THE WEBER PROBLEM: FREQUENCY OF DIFFERENT SOLUTION TYPES AND EXTENSION TO REPULSIVE FORCES AND DYNAMIC PROCESSES*
研究了韦伯问题中不同解类型（如位于吸引点、无穷远、多边形内外）的出现频率，并扩展到包含斥力点的情况，提出了三角形中一个斥力两个吸引点的三角解法，对动态区位过程分析有参考价值。
ABSTRACT. The frequency of occurrence of the different types of solutions to the Weber problem is studied. These solutions are: a location at an attraction point due to a dominant force, to incompatible angles, or to concavity; a location at infinity; a location inside the polygon; and a location outside the polygon. Situations involving both attraction and repulsion points are examined in the triangle and in the more‐than‐three‐sided polygon context, and methods for solving the corresponding problems are compared. A trigonometric solution is proposed for the triangle case involving one repulsion and two attraction points. The variation in the frequency of a location at an attraction point when the number of attraction points increases while the number of repulsion points remains the same is observed as well. Implications of the results are studied for the analysis of dynamic location processes.