CLASS: MCA
13A / 331
St. JOSEPH’S COLLEGE (AUTONOMOUS) TIRUCHIRAPPALLI – 620 002
SEMESTER EXAMINATIONS – APRIL 2013
TIME: 3 Hrs.
MAXIMUM MARKS: 100
SEM
SET
PAPER CODE
TITLE OF THE PAPER
II
2012
12PCA2109
OPERATIONS RESEARCH
SECTION – A
Answer all the questions:
20 x 1 = 20
Choose the correct answer:
1.
Which of the following is not associated with linear programming problem?
a) Additivity
b) Divisibility
c) Proportionality
d) Uncertainty
2.
The transportation problem deals with the transportation of
a) Single product from a source to several destinations
b) Single product from several sources to several destinations
c) Single product from several sources to a destination
d) Multi products from several sources to several destinations
3.
A two person game is said to be a zero-sum if
a) The algebraic sum of gains and losses of all the players is zero
b) Algebraic sum of gains and losses of all the players is not zero
c) The elements in the principal diagonal of the payoff matrix are zero
d) Each player has a finite number of strategies available to him
4.
A dummy activity in a project network always has _________ duration.
a) Unit
b) Infinite
c) Zero
d) The greatest
5.
Economic order quantity results in
a) Equalization of carrying cost and procurement cost
b) Favourable procurement price
c) Reduced chances of stock-outs
d) Minimization of set-up cost
Fill in the blanks:
6.
Linear programming deals with problems involving only a _________ objective.
7.
The dual of dual is _________.
8.
A sequencing problem involving 5 jobs and 2 machines requires evaluation of
_________sequences.
9.
_________ is a graphical representation of PERT to a time scale.
10.
The behavior of a customer who shifts from one queue to another because of its smaller size is
called _________.
State True or False:
11.
Decision variables in linear programming problem have either zero or positive values.
12.
Assignment technique is essentially a maximization technique.
13.
A game does not have more than one saddle point.
14.
The irreducible minimum duration of the project is called crashed duration.
15.
Inventory cycle is the time period between successive procurement actions.
Match the following:
16.
Linear programming
-
a) elapsed time between initiation of
an order and the receipt of goods
17.
Dual simplex
-
b) sum of the variance of the critical
activity times
18.
Sequencing
-
c) allocating limited resources among
the competing activities
19.
Lead time
-
d) LPP with infeasible but optimum
solution
20.
Variance of the overall project
completion time
-
e) Gantt Chart
SECTION – B
Answer all the questions:
21. a. Use simplex method to
Maximize z = 5x1 + 3x2
Subject to the constraints
x1 + x2 ≤ 2
5x1 + 2x2 ≤ 10
3x1 + 8x2 ≤ 12
x1 , x2 ≥ 0.
OR
5 x 7= 35
22.
b.
Solve graphically.
Maximize z = 300x1 + 400x2
Subject to the constraints
5x1 + 4x2 ≤ 200
3x1 + 5x2 ≤ 150
5x1 + 4x2 ≥ 100
8x1 + 4x2 ≥ 80
x1 , x2 ≥ 0.
a.
Use dual simplex method to solve
Maximize z = -3x1 - x2
Subject to the constraints
x1 + x2 ≥ 1
2x1 + 3x2 ≥ 2 and x1 , x2 ≥ 0.
OR
b.
Assign the programmers to the programs in such a way that the computer time is
minimum.
A
programs
B
C
1 120
programmers 2  80

3
110
23.
a.
80 
110 

120 

100
90
140
Six jobs go first over machine I and then over machine II. The order of the completion of
jobs has no significance. The following table gives the machine time in hours for six jobs
and the two machines.
Job No.
Time on Machine I
Time on Machine II
1
5
7
2
9
4
3
4
8
4 5
7 8
3 9
6
6
5
Find the sequence of jobs that minimizes the total elapsed time to complete the jobs and
the idle time on machine I and machine II.
OR
b.
Use dominance property to solve the game
Player B
1 7 2
Player A 6 2 7 


5 1 6
24.
a.
Determine
i) Critical path
ii) Probability of completing the project in 41.5 weeks if (0.52) = 0.1985 and
(1.44) = 0.4207
For the following network
Activity
Pr eceding Activity
Least Time
Greatest Time
Most likely Time
A

5
10
8
B

18
22
20
C

26
40
33
D
A
16
20
18
E F G
A B C
15 6
7
25 12 12
20 9 10
H
D
7
9
8
I
E, F
3
5
4
OR
b.
A project schedule has the following characteristics
Activity
1 2 1 3 2  4 3  4 3  5
Time( weeks )
4
1
1
1
6
49 56
5
4
5  7 6  8 7  8 8  10 9  10
8
1
2
5
7
Construct the network and identify critical path.
25.
a.
Briefly explain the M/M/1 model.
OR
b.
Briefly explain ABC analysis.
SECTION – C
Answer any THREE questions:
26.
3 x 15 = 45
Use two-phase simplex method to
Maximize z = x1 + x2
Subject to
2x1 + x2 ≥ 4
x1 +7x2 ≥ 7
x1 , x2 ≥ 0.
27.
A company has three factories Fi (i = 1, 2, 3) from which it transports the product to four
warehouses Wj = (j = 1, 2, 3, 4). The unit costs of production at the three factories are ` 4, 3, 5
respectively. Given the following information on unit costs of transportation, capacities at the
three factories and the requirement at the four warehouses, find the optimum allocation.
Unit cost of
production
Factory
Capacity
(`/unit)
W1
W2
W3
W4
F1
4
5
7
3
8
300
F2
3
4
6
9
5
500
F3
5
2
6
4
5
200
200
300
400
100
1000
Requirements
28.
Transportation cost (`/unit)
Solve the game using dominance property and graphical method.
Player B
 4  2 3  1
Player A   1 2
0
1


 2 1  2 0 
29.
Activity
Time estimate (weeks)
Direct cost estimates
i
j
Normal
Crash
Normal
Crash
1
2
2
1
10
15
1
3
8
5
15
21
2
4
4
3
20
24
3
4
1
1
7
7
3
5
2
1
8
15
4
6
5
3
10
16
5
6
6
2
12
36
i) Draw the project network corresponding to normal time.
ii) Determine critical path.
iii) Crash the activities so that the project completion time reduces to 9 weeks.
30.
Briefly explain the EOQ model with uniform rate of Demand.
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