1
Seat No.: Enrolment
GUJARAT TECHNOLOGICAL UNIVERSITY
MCA SEMESTER-IV EXAMINATION WINTER 2018
Subject Code: 2640003 Date: 22/11/2018
Subject Name: Operations Research
Time: 10.30 am to 1.00 pm Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q 1a
Do as directed
What is operation research
TRUE/FALSE Hungarian method is a method for solving assignment problem.
Write full form of NWCM
What is fair game
What is meaning of lead time in inventory control policy?
List out component of linear problem.
What is simulation
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Q 1b
Write difference between PERT CPM
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Q 2a
Find Initial basic feasible solutions NWCM. LCM
Destination
Source
D
E
F
G
Supply
A
11
13
17
14
250
B
16
18
14
10
300
C
21
24
13
10
400
Demand
200
225
275
250
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Q 2b
National Oil Company has three refineries and four depots. Transportation Cost per ton, capacities and requirements are given below:
D1
D2
D3
D4
Capacity
R1
19
30
50
10
7
R2
70
30
40
60
9
R3
40
8
70
20
18
Requirement
5
8
7
14
Determine initial basic feasible solution using Voggel's Approximation method(VAM).
07
OR
2
Q 2b
A lead draftsman has five drafting tasks to accomplish and five idle draftsmen. Each draftsman is estimated to require the following number of hours for each task.
Draftsmen
Tasks
A
B
C
D
E
1
60
50
100
85
95
2
65
45
100
75
90
3
70
60
110
97
85
4
70
55
105
90
93
5
60
40
120
85
97
If each draftsman costs the company Rs. 15.80 per hour including overhead, find the assignment of draftsmen to tasks that will result in the minimum total cost. What is the total cost?
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Q 3a
Write assumption of sequencing problem.
Write advantages of simulation.
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Q 3b
A book binder has one printing press, one binding machine, and manuscripts of a number of books. The time required performing the printing and binding operations on each book are shown below. The binder wishes to determine the order in which the books should be processed, so that the total time required to process all books is minimized find idle time for each machine.
Book
1
2
3
4
5
6
7
Printing Time (Hours)
20
90
80
20
120
15
65
Binding Time (Hours)
25
60
75
30
90
35
50
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OR
Q 3a
Find a sequence that minimizes the total elapsed time required to complete the following tasks. Find total elapsed time and idle time for different machine.
1
2
3
4
5
6
Time on Machine 1
3
12
5
2
9
11
Time on Machine 2
8
6
4
6
3
1
Time on Machine 3
13
14
9
12
8
13
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Q 3b
Suppose an organization is manufacturing two products P1 and P2. The profit per tone of the two products is Rs. 50 and Rs. 60 respectively. Both the products require processing in three types of machine. The following Table indicates the available machine hours per week and the time required on each machine for one tone of P1 and P2. Formulate this product mix problem in the linear programming form.
Profit /tonne
Product 1
Product 2
Total available
Machine hours/weeks
Machine 1
2
1
300
Machine 2
3
4
509
Machine 3
4
7
812
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Q 4a
Adjoining is a list and description of activities for a project XYZ building a boat. Draw the network:
Activity
Description
Predecessor Act.
A
Design hull
None
B
Prepare boot shed
None
C
Design Mmst and mast mount
None
D
Obtain hull
A
E
Design sails
A,B
F
Obtain mast mount

G
Obtain mast

H
Design rigging
F
I
Prepare hull
E,F
J
finish
I
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Q 4b
Find the saddle point of this game?
Player B
Player A b1 b2 b3
a1 1 2 2
a2 6 4 6
What is simulation? Give any two example of simulation Explain meaning of simulation by differentiate "simulation is…" "simulation is not".
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OR
4
Q 4a
A project consists of eight activities with the following relevant information:
Activity
Estimated duration(days)
Optimistic
Most likely
Pessimistic
1-2
1
1
7
1-3
1
4
7
1-4
2
2
8
2-5
1
1
1
3-5
2
5
14
4-6
2
5
8
5-6
3
6
15
Draw the PERT network and find out the expected project completion time.
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Q 4b
What is inventory management? List out the factors on which quantity of orders depends. list the various types of costs which involved in inventory system.
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Q 5a
Solve following LPP by graphical method:
Maximize Z 4X1 3X2
subject to
200X1 100X2 4000
50 X1 2X2
40X1 40X2 1400
where X1, X2
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Q 5b
Find Dual of following linear programming problem:
Max Z 7X1 3X2 8X3
subject to constraints
8X1 2X2 X3 3
3X1 6X2 4X3 4
4X1 X2 5X3 1
X1 5X2 2X3 7
where X1, X2,X3
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OR
Q 5a
How many network representation in project management Explain the behaviours of arrivals in queuing system.
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Q 5b
A Product's purchase price is 13000 Rs. And installation charge is Rs. 3600. Its scrap value is Rs. 1600. The operating cost of different year are given in following table.
Year
1
2
3
4
5
6
Operating cost
250
750
1000
1500
2100
2900
Determine optimal replacement policy.
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