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Friday, May 30, 2008

OPERATIONS RESEARCH - OR Paper 2 interview-questions

Download FREE Information Technology Engineering (IT Engg. Branch) Previous 5 Years solved Regular and Reappear Question Papers B.tech PTU 6th / 7th Semester (2007, 2006, 2005, 2004, 2003) and related Placement HR - Technical Interview Questions for subject OPERATIONS RESEARCH - OR

OPERATIONS RESEARCH 6/7th Semester ME 311 (MAY 2005)
I

  1. What are the main characteristics of operations research?
  2. Define a feasible region.
  3. When does simplex method indicate that the LPP has unbounded solution?
  4. What do you mean by degeneracy in transportation problem?
  5. What is Dynamic Programming?
  6. Define a Critical Activity.
  7. Distinguish between PERT and CPM
  8. Define a Queue
  9. Solve the game whose pay-off matrix is

Fig. 1

Player B

B1 B2 B3


(These Figures are Not Available)

  1. Write the dual of the following problem:

Maximize z=20x1 + 40x2
Subject to 2x1 + 20x2 =40
20x1 + 3x2 =20
4x1 + 15x2 =30
x1, x2 ≥ 0
II Use two-phase Simplex method to
Maximize z=5x1 - 4x2 +3 x3
Subject to 2x1 + x2 - 6x3 =20
6x1 + 5x2 +10 x3≤ 76
8x1 -3x2 + 6 x3≤ 50 and x1, x2 x3, ≥ 0
III Find the optimum solution to the following transportation problem:

Fig. 2

Factory

Warehouse

Capacity


D

E

F

G


A

42

48

38

37

160

B

40

49

52

51

150

C

39

38

40

43

190

Demand

80

90

116

160


IV At a central warehouse, vehicles arrive at the rate of 18 per hour and arrival rate follows Poisson distribution. The unloading time of the vehicle follows exponential distribution and he unloading rate is 6 vehicles per hour. There are 4 unloading crews. Find the following:

  1. Probability of having zero vehicles
  2. Average number of vehicles waiting in the queue and in the system.
  3. Average waiting time of the vehicles in queue and in the system.

V The annual demand for a component is 7200 units. The carrying cost is Rs. 500/ unit/ year, the ordering cost is Rs. 1500 per order and the shortage cost is Rs. 2000/ unit / year. Find the optimum value of:

  1. Economic order quantity
  2. Maximum inventory
  3. Maximum shortage quantity
  4. Inventory period
  5. Cycle time.

VI Solve the following sequencing problem, giving an optimal solution when passing is not allowed. What is the total elapsed time?

Fig. 3

Machine

Processing Time in Hours

Job

M1

M2

M3

M4

1

20

3

3

25

2

12

5

1

11

3

18

4

2

10

4

17

2

4

28

VII With the help of the information given in the table below, find out the critical path, earliest start and finish time, latest start and finish time of each event. Also calculate the total slack of each activity.

Fig. 4

Activity

Duration

Immediate Predecessor

1-2

6

-

1-3

8

-

2-3

3

1-2

3-4

4

1-3,2-3

3-6

12

1-3,2-3

3-5

10

1-3,2-3

2-4

8

1-2

4-6

8

2-4,3-4

5-6

6

3-5

5-7

12

3-5

6-7

8

4-6,3-6,5-6

7-8

7

6-7,5-7

VIII The data for the project is given below:

Fig. 5

Activity

Preceding Activity

Time (weeks)

Cost (Rs)

Normal

Crash

Normal

Crash

A

-

3

2

18000

19000

B

-

8

6

600

1000

C

B

6

4

10000

12000

D

B

5

2

4000

10000

E

A

13

10

3000

9000

F

A

4

4

15000

15000

G

F

2

1

1200

1400

H

C,E,G

6

4

3500

4500

I

F

2

1

7000

8000

    1. Draw the network diagram and find the critical path.
    2. If a dead line of 17 weeks is imposed for completion of he project, what activities will be crashed, what would be he additional cost, and what would be he critical activities o the network of the crashing?

IX A company is dealing with newly invested telephone device is faced with the problem of the following strategies:

  1. manufacture the device itself
  2. to be paid on royalty basis by another manufacturer
  3. sell the rights for its invention for a lumpsum.

The profit in thousand of rupees that can be expected in each case and the associated probabilities with the sales volume is shown in table:

Fig. 6

Event

Probability

Manufacture
Itself

Royalties

Sell the rights

High demand

0.2

100

40

20

Medium demand

0.3

30

25

20

Low demand

0.5

-10

15

20

  1. Represent the company’s problem in the form of a decision tree.
  2. Extend the diagram further for the following information:
  3. If the company manufactures itself and the sales are medium and high, it has he opportunity of developing a new version of its telephone.

(ii) Past experience says there is 60% chance of successful development.
(iii) If the cost of development is Rs. 20 and the profits are Rs. 35 and Rs. 10 for high and medium demand respectively.
All monetary values are in thousands.

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