DOEACC Society 2006 DOEACC B Level B10 Applied Operations Research ( ) - Question Paper

c) How will you replace B&B algorithm to fit minimization problem?
(8+6+4)
4.
a) Solve the subsequent linear programming issue by simplex method.
Maximize z = x1 + x2 + 3x3 - x4
subject to
x1 + 2x2 + 3x3 = 15,
2x1 + x2 + 5x3 =20,
x1 + 2x2 + x3 + x4 = 10 where x1, x2, x3, x4 > 0
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1
3
2
5
4 7
6
8
2
1 3
4 5
(4, 0) (8, 0)
(4, 6)
(6, 0)
(0, 2)
(4, 0)
(2, 0) (4, 4)
b) A company has 3 plants A, B and C, three warehouses X, Y, Z. The number of units
available at the plants is 60, 70, 80 and the demand at X, Y, Z are 50, 80, 80
respectively. The unit cost of the transportation is provided in the subsequent table:
X Y Z
A eight seven 3
B three eight 9
C 11 three 5
obtain the allocation so that the total transportation cost is minimum.
(9+9)
5.
a) A shipping company has single unloading berth with ships arriving in a Poisson fashion
at an avg. rate of there per days. The unloading time distribution of a ship with n
unloading crews is obtained to be exponential with avg. unloading time 1/2n days. The
company has large labour supply without regular working hours, and to avoid long
waiting lines, the company has a policy of using as many unloading crew on a ship as
there are ships waiting in line or being unloaded.
i) Under these conditions what will be the avg. number of unloading crew
working at any time?
ii) What is the probability that more than 4-crew will be needed?
b) A manufacturing company purchases 9,000 parts of a machine for its annual
requirements ordering 1-month usage at a time. every part cost Rs. 20. The ordering
cost per order is Rs. 15 and the carrying charges are 15% of the avg. inventory per
year. You have been asked to suggest a more economical purchasing policy for the
company. What advice would you offer? And how much would it save the company per
year?
(9+9)
6.
a) The activities for buying a new car are summarized beneath. Draw the network model and
carry out the calculations.
Activity Description Immediate
predecessor(s)
Duration
(days)
A Conduct feasibility study - 3
B obtain potential customer for current car A 14
C List possible models A 1
D Research all possible models C 3
E Conduct interviews with machines C 1
F Collect dealer propaganda C 2
G Compile and arrange all pertinent
information
D, E, F 1
H select top all 3 options G 1
I Test drive all 3 options H 3
J Gather warranty and financing info H 2
K chosen 1 car I, J 2
L Compare dealer and chosen dealer K 2
M Search for desired color and choices L 4
N Test drive chosen model once again L 1
O Purchase new car B, M, N 3
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b) explain the issue of n jobs and m machines and finds the sequence that minimizes
the elapsed time needed to complete the subsequent tasks. The processing time is provided
in hours. compute also the idle time.
Job one two three four five six seven eight nine 10
M1 two three four 15 three six 10 15 two 8
M2 six two four 10 six nine 15 three one 0
(9+9)
7.
a) Solve the subsequent issue using dynamic programming.
Minimize z = å
=
n
j 1
2j
y
subject to the constraints
nP
yj = b , yj ³ 0 for all j .
j=1
b) For a game with the subsequent payoff matrix, determine the optimal strategy and the
value of the game.
B
6 -3
A
-3 0
(12+6)
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Earning:   Approval pending.