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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI 600 034
M.Sc.DEGREE EXAMINATION STATISTICS
THIRDSEMESTER APRIL 2018
16PST3ES01- ADVANCED OPERATIONS RESEARCH
Date: 05-05-2018 Dept. No. Max. 100 Marks
Time: 09:00-12:00
SECTION A
Answer ALL questions. Each carries two marks. X 10 20)
1. Define a General Linear Programming Problem.
2. Define duality.
3. Define dynamic programming?
4. What is integer programming problem?
5. Define Non Linear Programming Problem?
6. Define a quadratic programming problem.
7. Give any two reasons for controlling inventory.
8. What are the costs associated with inventory?
9. What is queuing discipline?
10. What do you mean by a deterministic queuing system?
SECTION B
Answer any FIVE questions. Each carries eight marks. X 5 40)
11. Use two-phase simplex method to maximize Z 3 X1 2 X2
subject to the constraints, 2 X1 X2 3 X1 4 X2 12;and X1 X2 0.
12. Derive Gomory's constraint for solving a Mixed Integer Programming Problem.
13. State the need of DPP and explain its characteristics.
14. Test for extreme values of 2 2 2
1 2 3 1 2 3 f x x x x x x subject to the constraints,
x1 x2 3x3=2 and 5 x1 2 x2 x3=5.
15. Using Dynamic Programming Problem, maximize z {y1.y2.....yn} subject to the constraints, y1 y2
+..... yn and yj 0.
16. A corporation is entertaining proposals from its 3 plants for possible expansion of its facilities. The
corporation's budget is £ 5 millions for allocation to all 3 plants. Each plant is requested to submit its
proposals giving total cost C and total revenue R for each proposal. The following table summarizes the
cost and revenue in millions of pounds. The zero cost proposals are introduced to allow for the probability
of not
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allocating funds to individual plants. The goal of the corporation is to maximize the total revenue resulting from the allocation of £ 5 millions to the three plants.
Plant 1
Plant 2
Plant 3
Proposal
C1
R1
C2
R2
C3
R3
1
0
0
0
0
0
0
2
1
5
2
8
1
3
3
2
6
3
9


4


4
12


Use Dynamic Programming Problem to obtain the optimal policy for the above problem.
17. Explain the classical static Economic Order Quantity model and derive the expressions for Total Cost per Unit, order quantity, ordering cycle and effective lead time.
18. Explain the elements of a queuing system.
SECTION C
Answer any TWO questions. Each carries twenty marks. (20 X 2 40)
19. Find an optimum integer solution to the following LPP: Mazimize Z X1 4 X2, subject to the
constraints, 2 X1 4 X2 5 X1 3 X2 15 and X1 X2are non-negative integers.
20. Solve the following Non Linear Programming Problem: Max Z 2 X1- X12 X2, subject to the
constraints, 2 X1 3 X2 2 X1+ X2 and X1 X2
21. Solve the following Quadratic programming Problem, by Wolfe's algorithm.
Max Z 4 X1 6 X2 2 X1 X2 2 X12 2 X22 subject to the constraints,
X1 2 X2 X1 X2 0.
22. Explain the factors affecting inventory control.
For a queuing model in the steady-state case, derive the steady state difference
equations and obtain expressions for the mean and variance of queue length in terms of the
parameters λ and
(10 10)