Robust facility location model with two multiplicative uncertainties

Traditional facility location is usually viewed as a deterministic problem. But there exist many uncertain factors (i.e. demand, cost, risk) in a varying environment, which increase difficulties in facility location. Based on considering single uncertainty respectively, we integrate two independent multiplicative uncertainties (demand and transportation cost) together, introduce two budget uncertainty parameters, formulate a novel and intractable nonlinear robust facility location model, and then converse this nonlinear problem into a robust mixed integer linear counterpart. We also use CPLEX and MATLAB for programming to solve this problem. Finally, we choose 13 cities to decide the location-allocation solutions for temporary emergency supplies in Northwest Sichuan. Numerical results show that, compared with transportation cost uncertainty, demand uncertainty has a strong impact on the total cost. Demand disturbance also affects the total cost and location-allocation solution significantly. According to their risk preferences, decision-makers choose the optimal combination of budget uncertainty and demand disturbance proportion, so as to minimize the total cost and get optimal location-allocation solution.