Homework SourseA company wants to assign 14 employees to 10 offices There a
A company wants to assign 14 employees to 10 offices. There are four offices that require two employees, these are offices 5, 7, 8 and 9. The other offices require one employee. Each employee has given their preference for each office as shown in the table. A value of 1 means first choice, 2 means second choice, etc. There are some additional requirements:
Employees 3 and 4 do not like each other and then should be assigned to different offices.
Employee 10 should be assigned to one of his top three choices.
Employees 1 and 2 should be assigned to the same office.
The company wants to assign the employees to the offices to optimize the overall preferences of the employees.
The numbers in the table is the satisfaction rate which smaller numbers represent better choice, So to find an optimal solution we need to make the sum of numbers minimal
| O1 | O2 | O3 | O4 | O5 | O6 | O7 | O8 | O9 | O10 | |
| E1 | 3 | 2 | 1 | 4 | 6 | 5 | 8 | 9 | 10 | 7 |
| E2 | 5 | 3 | 2 | 6 | 1 | 7 | 9 | 8 | 4 | 10 |
| E3 | 10 | 8 | 1 | 9 | 7 | 4 | 3 | 6 | 2 | 5 |
| E4 | 7 | 3 | 2 | 9 | 5 | 4 | 8 | 6 | 1 | 10 |
| E5 | 1 | 3 | 6 | 8 | 5 | 2 | 9 | 10 | 7 | 4 |
| E6 | 4 | 9 | 1 | 5 | 6 | 8 | 2 | 7 | 10 | 3 |
| E7 | 2 | 1 | 10 | 9 | 5 | 3 | 6 | 8 | 4 | 7 |
| E8 | 6 | 5 | 1 | 3 | 2 | 4 | 7 | 8 | 9 | 10 |
| E9 | 8 | 9 | 10 | 5 | 4 | 3 | 2 | 1 | 6 | 7 |
| E10 | 9 | 10 | 3 | 2 | 5 | 4 | 1 | 7 | 8 | 6 |
| E11 | 7 | 3 | 5 | 2 | 9 | 8 | 1 | 10 | 4 | 6 |
| E12 | 6 | 5 | 1 | 9 | 10 | 2 | 3 | 4 | 7 | 8 |
| E13 | 6 | 8 | 10 | 9 | 1 | 2 | 3 | 4 | 5 | 7 |
| E14 | 6 | 3 | 5 | 9 | 1 | 2 | 10 | 4 | 8 | 7 |
Solution
E1 E2 can go together in either 5 , 7 , 8 or 9
they must go to 5 to optimise the preferences.
E3 and E4 can go either in 1,2,3,4 or 6.
E3 must go to 3
and E4 must go to 6 .
E10 should go to 7.
