We study a service center location problem with ambiguous utility gains upon
receiving service. The model is motivated by the problem of deciding medical
clinic/service centers, possibly in rural communities, where residents need to
visit the clinics to receive health services. A resident gains his utility
based on travel distance, waiting time, and service features of the facility
that depend on the clinic location. The elicited location-dependent utilities
are assumed to be ambiguously described by an expected value and variance
constraint. We show that despite a non-convex nonlinearity, given by a
constraint specified by a maximum of two second-order conic functions, the
model admits a mixed 0-1 second-order cone (MISOCP) formulation. We study the
non-convex substructure of the problem, and present methods for developing its
strengthened formulations by using valid tangent inequalities. Computational
study shows the effectiveness of solving the strengthened formulations.
Examples are used to illustrate the importance of including decision dependent
ambiguity.Comment: 29 page