This paper establishes and analyzes a service center location model with a simple but novel decision-dependent demand induced from a maximum attraction principle. The model formulations are investigated in the distributionally-robust optimization framework for the capacitated and uncapacitated cases. A statistical model that is based on the maximum attraction principle for estimating customer demand and utility gain from service is established and analyzed. Novel valid (facet defining) inequalities for the deterministic problem are investigated for an independent interest. The numerical experiments show that the model admits high computational efficiency in solving mid-and large-size instances.