Decentralization: How to Disperse Offices from the Capital

Objective

The objective is to maximize the following quadratic function:

\[ \Variable{NetBenefit} = \sum _{i \in \text {DEPTS}} \sum _{j \in \text {CITIES}} \Argument{benefit[i,j]} \cdot \Variable{Assign[i,j]} - \sum _{(i,j,k,l) \in \text {IJKL}} \Argument{comm[i,k]} \cdot \Argument{cost[j,l]} \cdot \Variable{Product[i,j,k,l]} \]

where

\[ \Variable{Product[i,j,k,l]} = \Variable{Assign[i,j]} \cdot \Variable{Assign[k,l]} \]