Distributionally robust facility location problem under decision-dependent stochastic demand

While the traditional facility location problem considers exogenous demand, in some applications, locations of facilities could affect willingness customers to use certain types services, e.g., carsharing, and therefore they also realizations random demand. Moreover, a decision maker may not know exact distribution such endogenous demand how it is affected by choices. In this paper, we consider distributionally robust problem, which interpret moments stochastic as functions facility-location decisions. We reformulate two-stage decision-dependent optimization model monolithic formulation, then derive mixed-integer linear programming reformulation well valid inequalities when means variances are piecewise solutions. conduct extensive computational studies, compare our with deterministic model, models without assumption. The results show superior performance approach remarkable improvement profit quality service under various settings, addition speed-ups given formulation enhancements. These draw attention need considering impact decisions on customer within strategic-level planning problem.