1

+ 2?? 2

= 8, 2?? 1

– 4?? 2

= 6, ?? 1

, ?? 2

= 0

07

OR

(c) Solve the following LPP using BIG ? M method.

???????????????? ?? = 40?? 1

+ 20?? 2

Subject to the constraints

2?? 1

+ 5?? 2

= 48, 8?? 1

+ 5?? 2

= 72, ?? 1

, ?? 2

= 0

07

Q.3 (a) Discuss the Northwest and Least cost method for finding initial basic solution.

Give its advantage and disadvantage.

03

(b) A company has three plants at location A, B and C which produce the same

product. It has to supply this to buyers located at P, Q and R. The weekly plant

capacities for A, B and C are 250, 800 and 350 units respectively, while the

buyer requirements are 700, 200 and 500 for P, Q and R respectively. The unit

shipping costs (in Rs) are given as:

Plant

Buyers

P Q R

A 8 4 10

B 9 7 9

C 6 5 8

Determine the distribution for the company so as to minimize the cost of

transportation using Least Cost Method.

04

(c) ABC company is engaged in manufacturing 5 brands of packed snacks. It has

five manufacturing setups, each capable of manufacturing any of its brands one

at a time, The costs to make a brand on these setups vary according to

following table.

S1 S2 S3 S4 S5

B1 4 6 7 5 15

B2 7 3 6 9 5

B3 8 5 4 6 9

B4 9 12 7 11 10

B5 7 5 9 8 11

Find the optimum assignment on these setups resulting in the minimum cost?

07

OR

Q.3 (a) Classify the Assignment problem in detail. 03

(b) Solve the following transportation problem using Vogel?s Approximation

Method.

To D1 D2 D3 D4 Available

Units From

F1 10 9 11 10 200

F2 12 10 8 7 60

F3 8 9 11 12 40

Demand 100 50 60 40

[D stands for destination. F stands for factory.]

04

(c) Define the simulation model. Distinguish between deterministic and stochastic

simulation mode.

07

Q.4 (a) Discuss the differences between CPM and PERT. 03

(b) What is critical path? State the necessary and sufficient condition of critical path.

Can a project have multiple critical paths?

04

(c) Determine the critical path for the following network. What is the total time

required for the project. Also find the free float and independent float for each

activity.

Activity 1-2 1-3 2-4 3-4 3-5 4-6 5-6

Duration 2 8 4 1 2 5 6

07

OR

Q.4 (a) Enlist the components of the Queuing System. Define Balking in Queuing

System.

03

(b) What do you mean by Minimum Spanning Tree? Discuss any algorithm for

finding minimum spanning tree.

04

(c) A researcher studying the ?Q? theory at a counter of a railway station has

concluded that the inter-arrival rate at a desk is 3 minutes while the inter-

service, both following Poisson distribution, is 2 minutes. Answer the

following questions using the given facts.

1) What is the average waiting time of a customer in the system?

2) How many customers are there waiting in the queue?

3) The management is ready to start a new counter if the average waiting time

in the system is 8 minutes; find the arrival rate (per hour) of the customers.

07

Q.5 (a) Explain Individual replacement versus group replacement. 03

(b) Determine the age at which the following type of machine be replaced:

Cost price = Rs 8,000

Operating Costs = Rs 1000 for the first Year, increasing by Rs 500 every year

Resale Value = Rs 4000 for first year, decreasing by Rs 500 every year.

04

(c) A company manufactures around 200 mopeds. Depending upon the

availability of raw materials and other conditions, the daily production has

07

been varying from 196 mopeds to 204 mopeds, whose probability is as given

below:

Production(Per

day)196 197 198 199 200 201 202 203 204

Probability 0.05 0.09 0.12 0.14 0.20 0.15 0.11 0.08 0.06

The finished mopeds are transported in 3-storyed lorry that can accommodate

only 200 mopeds. Use the following random numbers: 82, 89, 78, 24, 53, 61,

18, 45, 4, 23, 50, 77, 27, 54, 10. Simulate the mopeds waiting in the factory for

next 15 days.

1. What will be the average no. of mopeds waiting in the factory?

2. What will be the average no. of empty spaces in the lorry?

OR

Q.5 (a)What is simulation? What are the advantages and limitations of simulation?

03

(b) What is replacement problem? Describe some important replacement situations

and policies.

04

(c)A toll booth owner is presently using a manual system having service rate of 10

vehicles per minutes. On an average 8 vehicles are coming in minute. Calculate:

1. Utilization factor of booth operator

2. Idle time for booth operator in a day having working hour of 8 hours

3. Number of persons waiting in the system

4. Number of persons waiting in the queue

5. Average waiting time in the queue

07

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