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OPERATIONS RESEARCH
[As per Choice Based Credit System (CBCS) scheme]
(Effective from the academic year 2017 - 2018)
SEMESTER - VI
Subject Code 17CS653
IA Marks 40
Number of Lecture Hours/Week 3
Exam Marks 60
17CS653 - OPERATIONS RESEARCH
QUESTIONS BANK
Module 4
These Questions are being framed for helping the students in the "FINAL Exams" Only (Remember for Internals the Question Paper is set by your respective teachers). Questions may be repeated, just to show students how VTU can frame Questions.
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17CS653 - OPERATIONS RESEARCH
Question Bank - MODULE - 4
1. Determine an initial basic feasible solution to the following transportation problem using North West Corner's rule. (05 Marks) (Dec.2019/Jan.2020)
|
O/D |
D1 |
D2 |
D3 |
D4 |
Supply |
|
01 |
6 |
4 |
1 |
5 |
14 |
|
02 |
8 |
9 |
2 |
7 |
16 |
|
03 |
4 |
3 |
6 |
2 |
5 |
|
Required |
6 |
10 |
15 |
4 |
35 |
2. Four jobs are to be done on four different machines. The cost [in rupees] of producing ith job on jth machine is given below:
|
Machines Jobs |
M1 |
M2 |
M3 |
M4 |
|
J1 |
15 |
11 |
13 |
15 |
|
J2 |
17 |
12 |
12 |
13 |
|
J3 |
14 |
15 |
10 |
14 |
|
J4 |
16 |
13 |
11 |
17 |
Assign the jobs to different machine so as to minimize the total cost. (06 Marks) (Dec.2019/Jan.2020)
3. Find an initial basic feasible solution for the following transportation problem using least cost or matrix minima method:
|
19 |
30 |
50 |
10 |
7 |
|
70 |
30 |
40 |
60 |
9 |
|
40 |
80 |
70 |
20 |
18 |
|
5 |
8 |
7 |
14 |
|
(05 Marks) (Dec.2019/Jan.2020)
4. Determine the optimum basic feasible solution for the following transportation problem. Obtain initial basic feasible by Vogel's approximation method. (08 Marks) (Dec.2019/Jan.2020)
|
O/D |
D1 |
D2 |
D3 |
D4 |
Supply |
|
01 |
2 |
2 |
2 |
1 |
3 |
|
02 |
10 |
8 |
5 |
4 |
7 |
|
03 |
7 |
6 |
6 |
8 |
5 |
|
Required |
04 |
3 |
4 |
4 |
|
5. Solve the following assignment problem. If it is treated as a salesman problem and the cell entries represent cost in rupees. Find the least cost route such that salesman does not visit any city twice. (08 Marks) (Dec.2019/Jan.2020)
|
|
A |
B |
C |
D |
E |
|
A |
∞ |
2 |
5 |
7 |
1 |
|
B |
6 |
∞ |
3 |
8 |
2 |
|
C |
8 |
7 |
∞ |
4 |
7 |
|
D |
12 |
4 |
6 |
∞ |
5 |
|
E |
1 |
3 |
2 |
8 |
∞ |
6. Find the initial basic feasible solution by using North-West corner rule. (06 Marks) (June/July 2019)
|
O/D |
D1 |
D2 |
D3 |
D4 |
Supply |
|
01 |
1 |
5 |
3 |
3 |
34 |
|
02 |
3 |
3 |
1 |
2 |
15 |
|
03 |
0 |
2 |
2 |
3 |
12 |
|
Demands |
21 |
25 |
17 |
17 |
80 |
7. Find the initial basic feasible solution using Vogel's approximation method. (10 Marks) (June/July 2019)
|
|
W1 |
W2 |
W3 |
W4 |
Availability |
|
F1 |
19 |
30 |
50 |
10 |
7 |
|
F2 |
70 |
30 |
40 |
60 |
9 |
|
F3 |
40 |
8 |
70 |
20 |
18 |
|
Requirement |
5 |
8 |
7 |
14 |
8. Solve by matrix minima method and obtain an optimal solution for the following problem: (10 Marks) (June/July 2019)
9. Solve the following assignment problem: (06 Marks) (June/July 2019)
|
|
J1 |
J2 |
J3 |
J4 |
|
A |
2 |
10 |
9 |
7 |
|
B |
15 |
4 |
14 |
8 |
|
C |
13 |
14 |
16 |
11 |
|
D |
3 |
15 |
13 |
8 |
10. Find the initial basic feasible solution to the following transportation problem using VAM. (08 Marks) (Dec.2018/Jan.2019)
|
15 |
10 |
17 |
18 |
2 |
|
16 |
13 |
12 |
13 |
6 |
|
12 |
17 |
20 |
11 |
7 |
|
3 |
3 |
4 |
5 |
11. Find the optimal solution to the following assignment problem. (08 Marks) (Dec.2018/Jan.2019)
|
Jobs Machines |
J1 |
J2 |
J3 |
J4 |
J5 |
|
M1 |
11 |
17 |
8 |
16 |
20 |
|
M2 |
9 |
7 |
12 |
6 |
15 |
|
M3 |
13 |
16 |
15 |
12 |
16 |
|
M4 |
21 |
24 |
17 |
28 |
26 |
|
M5 |
14 |
19 |
12 |
11 |
13 |
12. Write the procedure of Hungarian method. (06 Marks) (Dec.2018/Jan.2019)
13. There are 3 factories A, B and C. Supply goods to 4 dealers D1, D2, D3 and D4. The production capacities of these factories are 1000, 700, 900 respectively. The requirement from this dealer are 900, 800, 500 and 400 per month respectively. The per unit returns excluding transportation cost are Rs.8/-, 7/-, 9/- at the 3 factories. The following table gives the unit production cost from the factories to dealers. Determine the optimum solution to maximize the total returns. (10 Marks) (Dec.2018/Jan.2019)
|
|
D1 |
D2 |
D3 |
D4 |
|
|
A |
2 |
2 |
2 |
4 |
1000 |
|
B |
3 |
5 |
3 |
2 |
700 |
|
C |
4 |
3 |
2 |
1 |
900 |
|
|
900 |
800 |
500 |
400 |
|
14. Find initial basic feasible solution by North-West corner method. (06 Marks) (June/July 2018)
|
Destination |
D1 |
D2 |
D3 |
D4 |
Requirement |
|
F1 |
3 |
3 |
4 |
1 |
100 |
|
F2 |
4 |
2 |
4 |
2 |
125 |
|
F3 |
1 |
5 |
3 |
2 |
75 |
|
Demand |
120 |
80 |
75 |
25 |
|
15. Solve the following transportation problem and determine optimal distribution for the company so as to minimize the total transportation cost. Use VAM method to find the initial basic feasible solution. (10 Marks) (June/July 2018)
|
Factories |
Warehouses |
|
||
|
W1 |
W2 |
W3 |
Available |
|
|
F1 |
16 |
20 |
12 |
200 |
|
F2 |
14 |
8 |
18 |
160 |
|
F3 |
26 |
24 |
16 |
90 |
|
Required |
180 |
120 |
170 |
|
16. Explain various steps involved in Hungarian algorithm with example. (06 Marks) (June/July 2018)
17. Solve the following assignment problem. Assign 4 tasks to 4 persons so as to minimize the total cost. (10 Marks) (June/July 2018)
|
|
Person |
||||
|
Tasks |
|
P1 |
P2 |
P3 |
P4 |
|
T1 |
42 |
35 |
28 |
21 |
|
|
T2 |
30 |
25 |
20 |
15 |
|
|
T3 |
30 |
25 |
20 |
15 |
|
|
T4 |
24 |
20 |
16 |
12 |
|
18. Explain Hungarian Algorithm to solve assignment problem. (10 Marks) (Dec.2017/Jan.2018| 10 Scheme)
19. Solve the following transportation problem by using (i) North-West corner method (ii) Vogel's approximation method. (10 Marks) (Dec.2016/Jan.2017 | 10 Scheme)
|
|
D1 |
D2 |
D3 |
D4 |
Supply |
|
F1 |
3 |
1 |
7 |
4 |
300 |
|
F2 |
2 |
6 |
5 |
9 |
400 |
|
F3 |
8 |
3 |
3 |
2 |
500 |
|
Demand |
250 |
350 |
400 |
200 |
|
20. Solve the following assignment problem. (10 Marks) (Dec.2016/Jan.2017 | 10 Scheme)
|
|
S1 |
S2 |
S3 |
S4 |
|
P1 |
2 |
10 |
9 |
7 |
|
P2 |
15 |
4 |
14 |
8 |
|
P3 |
13 |
14 |
16 |
11 |
|
P4 |
3 |
15 |
13 |
8 |
Find the schedule so as to minimize the total subject preparation time tor all subjects.
21. Find the initial basic feasible solution using North West corner rule and Vogel's approximation method for the following transportation problem: (10 Marks) (June/July 2017 | 10 Scheme)
|
19 |
30 |
50 |
10 |
7 |
|
70 |
30 |
40 |
60 |
9 |
|
40 |
8 |
70 |
20 |
18 |
|
5 |
8 |
7 |
14 |
22. Write the procedure of Hungarian method. (05 Marks) (June/July 2017 | 10 Scheme)
23. Find the optimal solution to the following assignment problem showing the costs (Rs) for assigning workers to jobs. (05 Marks) (June/July 2017 | 10 Scheme)
|
|
|
Jobs |
||
|
Workers |
W1 |
18 |
17 |
16 |
|
W2 |
15 |
13 |
14 |
|
|
W3 |
19 |
20 |
21 |
|
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