7/26/2019 Abm 1110 Operations Research, 16-05-2013, May 2013

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Course Code : ABM1110 Reg. No :

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GAYATRI VIDYA PARISHAD COLLEGE OF ENGINEERING (AUTONOMOUS)Madhurawada, Visakhapatnam

Affiliated to JNT University K, KakinadaB.Tech. VI-Semester Regular & Supplementary Examinations, May 2013

Operations Research(Mechanical Engineering)

Date : 16/05/2013 Time : 3 Hours Max. Marks : 60

1.

Question No. 1 is Compulsory.2. Answer any FOURfrom questions 2 to 8.

3. All parts of a Question must be answered in one place to get valued.

1. Answer all the following questions:

a) List out the characteristics of standard form of LPP.

b) What is degeneracy in Transportation problems?c) State the traveling salesman problem.

d) How is the concept of dominance used in simplifying the solution of game.e) List out the various costs involved in EOQ.

f) What are the situations which make the replacement of items necessary?

g) (M/M/1 : / FIFO) indicates.

h) State Bellmans principle of optimality.

2 Mark

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2. Solve the following LPP by using Simplex method.Minimize Z = 3x1+ 8x2

Subject to x180x1+ x2= 200

x260

x1, x20

11 Ma

3. A company has three plants F1, F2, F3from which it supplies to 4 markets ABCD. Determine theoptimal transportation plan from the following table.

Markets

Plant A B C D Supply

F1 13 11 15 20 2

F2 17 14 12 13 6

F3 18 18 15 12 7

Demand 3 3 4 5

Use VAM method for Initial basic feasible solution.

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4. a) Solve the following assignment problemMen

1 2 3 4

Work I 12 30 21 15

II 18 33 9 31III 44 25 24 21

IV 23 30 28 14

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Course Code : ABM1110 Reg. No :

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b) Solve the following game

Player B

Player A

I II III IV V

I 3 5 4 9 6

II 5 6 3 7 8III 8 7 9 8 7IV 4 2 8 5 3

4 Mark

5. Find the sequence that minimizes the total elapsed time required to complete the following tasks.Each job is processed in the order ACB.

Job 1 2 3 4 5 6 7

M/C A 12 6 5 11 5 7 6

M/C B 7 8 9 4 7 8 3

M/C C 3 4 1 5 2 3 4

Also find elapsed time.

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6. a) What are the assumptions in deriving EOQ?b) Alpha industry estimates that it will sell 12,000 units of its product for the forth coming year.

The ordering cost is Rs. 100/- per order and the carrying cost per unit per year is 20% of thepurchase price per unit. The purchase price per unit is Rs. 50/-. Find

(i) Economic order quantity (EOQ)(ii) No. of orders per year

(iii) Time between successive orders.

4 Mark7 Mark

7. A fleet owner finds from his past records that the costs per year of running a vehicle whose

purchase price is Rs. 50,000/- are as under

Year 1 2 3 4 5 6 7

Running cost 5000 6000 7000 9000 11500 16000 18000

Resale value 30000 15000 7500 3750 2000 2000 2000

At what age is a replacement due?

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8. a) Arrivals at a telephone booth are considered to be poisson, with an average time of 10 minutes

between one arrival and the next. The length of a phone call assumed to be distributedexponentially with mean 3 minutes. Then

(i) What is the probability that a person arriving at the booth will have to wait?(ii) What is the average length of the queues that form from time to time?

b) Briefly explain the Dynamic programming algorithm.

6 Marks

5 Marks

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