LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – STATISTICS

AC 54

FOURTH SEMESTER – APRIL 2007

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. What is a pure integer programming problem?
2. Write down the formula for mixed cut.
3. What is the basic principle used in Dynamic Programming?
4. What do you mean by problem of dimensionality?
5. When do you use e-model in stochastic programming ?
6. What are soft and hard constraints?
7. List the assumptions made in single item static model.
8. 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

 

1. Show that the following problem has two optimum solutions :

Maximize : subject to

 

 

 

1. Describe in detail “Fractional Algortithm”
2. Describe with an example of your choice Branch and Bound Method
3. Explain the method of solving  LPP using dynamic programming technique.
4. Explain how constrained non-linear programs are solved.
5. Describe the steps used in Beale’s Method
6. Solve the following inventory problem (Multi item static model with storage constraint).

 

 

1        10        2          0.3       1 sq. ft

2        5          4          0.1       1 sq. ft

3        15        4          0.2       1 sq. ft

 

Assume that = 25 sq. ft

 

 

1. Explain various elements of a queuing model.

 

 

SECTION C

(2 X 20 = 40)

 

ANSWER ANY TWO. EACH CARRIES TWENTY MARKS

 

 

1. 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

 

 

1. Solve the following problem by Wolf’s method.

Minimize

Subject to

,

1. 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      Annual Return                        Risk Index

 

Lavanya & Co             Rs.25/-             Rs.3/-               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 for             quantities below q and for quantities above q, . Find the economic lot     size.

 

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