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M.B.A. DEGREE EXAMINATION, JUNE 2010
Second Semester
BA 9226 APPLIED OPERATIONS RESEARCH FOR MANAGEMENT
(Regulation 2009)
Time : Three hours Maximum : 100 MarksAnswer ALL Questions
PART A (10 2 = 20 Marks)
1. Write down the standard form of a LP problem.
2. List the applications of operation research model.
3. Distinguish between a transportation problem and assignment
problem.
4. What do you understand by Travelling Salesman Problem?
5. Define Mixed strategy in a game.
6. What is meant by mixed integer programming problem?
7. Name the inventory control systems adopted in practice.
8. Define simulation.
9. What is meant by group replacement policy?
10. List the components of a queueing system.
PART B (5 16 = 80 Marks)
11. (a) A firm produces three products. These products are
processors on three
different machines. The time required to manufacture one of each
three
products and the daily capacity of the three machines are given
below :
Machine Time per
(minutes)
Product Machine Capacity
1 2 3 Minutes/day
M1 4 5 4 460
M2 5 - 4 480
M3 4 6 - 450
It is required to determine the daily number of units to be
manufactured
for each product. The profit per unit for product 1, 2 and 3 is
Rs. 50
Rs. 40 and Rs. 70 respectively. It is assumed that all the
products
produced are consumed in the market. Formulate a LP model
maximize
the daily profit also determine the optimum production. (16)
Or
(b) (i) Find the maximum value of (12)
2 1 3 2 x x z + =
Subject to :
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. y graphicall solve , 20 0
0
12
3
301
2 1
2
2
2 1
+
x
x x
x
x
x x
(ii) Write the dual for the problem (4)
Minimize 4 3 2 1 3 2 x x x x z + + =
Subject to :
0 , , ,
10 2
20 3 2
15 3 2
4 3 2 1
4 3 2 1
3 2 1
3 2 1
+ + +
= + +
+ +
x x x x
and x x x x
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x x x
x x x
12. (a) Find the basic feasible solution of the following
transportation problem
by VAM. Also find the optimal transportation plan (16)
1 2 3 4 5 AvailableA 4 3 1 2 6 80
B 5 2 3 4 5 60
C 3 5 6 3 2 40
D 2 4 4 5 3 20
Required 60 60 30 40 10 200 Total
Or
(b) (i) Explain transshipment model. (6)
(ii) A company has surplus truck in each of the cities A,B,C,D
and E
and one deficit truck in each of the cities 1,2,3,4,5 and 6.
The
distance between the cities in kilometers in shown in matrix
below.
Find the assignment to trucks from cities in surplus to cities
in
deficit so that the total distance covered by vehicle is
minimum. (10)
1 2 3 4 5 6
A 12 10 15 22 18 8
B 10 18 25 15 16 12
C 11 10 3 8 5 9
D 6 14 10 13 13 12
E 8 12 11 7 13 10
13. (a) (i) Solve the following 2 n game by method of sub - game
(8)
Player B
B1 B2 B3
Player A
A1 1 3 11
A2 8 5 2
(ii) Reduce the following game by dominance property and solve
it (8)
Player B
1 2 3 4 5
I 1 3 2 7 4
Player A II 3 4 1 5 6
III 6 5 7 6 5
IV 2 1 6 3 1
Or
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(b) Explain the branch and bound and cutting plane algorithms
for pure and
mixed integer programming problem. (16)
14. (a) (i) Explain decision making under uncertainty. (4)
(ii) A company has a demand of 12,000 unit / year for an item
and itcan product 2000 such items per month. The cost of one setup
is
Rs. 400 and the holding cost /unit/ month is Rs. 50. Find
the
optimal lot size and the total cost per year, assuming cost of
one
unit as Rs.5. Also find the maximum inventory, manufacturing
time
and total time.
(12)
Or
(b) (i) Discuss the application of simulation techniques for
decision
making. (4)
(ii) The demand for an item uniform at a rate of 50 units per
month.
The fixed cost is Rs. 80 each time a production is made. The
production cost is Rs. 5 per item and the inventory carrying
cost is
Rs. 0.50 per item per month. If the shortage cost is Rs. 2.5 per
item
per month, determine how often to make a production run and
of
what size it should be? (12)
15. (a) Ships arrive at a port at the rate of one in every 4
hours with exponential
distribution of inter arrival times. The time as ship occupies a
berth for
unloading has exponential distribution with an average of 10
hours. If
the average delay of ships waiting for berths is to be kept
below 14 hours,
how many berths should be provided at the port? (16)
Or
(b) The cost of machine is Rs. 16,100 and its scrap value is Rs.
1,100 the
maintenance costs found from experience are as follows
Year : 1 2 3 4 5 6 7 8
Maintenance : 300 450 600 800 100 1200 1500 2000
When should the machine, be replaced. (16)
