A new solution approach to two-stage fuzzy location problems with risk control

In the present paper, a two-stage fuzzy facility location problem under the Value-at-Risk (VaR) criterion is considered for controlling the risk in location decisions. Because the fuzzy parameters involved are represented in the form of regular fuzzy numbers (e.g., triangular, Gaussian, and Cauchy fuzzy numbers), it is shown that the VaR of a location decision can be determined exactly by solving the corresponding linear programming problem. This new solution approach has a significantly lower computation complexity compared with the already known approximation treatment of the problem. In this regard, the VaR-based two-stage fuzzy location model is transformed into a one-stage mixed-integer linear programming model, and is then solved using some standard programming techniques. Furthermore, the VaR-based solutions are shown to be linked to the robust optimization counterparts, and new results for the location decisions and the loss distribution under perfect information are deduced. Finally, numerical examples illustrate the effectiveness of our treatment.