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IMT 25 Operation Research M2

PART – A

Q1. State the different types of models used in operation research? Explain briefly the general

method for solving these O.R models?

Q2. Customer arrives at sales counter by a poison process with a mean rate of 20 per hr. The time

required to serve a customer has an exponential distribution with a mean of 100 seconds. Find the

average waiting & queue length of customer.

Q3. Obtain the optimal strategy for both persons & the value of game:

B1

B2

A1

1

-3

A2

3

5

A3

-1

6

A4

4

1

A5

2

2

A6

-5

0

Q4. Prepare network, activity time estimates, determine the expected project completion time &

variance.

Activity

Time estimates (days)

to

Tm

tp

1-2

5

8

17

1-3

7

10

1

2-3

3

5

7

2-4

1

3

5

3-4

4

6

8

3-5

3

3

3

4-5

3

4

5

5. What is queuing theory? Discuss the service mechanism in queuing theory.

PART – B

Q1. Determine a sequence for the 5 jobs that will minimize the elapsed time.

Job

1

2

3

A

5

1

9

B

2

6

7

Q2. What is meant by optimality test in a transportation problem? How would you determine

whether a given transportation solution is optimal or not?

Q3. OR advocates a system approach and its procedure is concerned with optimization. Discuss.

Q4. Discuss the importance and applications of PERT and CPM in project planning and control.

Q5. Write short notes on n- Johnson’s algorithm for n jobs m machines

PART – C

Q1. Solve the following transportation problem by VAM:

1

2

3

Supply

1

5

1

7

10

2

6

4

6

80

3

3

2

5

15

Demand

70

20

50

Q2. Write short notes on :

a) Failures in replacement theory.

b) Decision tree analysis.

Q3. The maintenance cost & resale value per year of machine whose purchase price is Rs 7000 is given

below:

Yr 1 2 3 4

Maintenance cost 900 1200 1600 2100

Resale value 4000 2000 1200 600

When should the machine be replaced?

Q4. Specify the characteristics of M/M/1 queue model.

Q5. Discuss the following terms in game theory: Saddle point; Pure strategy; Two person zero sum game;

Principle of dominance.

CASE STUDY – I

A firm manufactures three products A,B,C the profits are RS 3, Rs 2, & Rs 4respectively. The firm has

two machines M1& M2 and below given is the required processing time in minutes for each machine on

each product

MACHINE

PRODUCT

A

B

C

M1

4

3

5

M2

2

2

4

Machines M1 & M2 have 2000 & 2500 machine minutes respectively. The firm must manufacture 100 A’s, 200

B’s & 50 C’s, but not more than 150 A’s. Set up an LPP to maximize profits.

CASE STUDY II

A fruit vendor purchases fruits for Rs 3 a box and sells for Rs 8 a box. The high markup reflects the

perish ability of the fruit and the great risk of stocking it., the product has no value after the

first day it is offered for sale. The vendor faces the problem of how many boxes to order for

tomorrow’s business. A 90 day observation of the past sales gives the following information.

Daily Sales

No. of days sold

Probability

10

11

12

13

Total

18

36

27

9

90

.20

.40

.30

.10

1.00

Determine the number of boxes he should order to maximize its profit. Also find the expected monetary

value and regret table.

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