JOSEPH’S COLLEGE OF COMMERCE (AUTONOMOUS)

END SEMESTER EXAMINATION – MARCH /APRIL 2015

B.COM (T. t.) – VI SEMESTER

OPERATION RESEARCH

Duration: 3 Hours Max. Marks: 100

SECTION – A

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

What is the structure of a Linear Programming Problem?

Mention any Four important features of Operations Research.

In graphical approach of solving a LPP, differentiate between feasible solution and optimum solution.

With the help of a rough graph plot x – y < 0 .

What is a model? How are operation Research Models classified?

How do you treat an unbalanced transportation problem before attempting to solve?

What is an assignment problem? Name the method used to solve.

A customer arrives at a bank counter every three minutes and it requires on an average two minutes for service. Find arrival rate (λ) and service rate (µ)

What is (a) Jockeying

(b) Reneging

10.

Mention any 2 applications of simulation.

SECTION – B

II)

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

11.

A factory is engaged in manufacturing of three products A,B and C for which profits per unit are Rs. 10, Rs.6 and Rs. 4 respectively. The time taken for preparatory work, machining and packing and maximum time available is stated in the table. Determine the most profitable mix, assessing that which is produced can be sold. Formulate the LPP. (Do not solve.)

Time Required (in hrs)

Product	Preparatory Work	Machining	Packing
A	1	10	2
B	1	4	2
C	1	5	6
Time Available (Hrs)	100.	600.	300.

12.

Find the dual of :

Minimize Z= 8x + 4y + 2z

Subject to ,

4x + 2y+ z ≤ 8

3x + 2y ≤10

x + y + z ≥ 5

x + y = 3

Where x, y , z ≥ 0

13.

Mention the different methods used in finding an initial solution to a transportation problem. Which is the most preferable method? Give reasons.

	Warehouses			Plant Capacity
Plants	A	B	C	Plant Capacity
W	12	8	18	400
X	20	10	16	350
Y	24	14	12	150
Warehouse demand	500	200	300

Find IBFS by NWCM. Determine the cost of transportation.

14.

The table below shows the possible assignments of 5 jobs to 5 machines and gives the relative cost. Find the minimum cost assignment.

Machines → Jobs ↓	M1	M2	M3	M4	M5
J1	8	4	2	6	1
J2	0	9	5	5	4
J3	3	8	9	2	6
J4	4	3	1	0	3
J5	9	5	8	9	5

15.

A departmental store has a single cashier. During the rush hours, customers arrive at the rate of 20 customers per hour. The average number of customers that can be processed by the cashier is 24 per hour. Assume that the conditions for the single channel queuing model apply, find the following.

(a) Probability that the cashier is busy.

(b) Probability that you can approach the cashier directly

16.

Seven Star Tours and Travels organize various trips to tourists. Number of trips organized per month varies between 5 to 10 . The number of trips organised and their respective probabilities are given in the table. Using Monte-Carlo simulation technique find the approximate number of trips organised in 6 months.

Random numbers : 67, 84, 01, 77, 90, 14

Trips Organised	5	6	7	8	9	10
Probability	0.10	0.20	0.45	0.10	0.10	0.05

SECTION – C

III)

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

17.

(a) What are the steps to be followed in the OR approach of solving problems.

(b) “ Any real life problem is an OR problem”. In this context explain five techniques of OR. (5+10)

18.

Solve the following LPP by graphical method.

Min Z = 20x + 40y

Subject to constraints,

36x + 6y ≥ 108

3x + 12y ≥ 36

20x + 10y ≥ 100

Where x, y ≥ 0

19.

Solve the following transportation problem using Vogel’s approximation method and MODI method to find minimum cost of transportation.

Direct Source	D1	D2	D3	D4	Supply
S1	19	30	50	10	7
S2	70	30	40	60	9
S3	40	8	70	20	18
Demand	5	8	7	14

20.

Using Hungarian Method find the optimum assignment schedule and the minimum cost of assignment.

	P	Q	R	S	T
A	10	5	9	18	11
B	13	9	6	12	14
C	3	2	4	4	5
D	18	9	12	17	15
E	11	6	14	19	10

21.

At The Family Doctor Clinic patients arrive at an average of 6 patients per hour. The clinic is attended by Dr. Satyanarayan. Some come for minor check up while some others require thorough inspection for the diagnosis. The doctor can check 10 patients per hour on an average . It can be assumed that arrivals follow Poisson Distribution and doctor’s inspection time follows an exponential distribution Determine.

(i) The percentage of time that a patient can walk to the doctor without having to wait.

(ii) The expected average number of patients in the system and the queue.

(iii) The expected average waiting time (in minutes) of a patient in the system and the queue.

(iv) The average time the doctor is free on a 7 hours working day.

SECTION – D

IV)

Case Study (1×15=15)

22.

A flight is scheduled to leave from Delhi to Hyderabad at 10 a.m The pattern of departure of the flight is as follows:

Delay in minutes	0	5	10	15	20	25	30
Probability	0.25	0.15	0.10	0.06	0.10	0.20	0.14

The flight normally takes 75 minutes, but actual time varies as follows:

Actual flight time in minutes	70	75	77	78	80
Probability	0.20	0.20	0.25	0.15	0.20

If the scheduled time of arrival at Hyderabad is 11.a.m Using Monte Carlo method of simulation find out the arrival time for 8 consecutive days. How many days do flights arrive after 11.30 and how many reach before 11.10 ?

Random no for Delay in minutes	28	57	60	17	64	20	27	58
Random no for Actual Flight time	28	29	83	58	41	18	67	16

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