Avoiding cannibalisation and/or competitor reaction in planar single facility location

A single facility has to be located in the plane in competition with fixed existing facilities, some belonging to the same chain, the others to competing chains. Demand points patronise the facility to which they are most attracted. Attraction is increasing with the quality of the facility and decreasing with its distance to demand. We study the lexicographic optimisation problem with primary objective to maximise the total market share of the chain, and secondarily to minimise the market losses of friendly facilities and/or the risk that competing facilities would raise their current quality in order to gain back lost customers.