考虑设施可靠性的线状需求物流节点选址研究

为了解决交通线路建设物资的物流节点选址问题，在服务线路和需求密度已知的前提下，考虑物流节点可靠性以及物资运输时间约束，建立以运输成本和时间惩罚成本之和为目标函数的数学模型。为了求解该模型，在经典p-中值选址模型基础上，采用线积分取代离散点来表示线状需求，证明目标函数在给定区间内为凸函数，并利用二次插值和黄金分割法相结合的算法对模型进行求解。通过对是否考虑可靠性的2种选址结果进行对比研究，以及对可靠性间的相关性对选址结果的影响进行灵敏度分析。算例分析表明，与不考虑可靠性相比，提高可靠性可以降低选址系统运营总成本，也可定量地刻画出可靠性间的相关性对选址结果的影响。

Logistics Node Location Problem with Curved Demands Considering Facility Reliability

In order to solve the problem of logistics node location for construction materials of the transportation routes, the constraint of material transportation time is considered under the premise that service routes and demand density are given, and a mathematical model is established with the objective function to minimize the sum of transportation cost and time penalty. For the purpose of solving the model, based on the classic p-median location model, the line integration is used to replace the discrete points to represent the demand of a line. The objective function is proved to be convex within a given interval, and solved by the combined algorithm of parabolic interpolation method and golden section search. Through a comparative study on whether to consider the reliability of two facilities location results, and a sensitivity analysis of the impact of the correlation between reliability on the location results, the final example analysis shows that improving reliability can reduce the total operating cost of the location system compared without considering reliability; at the same time, it quantitatively characterizes the impact of the correlation between reliability on the location result.