(Based on Step 1, 2, 3)
1. The departmental head has four subordinates and four tasks to be performed. The subordinates differ in efficiency and the tasks differ in their intrinsic difficulty. His estimates of the times each man would take to perform each task is given below. How should the tasks be allocated to subordinates so as to minimize the total man-hours ?
|
Tasks |
|||||
|
Subordinates |
|
I |
II |
III |
IV |
|
P |
8 |
26 |
17 |
11 |
|
|
Q |
13 |
28 |
4 |
26 |
|
|
R |
38 |
19 |
18 |
15 |
|
|
S |
19 |
26 |
24 |
10 |
|
(Ans : P ® I, Q ® III, R ® II, S ® IV; Manhours = 8 + 4 + 19 + 10 = 41)
2. Consider the following problem of assigning five jobs to five persons. The cost matrix is given below. The total cost of assignment should be minimum i.e. assignment should be optimum.
|
Persons |
Jobs |
||||
|
A |
B |
C |
D |
E |
|
|
1 |
8 |
4 |
2 |
6 |
1 |
|
2 |
0 |
9 |
5 |
5 |
4 |
|
3 |
3 |
8 |
9 |
2 |
6 |
|
4 |
4 |
3 |
1 |
0 |
3 |
|
5 |
9 |
5 |
8 |
9 |
5 |
(Ans : 1 ® E, 2 ® A, 3 ® D, 4 ® C, 5 ®B; Total Cost = 1 + 0 + 2 + 1 + 5 = 9)
3. The following cost matrix related to 5 different jobs on 5 different machines. Determine the optimum assignment.
|
Persons |
Jobs |
||||
|
A |
B |
C |
D |
E |
|
|
1 |
9 |
2 |
2 |
1 |
7 |
|
2 |
8 |
6 |
7 |
1 |
6 |
|
3 |
6 |
4 |
5 |
1 |
3 |
|
4 |
3 |
5 |
8 |
2 |
4 |
|
5 |
8 |
9 |
8 |
2 |
9 |
(Ans : 1 ® C, 2 ® B, 3 ® E, 4 ® A, 5 ® D; Total Cost = 2 + 6 + 3 + 3 + 2 = 16)
4. A company has 5 jobs A, B, C, D & E to be done by 5 workers 1, 2, 3, 4 & 5.
Each worker is assigned one and only one job. The number of hours each worker would take to complete each job is given by the following table.
|
Worker |
Jobs |
||||
|
A |
B |
C |
D |
E |
|
|
1 |
28 |
27 |
24 |
35 |
38 |
|
2 |
26 |
24 |
23 |
32 |
39 |
|
3 |
18 |
20 |
22 |
30 |
32 |
|
4 |
27 |
30 |
25 |
24 |
27 |
|
5 |
29 |
31 |
40 |
40 |
36 |
(Ans : 1 ® C, 2 ® B, 3 ® A, 4 ® D, 5 ® E; Time (hrs.) = 24+24+18+24+36 = 126)
5. The MBI manufacturing company plans to manufacture 4 types of new minicomputers. Each of the plant has manufacturing capacity for one product only.
The unit manufacturing cost for producing the different minicomputers at the four plants are shown in table below.
What is the lowest total manufacturing cost ?
|
Minicomputers type |
|||||
|
Plants |
|
1 |
2 |
3 |
4 |
|
1 |
24 |
18 |
22 |
28 |
|
|
2 |
28 |
20 |
16 |
24 |
|
|
3 |
26 |
28 |
20 |
24 |
|
|
4 |
22 |
32 |
24 |
22 |
|
(Ans : 1 ® 2, 2 ® 3, 3 ® 4, 4 ® 1; Cost = 18 + 16 + 24 + 22 = 80)
6. An automobile dealer wishes to put four repairmen to four different jobs. The repairmen have somewhat different kinds of skills and they exhibit different levels of efficiency from one job to another. The dealer has estimated the number of man hours that would be required for each job man combination.
This is given in following matrix. Find the optimum assignment that will result in minimum man hours needed.
|
Job Man |
A |
B |
C |
D |
|
|
1 |
5 |
3 |
2 |
8 |
|
|
2 |
7 |
9 |
2 |
6 |
|
|
3 |
6 |
4 |
5 |
7 |
|
|
4 |
5 |
7 |
7 |
8 |
|
(Ans : 1 ® C, 2 ® D, 3 ® B, 4 ® A, Time = 2 + 6 + 4 + 5 = 17)
7. A company has 4 jobs, the following matrix shows the cost of assigning each job to each machine.
How should the task be assigned to all machines to minimize total cost.
Does alternate optimum solution exist ? If yes find.
|
Machines |
|||||
|
Jobs |
|
M1 |
M2 |
M3 |
M4 |
|
W1 |
40 |
50 |
60 |
65 |
|
|
W2 |
30 |
38 |
46 |
48 |
|
|
W3 |
25 |
33 |
41 |
43 |
|
|
W4 |
39 |
45 |
51 |
59 |
|
(Ans : W1 ® M1, W2 ® M2, W3 ® M4, W4 ® M3; Cost = 40 + 38 + 43 + 51 = 172)
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