We establish and analyze a service center location model with a simple but novel decision-dependent demand induced from a maximum attrac- tion principle. The model formulations are investigated in the distributionally- robust optimization framework. A statistical model that is based on the max- imum attraction principle for estimating customer demand and utility gain from service is established and analyzed. Combinatorial properties such as the submodularity and novel valid (facet defining) inequalities for the determinis- tic problem are investigated. The numerical experiments show that the model admits high computational efficiency in solving mid-size instances.