General forms of the quadratic assignment problem

In this paper, a general model has been formulated for facility location. The proposed model allows for locating several facilities in a single location, and as such, it is therefore a generalisation of the well‐known quadratic assignment problem (QAP) and other variants. The general model has a wide range of applications in facility location, operations research and business. A branch‐and‐bound algorithm is developed for the generalised quadratic semi‐assignment problem (GQSAP), which is a special form of the general model. The branch‐and‐bound algorithm is based on a modified version of the well‐known Gilmore bound. Computational results are presented to corroborate the theoretical model developed here.