Generalized median location principle and dispersion-aggregation principle for urban facilities based on the expected maximum utility associated with a disaggregate logit model

Abstract

Assuming that there are multiple facilities of the same type on a line where demand is continuously distributed, we give the facility choice probability of residents by a disaggregate logit model. The utility function is supposed to be the weighted sum of travel distance and attractiveness of facility. Measuring the benefit of residents depending on the location of facilities by the average value of the expected maximum utility, we consider its maximization problem. It is proved that dispersion and aggregation phases exist in the optimal facility location. The critical point of the phase transition depends on the regional mobility level.