Loyola College M.Sc. Statistics April 2009 Advanced Operations Research Question Paper PDF Download

     LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – STATISTICS

YB 49

FOURTH SEMESTER – April 2009

ST 4807 – ADVANCED OPERATIONS RESEARCH

 

 

 

Date & Time: 23/04/2009 / 9:00 – 12:00  Dept. No.                                                    Max. : 100 Marks

 

 

SECTION -A                                                                                                                                 

Answer all the questions                                                                  10 x 2 = 20 marks

 

  1. When a solution to an LPP is called infeasible?
  2. How dual simplex method differs from other simplex methods ?
  3. Define holding and penalty costs.
  4. Write basic components of a queuing model.
  5. Write the significance of integer programming problem.
  6. Define Dynamic Programming Problems.
  7. Differentiate goal programming from other programming problems.
  8. Write a note on complementary slackness condition.
  9. Provide any two  applications for parallel  and sequence service systems.
  10. For a single item static model if D = 100 , h = $0.02 , K = $100 and lead

time is 10 days,find the economic order quantity and re order point.

 

                                                                SECTION -B                                                                                                                                 

Answer any five questions                                                                 5 x 8 = 40 marks

 

  1. Use the graphical method to solve the following LPP:

Maximize Z = 2x1 + 3x2

Subject to the constraints:                                                                                                           x1 + x2 ≤ 30 ,  x1 – x2 ≥ 0 , x2 ≥ 3 , 0≤ x1 ≤ 20 and 0 ≤ x2 ≤ 12.

  1. Write big M method algorithm.
  2. Use duality to solve the following LPP:

Maximize Z = 2x1 + x2

Subject to the constraints:

x1 + 2x2 ≤ 10  ,   x1 + x2 ≤ 6 ,  x1 – x2 ≤ 2 , x1 – 2x­2 ≤ 1 ; x1,x2 ≥ 0 .

  1. Write briefly about inventory management.
  2. Derive the steady state measures of (M/M/1) : (GD/∞/∞) queuing model.
  3. Write Beale’s algorithm to solve Quadratic Programming Problem.
  4. Obtain the set of necessary and sufficient conditions  for the following NLPP.

Minimize Z = 2x12 – 24x1 + 2x22 – 8x2 + 2x32 – 12x3 + 200

Subject to the constraints:

x1 + x2 + x3 = 11 ,  x1,x2, x3 ≥ 0 .

  1. Solve the following NLPP using Kuhn- Tucker conditions :

Maximize Z =  –x12 – x22 – x32 + 4x1 + 6x2

Subject to the constraints:

x1 + x2  ≤ 2  ,   2x1 + 3x2 ≤ 12 ; x1, x2 ≥ 0

 

 SECTION -C                                                                                                                              

Answer any two questions                                                                    2x 20 = 40 marks

 

19.(a) Use two-phase simplex method to

Maximize Z =  5x1 + 8x2

Subject to the constraints:

3x1 + 2x2 ≥ 3 , x1 + 4x2 ≥ 4 , x1 + x2 ≤ 5 ; x1, x2 ≥ 0

 

  • Use dynamic programming to solve:

Minimize Z = x12 + 2x22 + 4x3

Subject to the constraints:

x1 + 2x2 + x3 ≥ 8 ;  x1 ,x2 , x3 ≥ 0.

(12 + 8 )                                                                 20(a)  Derive probabilistic EOQ model.

 

(b)  Electro uses resin in its manufacturing process at the rate of 1000 gallons

Month. It cost Electro $100 to place an order for a new shipment .The holding

Cost per gallon per month is $2 and the shortage cost per gallon is $10.Historical

data show that the demand during lead time is uniform over the  range(0, 100)

gallons. Determine the optimum ordering policy for Electro.

(10 + 10)

  1.    Use Wolfe’s method to solve the following QPP:

Maximize Z = 6x1 + 3x2 – 4x1x2 – 2x12 – 3x22

Subject to the constraints:

x1 + x2 ≤ 1  ,  2x1 + 3x2 ≤ 4 ; x1, x2 ≥ 0 .

 

  1. Use cutting plane algorithm to solve the following LPP:

Maximize Z = 200x1 + 400x2 + 300x3

Subject to the constraints:

30x1 +  40x2 + 20x3 ≤  600

20x1 + 10x2 + 20x3  ≤  400

10x1 + 30x2 + 20x3  ≤  800

x1, x2, x3 ≥ 0  and are integers.

 

 

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