Assignment and Sequencing Important Questions for Board Exam 2019
1. Solve the following minimal assignment problem and hence find the minimum value:
I
|
II
|
III
|
IV
| |
A
|
2
|
10
|
9
|
7
|
B
|
13
|
2
|
12
|
2
|
C
|
3
|
4
|
6
|
1
|
D
|
4
|
15
|
4
|
9
|
2. There are three jobs to be completed. Each job must go through Machines Machines M1, M2, M3 in the order M1- M2, - M3. Processing time in hours is given below. Determine the optimal sequence and idle time for Machine M1.
Jobs
|
A
|
B
|
C
|
D
|
M1
|
5
|
8
|
7
|
3
|
M2
|
6
|
7
|
2
|
5
|
M3
|
7
|
8
|
10
|
9
|
3. Find the sequence that minimizes the total elapsed time (in hours) required to complete the following jobs on the machine M1 , M2 and M3 in the order M1 M2 M3 :
Jobs
|
A
|
B
|
C
|
D
|
Machine
| ||||
M1
|
5
|
6
|
9
|
5
|
M2
|
2
|
4
|
5
|
3
|
M3
|
3
|
5
|
6
|
7
|
4. Solve the following minimal assignment problem:
Machines
|
A
|
B
|
C
|
D
|
E
|
M1
|
27
|
18
|
∞
|
20
|
21
|
M2
|
31
|
24
|
21
|
12
|
17
|
M3
|
20
|
17
|
20
|
∞
|
16
|
M4
|
21
|
28
|
20
|
16
|
27
|
5. Solve the following minimal assignment problem:
Jobs
|
I
|
II
|
III
|
Machines
| |||
M1
|
1
|
4
|
5
|
M2
|
4
|
2
|
7
|
M3
|
7
|
8
|
3
|
6. We have seven jobs each of which has to go through two machines M1 and M2 in the order M1 - M2. Processing time (in hours) are given as:
Jobs
|
A
|
B
|
C
|
D
|
E
|
F
|
G
|
Machines
| |||||||
M1
|
3
|
12
|
15
|
6
|
10
|
11
|
9
|
M2
|
8
|
10
|
10
|
6
|
12
|
1
|
3
|
Determine a sequence of these jobs that will minimize the total elapsed time 'T'. and idle time for each machine.
7. Three different aeroplanes are to be assigned to carry three cargo consignments with a view to maximize profit. The profit matrix (in lakhs of Rs. ) is as follows:
Cargo Consignments
|
C1
|
C2
|
C3
|
Aeroplanes
| |||
A1
|
1
|
4
|
5
|
A2
|
2
|
3
|
3
|
A3
|
3
|
1
|
2
|
How should the cargo consignments be assigned to the aeroplanes to maximize the profit?
8. A pharmaceutical company has four branches, one each oat city A, B, C, D, A branch manager is to be appointed one at each city, out of four candidates P, Q, R and S. the monthly business depending upon the city and the effectiveness of the branch manager in that city is given below:
City
|
A
|
B
|
C
|
D
|
Manager
| ||||
P
|
10
|
10
|
8
|
8
|
Q
|
12
|
15
|
10
|
9
|
R
|
11
|
16
|
12
|
7
|
S
|
15
|
13
|
15
|
11
|
Which manager should be appointed at which city so as to get the maximum total monthly business?
9. There are five jobs each of which is to be processed through these machines A, B and C in the order ABC. Processing times in hours are as shown in the following table.
Jobs
|
1
|
2
|
3
|
4
|
5
|
Machines
| |||||
A
|
3
|
8
|
7
|
5
|
4
|
B
|
4
|
6
|
1
|
2
|
3
|
C
|
7
|
9
|
5
|
6
|
13
|
Determine the optimum sequence for the five jobs and minimum elapsed time.
10. Solve the following minimal assignment problem and hence find minimum time where '---' indicates that job cannot be assigned to the machine.
Jobs
|
A
|
B
|
C
|
D
|
E
|
Machines
| |||||
M1
|
9
|
11
|
15
|
10
|
11
|
M2
|
12
|
9
|
---
|
10
|
9
|
M3
|
---
|
11
|
14
|
11
|
7
|
M4
|
14
|
8
|
11
|
7
|
8
|
11. Solve the following maximal assignment problem:
Monthly Business in City. (Rs. in lakh)
|
A
|
B
|
C
|
D
|
Manager
| ||||
P
|
11
|
11
|
9
|
9
|
Q
|
13
|
16
|
11
|
10
|
R
|
12
|
17
|
13
|
8
|
S
|
16
|
14
|
16
|
12
|
12. For the following problem find the sequence that minimizes total elapsed time (in hrs) required to complete the jobs on 2 machines M1 and M2 in the order M1 - M2 . Also find the minimum elapsed time?
Jobs
|
A
|
B
|
C
|
D
|
E
|
F
|
Machines
| ||||||
M1
|
4
|
8
|
3
|
6
|
7
|
5
|
M2
|
6
|
3
|
7
|
2
|
8
|
4
|
