Abstract: 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.

Key words: curved demands, facility location, reliability, time penalty, p-median problem