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

A Note on Two-Stage Fuzzy Location Problems Under VaR Criterion With Irregular Fuzzy Variables

“…Since the method of fuzzy simulation is time-consuming, these algorithms are hard to work out the exact optimal solutions within a reasonable time. Recently, Yang et al [18] developed a new solution approach to the two-stage location model proposed by Wang et al [15], which significantly reduced the computational complexity, and meanwhile, exactly figured out the optimal solution.…”

“…In the remainder of this note, our interest is focused on the two-stage location model discussed in [15] and [18] and its solution approaches. For more detailed comparisons of the optimization models and solution approaches to the location problem with fuzzy parameters, readers are recommended to visit the literature review in [18].…”

“…However, Yang et al [18] showed that the VaR of a location decision can be determined exactly by solving its corresponding linear programming if all the fuzzy parameters in the model are regular fuzzy variables (e.g., triangular and Gaussian fuzzy numbers) based on the operational law proposed by Zhou et al [20]. Accordingly, the VaR-based TFL model can be transformed into a one-stage deterministic programming.…”

“…Nevertheless, in [18], the proposed approach was designed for the case with regular fuzzy variables. This restriction limits its applications to other situations.…”

“…For instance, when the problem's fuzzy parameters are modeled by the commonly used trapezoidal fuzzy numbers (as stated in Section I-A), the approach is not amenable to solution. If the fuzzy parameters have discrete support such as the example introduced in [15] (this example is elaborated and discussed in Section IV-A), then the approach developed by Yang et al [18] is ineffective as well. Therefore, to overcome this drawback, this note intends to extend the work of Yang et al [18] to more generalized cases.…”