A large company wishes to move some of its departments out of London.[11] There are benefits to be derived from doing this (cheaper housing, government incentives, easier recruitment, etc.) which have been costed. Also, however, there will be greater costs of communication between departments. These have also been costed for all possible locations of each department.
Where should each department be located so as to minimize overall yearly cost?
The company comprises five departments (A, B, C, D, E). The possible cities for relocation are Bristol and Brighton, or a department may be kept in London. None of these cities (including London) may be the location for more than three of the departments.
Benefits to be derived from each relocation are given below (in thousands of pounds per year):
|
A |
B |
C |
D |
E |
|
|
Bristol |
10 |
15 |
10 |
20 |
5 |
|
Brighton |
10 |
20 |
15 |
15 |
15 |
Communication costs are of the form 
where 
is the quantity of communication between departments 
and 
per year and 
is the cost per unit of communication between cities 
and 
. and are given by the tables below:
|
Quantities of communication |
|||||
|
(in thousands of units) |
|||||
|
A |
B |
C |
D |
E |
|
|
A |
0.0 |
1.0 |
1.5 |
0.0 |
|
|
B |
1.4 |
1.2 |
0.0 |
||
|
C |
0.0 |
2.0 |
|||
|
D |
0.7 |
||||
|
Costs per unit of communication |
|||
|
|
|||
|
Bristol |
Brighton |
London |
|
|
Bristol |
5 |
14 |
13 |
|
Brighton |
5 |
9 |
|
|
London |
10 |
||