LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
M.Sc. DEGREE EXAMINATION – STATISTICS
FOURTH SEMESTER – APRIL 2007
AC 54
ST 4807 - ADVANCED OPERATIONS RESEARCH
Date & Time: 20/04/2007 / 9:00 - 12:00
Dept. No.
Max. : 100 Marks
SECTION A
(10 X 2 = 20)
ANSWER ALL QUESTIONS. EACH CARRIES TWO MARKS
1.
2.
3.
4.
5.
6.
7.
8.
What is a pure integer programming problem?
Write down the formula for mixed cut.
What is the basic principle used in Dynamic Programming?
What do you mean by problem of dimensionality?
When do you use e-model in stochastic programming ?
What are soft and hard constraints?
List the assumptions made in single item static model.
Mention how the objective function is expressed at the beginning of each iteration
in Beal’s method.
9. Give two examples for setup cost.
10. What will be your conclusion when the value of the objective function at the end
of Phase 1 is non zero in two-phase simplex method?
SECTION B
(5 X 8 = 40)
ANSWER ANY FIVE. EACH CARRIES EIGHT MARKS
11. Show that the following problem has two optimum solutions :
Maximize : z  2x1  x2 subject to
x1  x2  10
x1  20
x1 , x2  0
12. Describe in detail “Fractional Algortithm”
13. Describe with an example of your choice Branch and Bound Method
14. Explain the method of solving LPP using dynamic programming technique.
15. Explain how constrained non-linear programs are solved.
16. Describe the steps used in Beale’s Method
17. Solve the following inventory problem (Multi item static model with storage
constraint).
i
1
2
3
Ki
10
5
15
i
2
4
4
Assume that A = 25 sq. ft
hi
0.3
0.1
0.2
ai
1 sq. ft
1 sq. ft
1 sq. ft
18. Explain various elements of a queuing model.
SECTION C
(2 X 20 = 40)
ANSWER ANY TWO. EACH CARRIES TWENTY MARKS
19. Explain Capital Budgeting Model. Develop DP solution for the same and
illustrate the solution for the following data :
Plant 1
Plant 2
Plant 3
Proposal
c1
R1
c2
R2
c3
R3
1
3
5
3
4
0
0
2
4
6
4
5
2
3
3
--
--
5
8
3
5
4
--
--
--
--
6
9
20. Solve the following problem by Wolf’s method.
Minimize z  x12  2 x22  2 x1 x 2  2 x1  5x2
Subject to 2 x1  3x2  20
3x1  5x2  4 , x1 , x2  0
21. Kumaravel has Rs.80000/- with him. He wants to buy shares of Lavanya & Co
and Sathish & Co. The following table gives the necessary data.
Share Price
Lavanya & Co
Annual Return
Rs.25/-
Rs.3/-
Risk Index
0.50
Sathish & Co
Rs.50/Rs.5/0.25
Kumaravel wants to have a minimum return of Rs.9000/- and does not like to lose
more than Rs.700/- . Formulate this as a goal programming problem and solve the
same.
22. In the deterministic model with instantaneous stock replenishment, no shortage,
and constant demand rate, suppose that the holding cost per unit is given by h1 for
quantities below q and h2 for quantities above q, h1  h2 . Find the economic lot
size.
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