Decentralization: How to Disperse Offices from the Capital

Problem Statement

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 $C_{ik} D_{jl}$ where $C_{ik}$ is the quantity of communication between departments i and k per year and $D_{jl}$ is the cost per unit of communication between cities j and l. $C_{ik}$ and $D_{jl}$ are given by the tables below:

 

Quantities of communication $C_{ik}$

 

(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

 

$D_{jl}$ (in £)

 

Bristol

Brighton

London

Bristol

5

14

13

Brighton

 

5

9

London

   

10


[11] Reproduced with permission of John Wiley & Sons Ltd. (Williams 1999, p. 242).