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

x1+2x2 + 5x3 = 4, x1, x2, x3, >0.
(7x4)
2.
a) Solve the subsequent linear programming issue by simplex method.
Max. z = x1 + x2 + 3x3 - x4
s.t. x1 + 2x2 + 3x3 = 15,
2x1 + x2 + 5x3 =20,
x1 + 2x2 + x3 + x4 = 10, x1, x2, x3, x4 > 0
b) decrease the subsequent transportation issue to an assignment issue and solve it.
Distances (in km) are provided subsequent table:
Depot buses needed
a b c
Terminal A six 10 15 2
B four six 16 2
C 12 five eight 1
buses available one 1 3
Make an allocation so that total distance traveled is minimum.
(9+9)
3.
a) obtain the optimal sequence for processing four jobs A, B, C, D on 4 Machines A1, A2, A3,
A4 in the order A1 A2 A3 A4. Processing times are as provided below:
Processing times (aij) in hours
Job/Machine A1(ai1) A2(ai2) A3(ai3) A4(ai4)
A 15 five four 14
B 12 two 10 12
C 13 three six 15
D 16 0 three 19
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b) compute the different time estimates for the network in fig.
(9+9)
4.
a) A telephone exchange has 2 long distance operators. The telephone company obtains
that during the peak load, long distance calls arrive in Poisson fashion at an avg.
rate of 15 per hour. The length of service on these calls is approximately exponentially
distributed with mean length five minuets. What is the probability that a subscriber will have
to wait for his long distance call during the peak hours of the day? If subscribers wait and
are serviced in turn, what is the expected waiting time?
b) Use the concept of dominance of dominance to solve the game
(9+9)
5.
a) Solve the subsequent issue using dynamic programming.
Minimize å =
= y ,
J 1
n z 2j Subject to the constraints
Õ=
= ³
n
j 1
j j y b, y 0 for all j.
b) Consider the inventory system with the subsequent data in usual notations:
R =1000 units/year, I =0.30, P= Re. 0.50 per unit
C3 =Rs.10.00, L= 2=years (lead time).
Determine:
i) Optimal order volume
ii) Reorder point
iii) Minimum avg. cost
(9+9)
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B
I II III IV
I three two four 0
II three four two 4
A III four two four 0
IV 0 four 0 8
6.
a) There are 3 parties who supply the subsequent volumes of coal and 3 consumers
who require the coal as follows:
Party one 14 tons Consumer A six tons
Party two 12 tons Consumer B 10 tons
Party three five tons Consumer C 15 tons
Total 31 tons
A B C
1 six eight 4
2 four nine 3
3 one two 6
The cost matrix is as shown here.
obtain the schedule of a transportation policy, which minimizes the cost.
b) avg. time taken by an operator on a specific machine is tabulated beneath. The
management is considering replacing 1 of the old machines by a new 1 and the
estimated time for operation by every operator on the new machine is also indicated.
Machines
operators one two three four five six new
A 10 12 eight 10 eight 12 11
B nine 10 eight seven eight nine 10
C eight seven eight 8 eight six 8
D 12 13 14 14 15 14 11
E nine 9 nine eight 8 10 9
F seven eight nine 9 nine eight 8
i) obtain out an allocation of operators to old machines to achieve a minimum
operation time.
ii) Reset the issue with the new machine and obtain out the allocation of the
operator to every machine and comment on whether it is advantageous to change
an old machine to achieve education in operating time only.
iii) How will the operators be allocated to the machines after replacement?
(9+9)
7.
a) A firm can backorder, if out of stock, the demands of its customers. The provided facts are
as follows:
Total annual demand D = 100 units
Ordering Cost O = Rs. 10 per order
Price of the item P = Rs. 20 per unit
Inventory carrying cost I = 20%
Penalty cost of backordering K = Rs. five per unit per year
Determine the optimum order size ad the amount backordered for every cycle on the
basis of above info.
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b) 3 manufacturers A, B and C are competing with every other. The transition-matrix
provided beneath provide the probabilities that customers will move from 1 manufacture to
other in any month. Interpret the matrix in terms of
a) retention and loss and
b) retention and gain.
Transition Matrix
To
From
A B C
A 0.7 0.1 0.2
B 0.1 0.8 0.1
C 0.2 0.1 0.7
(9+9)
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Earning:   Approval pending.