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设施网络可能面临各种失灵风险,而设施选址属于战略决策问题,短期内难以改变,因而在选址设计时需要充分考虑设施的非完全可靠性。本文针对无容量限制的可靠性固定费用选址问题进行扩展,进一步考虑设施的容量约束,基于非线性混合整数规划方法建立了一个有容量限制的可靠性固定费用选址问题优化模型。针对该模型的特点,应用线性化技术进行模型转化,并设计了一种拉格朗日松弛算法予以求解。通过多组算例分析,验证了算法的性能。算例分析结果表明设施失灵风险和设施容量对于选址决策有显著影响,因而在实际的选址决策过程中有必要充分考虑设施的失灵风险及容量约束。
Facilities networks may face a variety of failure risks, and the location of facilities is a matter of strategic decision making and difficult to change in the short term. Therefore, the incomplete reliability of facilities needs to be fully considered in site design. In this paper, we extend the problem of fixed cost location without reliability and consider the capacity constraints of the facility. Based on the nonlinear mixed integer programming, we establish a cost-constrained optimization model of fixed cost location problem. According to the characteristics of the model, the linear transformation technique is applied to model transformation and a Lagrangian relaxation algorithm is designed to solve the problem. Through multiple sets of example analysis, the performance of the algorithm is verified. The case study shows that the risk of facility failure and facility capacity have a significant impact on the site selection decision. Therefore, it is necessary to fully consider the failure risk and capacity constraint of the facility during the actual site selection decision-making process.