St. joseph’s college of commerce (autonomous)

End semester examination – MARCH / april 2012

MIB – II SEMESTER 

Operations Research

Time: 3 hours                                                                                                                           Marks: 100

SECTION – A

I   Answer any SEVEN  questions. Each carries FIVE  marks.                             (7 X 5 = 35)

1. A city police department has the minimal daily requirement for policemen.

Time of the day (24 hours clock)	Period	Minimum number Of policemen required
2-6	1	20
6-10	2	50
10-14	3	80
14-18	4	100
18-22	5	40
22-2	6	30

Period1 follows immediately after period6. Each policeman works for 8 consecutive hours. Formulate the linear programming problem to find the optimum daily manpower schedule. (do not solve.)

2. Use graphical method to solve the following Linear Programming Problem.

Minimize Z= 40x + 24y

Subject to constraints

20x+50y>=4800

80x+50y>=7200

Where x, y  >=0

3. A company has three factories at Amethi, Bagathpur and Gwalior and four distribution centers at Allahabad, Bombay, Calcutta and Delhi. With identical cost of production at three factories and only variable cost involved is transportation cost . the production at three factories is 50 tons, 60 tons and 25 tons resp. The demand at four distribution centers is 60,40,20 and 15 tons resp. The transportation costs per ton from different factories to different centers are given below. Suggest the transportation schedule using VAM method.

Distribution Center -> Factory	Allahabad	Bombay	Calcutta	Delhi
Amethi	3	2	7	6
Bagathpur	7	5	2	3
Gwalior	2	5	4	5

 

4. Briefly explain the essential features of game theory.
5. What is an assignment problem? How does Hungarian method arrive at optimum solution. Give a brief outline.
6. Solve the following game by dominance principle.

Firm B à Firm A	B1	B2	B3	B4
A1	35	65	25	5
A2	30	20	15	0
A3	40	50	0	10
A4	55	60	10	15

 

7. Construct the network diagram for the following project. Identify the critical path and project duration.

Activity	Duration (week)
1-2	5
1-3	2
2-4	3
3-6	4
4-5	2
4-6	4
5-7	7
6-7	6

 

8. What is queuing theory? Mention some common queuing situations describing the arrivals in queue and service process.
9. In a petropure service station, customers purchasing petrol receive a discounted car wash depending on the quality of petrol they buy. The automatic car wash bay can accommodate one car at a time and it requires a constant time of 4 mins for a wash. Cars arrive at the car wash facility at an average rate of 10 per hour.(poisson arrival). The service station manager wants to determine the average length of the queue and the average waiting time at the car wash.
10. Discuss the role of Simulation in Operations Research.

 

 

 

 

SECTION – B

III   Answer any THREE questions. Each carries FIFTEEN marks.                     (3 X15 = 45)

11. Solve the following LPP by problem by Simplex Method.

Maximize Z= 10x +15y +20z

Subject to

2x+4y+6Z<=24

3x+9y+6z<=30

Where x, y,z >=0

12. Solve the following Transportation problem using NWCM  and  MODI method. What is the minimum transportation cost? Does the problem have multiple solution? ( The numbers in the table indicate the transportation cost per unit.)

Stores  -> Warehouses	P	Q	R	Supply
A	7	4	1	35
B	3	9	8	30
C	5	4	2	35
Demand	10	60	30	100

 

13. Pleasant Travels has one car at each of the depots P, Q, R, S, T. A customer requires a car in each city namely A,B,C,D,E. Distance in kilometers between depots and cities are given in the following distance matrix. How should the cars be assigned to customers so as to minimize the distance travelled. Solve by Hungarian method.

Depots –> Cities	P	Q	R	S	T
A	160	130	175	190	200
B	135	120	130	160	175
C	140	110	155	170	185
D	50	50	80	80	110
E	55	35	70	80	105

 

14. In a market analysis, the following information was collected.

Selling Price	Probability	Unit Cost	Prob	Sales Volume	Prob	Advertising Cost	Prob
350	0.30	300	0.40	80,000	0.15	25 Lakhs	0.25
450	0.40	350	0.25	65,000	0.45	20 Lakhs	0.25
500	0.20	400	0.15	50,000	0.30	18 Lakhs	0.25
550	0.10	450	0.20	45,000	0.10	15 lakhs	0.25

Workout the average profit and probability of profit more than Rs.50,000.

Use the following random numbers-

Selling price- 78, 43, 92, 87, 47, 83, 67, 19, 52, 05

Unit Cost- 23, 08, 28, 17, 73, 87, 28, 37, 32, 02

Sales volume- 58, 86, 62, 06, 03, 52, 19, 30, 29, 04

Advertising Cost- 21, 93, 15, 27, 06, 05, 57, 08, 62, 85

15. What are the different types of Operations research models. Briefly explain any ten OR techniques.

Section – C

III) Compulsory Question.                                                                                        (1X20=20)

16. a) State the differences between PERT and CPM.
17. b) Draw the network diagram of the following Find the earliest and latest times of each event. Identify the critical path and expected project duration. Calculate all floats.

Activity	Duration (days)
1-2	10
2-3	2
2-5	6
3-4	12
3-7	9
4-5	8
4-6	5
4-8	10
5-8	4
6-7	0 ( dummy)
7-9	7
8-10	5
9-11	8
10-11	10

 

 

 

 

 

 

 

(5 + 15)

 

 

 

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