Submodularity in competitive location models

Most locational models assume that nodes are allocated to services according to a 0/1 allocation rule. This assumption is not realistic in models where clients of services are independent decision-makers and take decisions that are probabilistic in nature. In this paper the author surveys many techniques available in the literature to model customers’ behaviour in a geographical market and the main result is that despite the fact that models are apparently very different, they hide a common submodular structure. This discovery shows that in the future it will be possible to develop computational approaches to problems not yet solved, to define synthetic and more complex models of competition and maybe to make new discoveries exploiting the submodular property of the objective function.