Value-at-Risk-Based Two-Stage Fuzzy Facility Location Problems
Value-at-Risk-Based Two-Stage Fuzzy Facility Location Problems
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DOI：
10.1109/tii.2009.2022542
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发表时间：
2009-11-01
影响因子：
12.3
通讯作者：
Pedrycz, Witold
中科院分区：
文献类型：
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作者：
Wang, Shuming;Watada, Junzo;Pedrycz, Witold
在应对不准确信息时减少选址决策的风险，对于供应链管理至关重要，以提高竞争力和盈利能力。本文提出了一个带有风险值的两阶段模糊设施选址问题（VaR-FFLP），其结果是一个两阶段模糊0 - 1整数规划问题。讨论了VaR-FFLP的一些性质，包括完全信息值（VPI）、模糊解值（VFS）和模糊解的界。由于选址问题的模糊参数是以连续模糊变量的形式表示的，因此，VaR的确定本质上是一个无限维的优化问题，无法解析求解。因此，提出了一种基于模糊变量离散化的方法来近似VaR。近似方法将原始问题转换为有限维优化问题。证明了该逼近方法的一个收敛性定理。随后，结合单纯形算法、近似方法和基于基因型-表型-变异的二进制粒子群优化（GPM-BPSO）机制，提出了一种混合GPM-BPSO算法来求解VaR-FFLP。一个数值例子说明了混合GPM-BPSO算法的有效性，并显示其增强的性能相比，通过其他方法，使用遗传算法（GA），禁忌搜索（TS），布尔BPSO（B-BPSO）得到的结果。
Reducing risks in location decisions when coping with imprecise information is critical in supply chain management so as to increase competitiveness and profitability. In this paper, a two-stage fuzzy facility location problem with Value-at-Risk (VaR), called VaR-FFLP, is proposed, which results in a two-stage fuzzy zero-one integer programming problem. Some properties of the VaR-FFLP, including the value of perfect information (VPI), the value of fuzzy solution (VFS), and the bounds of the fuzzy solution, are discussed. Since the fuzzy parameters of the location problem are represented in the form of continuous fuzzy variables, the determination of VaR is inherently an infinite-dimensional optimization problem that cannot be solved analytically. Therefore, a method based on the discretization of the fuzzy variables is proposed to approximate the VaR. The Approximation Approach converts the original problem into a finite-dimensional optimization problem. A pertinent convergence theorem for the Approximation Approach is proved. Subsequently, by combining the Simplex Algorithm, the Approximation Approach, and a mechanism of genotype-phenotype-mutation-based binary particle swarm optimization (GPM-BPSO), a hybrid GPM-BPSO algorithm is being exploited to solve the VaR-FFLP. A numerical example illustrates the effectiveness of the hybrid GPM-BPSO algorithm and shows its enhanced performance in comparison with the results obtained by other approaches using genetic algorithm (GA), tabu search (TS), and Boolean BPSO (B-BPSO).