Abstract: Infrastructure networks have the risk of disruptions. Because facility location is a strategic decision that can not be changed in a short time, it is critical to account for the non-complete reliability of facility in designing the network. The classical reliability uncapacitated fixed-charge location problem is extended by considering the capacity constraint. And the reliability capacitated fixed-charge location problem under the risk of disruptions is formulated as a mixed integer nonlinear programming model. Considering the characteristics of the model, a linearization technique is applied to convert the model and a lagrangian relaxation algorithm is developed to solve the problem. A numerical example is given to verify the model and algorithm performance. The results show that facility capacity has a notable impact on location decision, and the unexpected failures of facility and capacity constraint of facility should be fully considered in real-life location decision process.

Key words: facility location, facility disruptions, reliability, capacitated, Lagrangian relaxation

摘要： 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。

关键词: 设施选址, 设施失灵, 可靠性, 容量限制, 拉格朗日松弛