Code: A-33 Subject: OPERATIONS RESEARCH

Time: 3 Hours Max. Marks: 100

 

NOTE: There are 11 Questions in all.

      Question 1 is compulsory and carries 16 marks. Answer to Q. 1. must be written in the space provided for it in the answer book supplied and nowhere else.

      Answer any THREE Questions each from Part I and Part II. Each of these questions carries 14 marks.

      Any required data not explicitly given, may be suitably assumed and stated.

 

 

 

Q.1 Choose the correct or best alternative in the following: (2x8)

a.       What is the value of the Game

PLAYER B

PLAYER A

 

2

6

 

(A) 4. (B) 3.

(C) 2. (D) 1.

b. The average expected waiting time of a customer in the M/M/1 queue with arrival rate and service rate is given by

(A) . (B) .

(C) . (D) .

c. A particular product has an annual demand of 9000 units / year. The ordering cost is Rs.100 / order and the inventory carrying cost is Rs.2.40 / year. The number of orders per year in EOQ model is

 

(A)    10. (B) 10.4.

(C) 12. (D) 13.5.

 

d. In PERT / CPM the process of making a review and adding necessary clarifications to the next work is called

 

(A)    updating. (B) queueing.

(C)    transporting. (D) duality.


e. An OR model that makes use of a set of mathematical symbols to represent the decision variables of the system under study is

 

(A) iconic model. (B) deterministic model.

(C) analogue model. (D) symbolic model.

 

f. If arrival rate is per minute and service rate per minute in a M/M/1 queue, then Average queue length is

 

(A)     2. (B) 1.5.

(C) 1. (D) 2.5.

 

g. An activity having Zero total float is called

 

(A) critical activity. (B) network activity.

(C) slack activity. (D) critical path.

h. ABC Analysis is a

 

(A)    quantitative control of machines.

(B)    selective control of inventory.

(C)    quantitative control of inventory.

(D)    financial control technique.

 

PART I

Answer any THREE Questions. Each question carries 14 marks.

 

Q.2 a. Define OR and explain the use of inter-displinary teams as a characteristic of OR. (7)

 

b. Model building is the essence of OR approach Discuss. (7)

Q.3 a. Give the meaning and use of the dual programme of L.P. Model? (5)

 

Maximise

Subject to
 
b. Construct the dual of the problem

(9)

Q.4 A colliery working one shift per day uses large number of locomotives which break down at random intervals. On an average one failing per 8 hour shift. The fitter carries out a standard maintenance schedule on each faulty locomotive. Each of the five main parts of this schedule takes an average of hour but the time varies widely.

(i)                  How much time on average per shift will the fitter have for other tasks?

(ii)                What is the average time a locomotive is out of service? (14)

Q.5 Solve the following transportation problem. (14)

DESTINATIONS

 

 

1

2

3

4

AVAILABILITY

SOURCES

1

21

16

25

13

11

 

2

17

18

14

23

13

 

3

32

27

18

41

19

REQUIREMENTS

 

6

10

12

15

43

 

Q.6 a. Explain selective control of Inventory. (4)

 

b.      Find the optimal order quantity for a product for which the price breaks are as follows:

Quantity

Unit Cost (Rs.)

0 < q < 500

Rs. 10

500 q < 750

Rs.9.25

750 q

Rs.8.75

 

 

 

The monthly demand for the product is 200 units, storage cost is 2% of the unit cost and cost of ordering is Rs.100. (10)

PART II

Answer any THREE Questions. Each question carries 14 marks.

 

Q.7 A project is represented by the network shown in the figure. The activity times (in weeks) are given below:-

 

Activity

A

B

C

D

E

F

G

H

I

Optimistic Time

5

18

26

16

15

6

7

7

3

Most Likely Time

8

20

33

18

20

9

10

8

4

Pessimistic Time

10

22

40

20

25

12

12

9

5

 
 

 

 

 

 

 

 

 

 


Determine the following:-

 

(i)                  Expected task time and their variances.

(ii)                The earliest and latest occurrence times of each event.

(iii)               The critical path. (14)

 

Q.8 a. Define Game Theory and list the basic assumptions in it. (4)

b. Reduce the following game by dominance property and solve it. (10)

 

PLAYER B

PLAYER A

 

1

2

3

4

5

I

1

3

2

7

4

II

3

4

1

5

6

III

6

5

7

6

5

IV

2

0

6

3

1

 

Q.9 A library wants to improve its services in terms of the waiting time of its borrowers. The library has two counters at present and borrowers arrive according to Poisson process with arrival rate 1 every 6 minutes and service time follows exponential distribution with a mean of 10 minutes. The library has relaxed its membership rules and substantial increase in the number of borrowers is expected. Find the number of additional counters to be provided if the arrival rate is expected to be twice the present value and the average waiting time of the borrower must be limited to half the present value. (14)

Q.10 a. Distinguish between Individual Replacement Policy and Group Replacement Policy. (5)

 

b. Let p(t) be the probability that any machine in a group of 30 machines would have a life of t units of time. The cost of repairing a broken machine is Rs.200. Preventive maintenance is performed by servicing all the 30 machines at the end of T units of time. Preventive maintenance cost is Rs.15 per machine. Find optimal T which will minimise the expected total cost per period of servicing given that: (9)

 

t

1

2

3

4

5

6

p(t)

0.03

0.04

0.05

0.06

0.07

0.08

 

 

 

 

 

 

 

t

7

8

9

10

11

12

p(t)

0.09

0.10

0.11

0.12

0.13

0.12

Q.11 Write short notes on any TWO of the following :

 

(i) EOQ

(ii) PERT.

(iii) Computers and OR.

(iv) Goal Programming. (7 x 2=14)

 

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