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Operations Research
3
2
1
r
n1
n
s
5. If there are n jobs, first write n number of rectangles as shown. When ever the smallest
elements falls in column 1 then enter the job number in first rectangle. If it falls in second
column, then write the job nu

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Operations Research
Draw X - axis and Y- axis, represent the time on X - axis and two machines by two bars on Yaxis. Then mark the times on the bars to show processing of each job on that machine.
Sequence 1,2
Total = elapsed time = 9 Hrs. (optimal se

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Operations Research
elapsed time ( i.e. time taken to process all the jobs). The usual notations used in this problem are:
Ai = Time taken by i th job on machine A where i = I, 2,3n. Similarly we can interpret for
machine B and C i.e. Bi and Ci etc.
T

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Operations Research
15. The total opportunity cost matrix is obtained by doing:
(a) Row operation on row opportunity cost matrix,
(b) by doing column operation on row opportunity cost matrix,
(c) By doing column operation on column opportunity cost ma

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Operations Research
Machines.
Particulars.
P
Q
R
S
T
Basic productionPieces per shift.
8
10
8
7
7
Incentive bonusPer piece in Rs.
1.0
1.0
1.6
2.0
2.0
MULTIPLE CHOICE QUESTIONS
1.
2.
3.
4.
5.
6.
Assignment Problem is basically a
(a) Maximization Proble

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Operations Research
(b) If the given matrix happens to be returns to the company by assigning a particular job to a
machine, then what will be the assignment? Will the same assignment hold well? If not what
will you do to get the new solution.
Jobs (h

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Operations Research
5
5
M
10
0
0
0
E
D
M
C
0
B
A
M
A
Places
TOCM:
M
C
M
0
M
0
B
M
0
0
10
5
Places
A
B
M
C
M
D
E
5
10
0
E
D
TOCM:
0
5
M
0
M
A
0
M
5
M
5
B
5
M
A
B
C
D
E
M
0
M
5
0x
B
0x
M
0
M
0x
C
M
0x
M
0
0x
D
5
M
0x
M
0
E
0
0x
0x
0x
M

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Operations Research
The assignment is A to B, B to C, C to D and D to E and E to A. (If we start with the element DC
then cycling starts.
Now the total distance is 5 + 3 + 4 + 5 + 1 = 18 + 1 + 1 = 20 Km. The ones we have assigned are
to be added as pe

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Operations Research
B
C
D
M
1
3
0
B
7
M
0
13
C
0
0
M
3
E
A
A
7
Cities
TOCM:
0
9
5
6
M
4
0
3
0
10
0
E
D
M
3
5
6
M
0
3
0
0
9
M
0
7
10
M
13
0
0
3
1
M
E
4
E
0
D
0
C
7
D
M
B
C
A
B
A
Cities
We can make only 4 assignments. Hence modify the matrix. Smallest e

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Operations Research
Solution
Now let us consider the layover times separately for crew based at Mumbai and crew based at
Bangalore.
Let us consider one flight and discuss how to calculate layover time. For example, flight No. 101
leaves Mumbai at 6.30

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Operations Research
Tableau I. (The ranking is on a 20 point scale). Assign one project to one region depending on the
maximum total effectiveness. (Plants are given serial numbers 1 to 5)
Tableau I.
Local Employment
Potential.
Reg. 1 2 3 4
5
long.
A

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Operations Research
Assignment: A to P, B to R, C to T, D to U, E to S and DR to Q i.e the van at Q will not go to any
destination.
Total Distance: 18 + 18 + 18 + 20 + 15 = 89 Km.
Other alternative assignments are:
From:
A
B
C
D
E
DR
Station for which

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Operations Research
Problem 5.9.
On a given day District head quarter has the information that one ambulance van is stationed at each of
the five locations A, B, C, D and E. The district quarter is to be issued for the ambulance van to reach
6 locatio

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Operations Research
Solution
ROCM:
Machines (time in hours)
Jobs
A
B
C
D
P
0
4
12
2
Q
6
0
8
2
R
0
6
12
6
S
14
2
10
0
TOCM:
Machines (time in hours)
A
B
D
4
2
0
0
2
C
4
Jobs
0
P
6
Q
0
6
4
6
2
2
0
R
TOCM:
14
S
Machines (time in hours)
A
P
0
Q
B
6
D
4
2

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Operations Research
As five lines are there we can make assignment.
Clerks (effective performance)
Counters
A
B
C
D
E
R
1
0
2
1
0x
S
3
3
4
2
0
M
0
0x
3
2
2
P
1
2
1
0
0x
I
3
3
0
0x
1
Assignment: R to B, S to E, M to A, P to D and I to C. Total effectiv

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Operations Research
TOCM:
Market segments.
A
B
C
D
0
2
5
8
0
0
1
2
0
0
1
2
1
0
0
0
SalesMen
W
X
Z
Y
TOCM:
B
C
D
4
7
0
1
2
0
W
A
SalesMen
Market segments.
0
0
0
1
0
0
1
2
Z
0
0
Y
X
Assignment (First solution)
Market segments.
SalesMen
A
B
C
D
W
0
2
4
7

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Operations Research
As every row has a zero, we can consider it as ROCM and by doing column operation, we can
write TOCM. Now apply step 7.
Men (Time taken in hours).
0
9
DC
6
Z
0
Y
A
X
Jobs
0
0
7
4
B
0
9
0
26
C
10
14
0
9
D
Men (Time taken in hours).

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Solution
Machines (time in hours)
Jobs
V
W
X
Y
Z
A
2
4
3
5
4
B
7
4
6
8
4
C
2
9
8
10
4
D
8
6
12
7
4
E
2
8
5
8
8
COCM
Y
Z
0
3
3
0
5
B
0
0
0
0
0
A
X
W
V
Jobs
Machines (time in hours)
5
5
5
0
6
2
9
2
0
E
0
4
2
3
4
0
D
C
As the COCM has

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Operations Research
ROCM:
Machines
Returns in Rs.
Jobs
A
B
C
D
E
V
7
1
2
0
8
W
4
2
0
3
1
X
11
2
9
0
8
Y
8
0
10
3
7
Z
5
3
4
0
7
By doing column operation on ROCM, we get the total opportunity cost matrix.
TOCM:
Machines
Returns in Rs.
2
0
10
3
0
0
7
6

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Operations Research
The procedure: Let Job 1 is loaded on machine A first at zero th time. It takes two hours to
process on the machine. Job 1 leaves the machine A at two hours and enters the machine 2 at 2-nd
hour. Up to the time i.e first two hours,

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Operations Research
9.9. MULTI CHANNEL QUEUING MODEL: M / M / c: ( / FCFS)
The above symbols indicate a system with Poisson input and Poisson output with number of channels
= c, where c is > 1, the capacity of line is infinite and first come first ser

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Operations Research
Problem 9.19.
A tax-consulting firm has 3 counters in its office to receive people who have problems concerning
their income, wealth and sales taxes. On the average 48 persons arrive in an 8- hour day. Each tax
adviser spends 15 mi

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Operations Research
Problem 9.15.
Trains arrive at the yard every 15 minutes and the service time is 33 minutes. If the line capacity
of the yard is limited to 4 trains, find (a) the probability that the yard is empty and (b) The average
number of tra

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Operations Research
of using as many unloading group of workers in a vehicle as there are vehicles waiting in line or being
unloaded. Under these conditions find (a) What will be the average number of unloading group of
workers working at any time? (b

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Operations Research
(e) What is the probability that they will have to wait for more than 10 minutes before the phone
is available and the call is also complete?
(f) Find the fraction of a day that the phone will be in use.
Solution
Data: Arrival rate

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Operations Research
Problem 9.6.
A repairman is to be hired to repair machines, which break down at an average rate of 3 per hour. The
breakdown follows Poisson distribution. Non - productive time of a machine is considered to cost Rs.
16/- per hour.

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Operations Research
Solution
Data: Time interval between two arrivals = 10 min. = 1/ , Length of phone call = 3 min. = 1 / .
Hence = 1/10 = 0.1 per min and = 1/3 = 0.33 per min., and = / = 0.10 / 0.33 = 0.3
(a) Any person who is coming to booth has to