ST. JOSEPH’S COLLEGE OF COMMERCE (AUTONOMOUS)

END SEMESER EXAMINATION – MARCH/APRIL 2016

B.Com (T.T.) – VI SEMESTER

C2 12 602: OPERATION RESEARCH

Duration: 3 Hours Max. Marks: 100

SECTION – A

Answer ALL the questions. Each carries 2 marks. (10×2=20)

Give the meaning of Operation Research.

What do you mean by a “feasible solution” in a transportation problem? State any 3 methods of obtaining IBFS.

What is an unbounded solution and a redundant solution of a LPP?

What is a loop in transportation problem? Draw any 2 types of loops.

Explain the term unbalanced and degenerancy in a Transportation Problem.

What is an assignment problem?

The Customers arrive at a booking office window every 2 minutes. It takes 1 minute for the person to serve the customer. Find Arrival rate and service rate of the queing system.

State the advantages of simulation.

Mention the steps involved in formulation of LPP.

10.

List any 4 areas of LPP applications.

SECTION – B

II)

Answer any FOUR questions. Each carries 5 marks. (4×5=20)

11.

A firm produces two spare parts A and B using milling machine and grinding machine. The machine time required for each spare part and machine time available for each machine are given in the following table. The profit on selling each spare part is also given:

Machines	Time required per unit for		Maximum time available per day
Machines	Spare part A	Spare part B	Maximum time available per day
Milling machine	10 minutes	5 minutes	2500 minutes
Grinding machine	4 minutes	10 minutes	2000 minutes
Profit per spare part	Rs.50	Rs.100

Formulate a linear programming problem such that the number of spare parts A and B manufactured per week maximizes the profit.

12.

Explain the scope of Operation Research.

13.

Determine the initial basic feasible solution for the following Transportation problem by Least Cost method. The table given transportation cost from origins to destinations in ‘000s of rupees.

		Warehouses			Availabilities
		W1	W2	W3	Availabilities
Factories	F1	9	8	16	120
	F2	15	10	17	80
	F3	3	9	12	80
Requirements		150	80	50	280

14.

A company has 4 salesmen A, B, C and D. These salesmen are to be allotted to 4 districts1, 2, 3 and 4. The estimated profit per day for each salesman in each district is given in the following table. What is the optimal assignment which will yield maximum profit?

	1	2	3	4
A	16	10	14	11
B	14	11	15	15
C	15	15	13	12
D	13	12	14	15

15.

In a drive-in restaurant the arrivals follow Poisson distribution with an average of 2 cars in every 15 minutes. The restaurant can serve the customers at the rate of 5 minutes per customer and obey exponential probability distribution. Find out a) The probability that the service is idle.

b) Expected time that the customer has to spend in the queue.

c) Average length of the queue.

16.

The daily production of mopeds in a factory varies from 146 to 154 depending upon the availability of raw material and other working conditions. The associated probabilities for various levels of production are highlighted in the following table:

Production per day	146	147	148	149	150	151	152	153	154
Probability	0.04	0.09	0.12	0.14	0.11	0.10	0.20	0.12	0.08

The finished mopeds are transported in a specially designed lorry accommodating only 150 mopeds to the maximum. If there is any excess moped produced over and above 150, they cannot find space in the lorry and hence can be carried over to the next day’s lorry for transport. Using the following random numbers 43, 18, 26, 10, 12 simulate the production levels for 5 days and obtain the answer to the following questions:

a) What is the average number of mopeds waiting in the factory?

b) What will be the average number of empty spaces on the lorry?

SECTION – C

III)

Answer any THREE questions. Each carries 15 marks. (3×15=45)

17.

a) “Model building is the essence of OR approach”. Describe the classification of models in detail.

b)Explain the features of Operation research

(10+5)

18.

Plot a graph for the following constraints, Identify the feasible region and the Optimum solution of the LPP.

Max Z= 3x + 4y

Subject to constraints,

3x + y >= 6

x + y <=8

y<=4

x>= 2

where x, y >=0

19.

Determine the initial basic feasible solution for the following transportation problem by Vogel’ Approximation Method and also find optimal solution by MODI method.

Origins	Destinations			Availabilities
Origins	D1	D2	D3	Availabilities
O1	2	8	7	100
O2	10	11	12	90
O3	5	6	9	60
O4	8	3	5	100
Requirements	80	120	150	350

20.

Given the following cost matrix obtain the minimum operation time cost. Also state the optimum assignment using Hungarian method.

Men -> Task	I	II	III	IV	V
A	1	3	2	3	6
B	2	4	3	1	5
C	5	6	3	4	6
D	3	1	4	2	2
E	1	5	6	5	4

21.

In a market analysis, the following information was collected. Simulate for 6 trials . Workout the average profit.

RN for Selling Price – 78, 43, 92, 87, 47, 83

RN for Unit Cost – 23, 08, 28, 17, 73, 87

RN for sales volume – 58, 86, 62, 06, 03, 52

Selling Price	Prob.	Unit Cost	Prob.	Sales Volume	Prob.
35	0.30	30	0.40	800	0.15
45	0.40	35	0.25	650	0.45
50	0.20	40	0.15	500	0.30
55	0.10	45	0.20	450	0.10

SECTION – D

IV)

Case Study – Compulsory question. (1×15=15)

22.

A departmental store has a single cashier. During the rush hours, customers arrive every 3 minutes. The average number of customers that can be processed by the cashier is 24 per hour. Assuming that the conditions for the single channel queuing model apply, find the following

a) Utilization rate

b) Probability that the cashier is idle

c) Average number of customers in the queuing system.

d) Average time a customer spends in the system.

e) Average number of customers in the queue.

f) Average time a customer spends in the queue waiting for service.

g) The number of hours the cashier is idle if he works from 9am to 6pm.

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