<p>A family of set-induced valid inequalities and conditional facet-defining inequalities for a service center location problem with a special location-dependent demand has been investigated in this paper. The location-dependent demand is defined based on a maximum-attraction-principle assumption, which leads to a case-dependent right-hand-side of constraint inequalities. This novel structure makes the polyhedral study appealing and inspiring as it could be extended to other cases. The effectiveness of the valid inequalities has been tested via numerical investigations.</p>