Determining the coordinates of the location of the distribution center in logistics taking into account the random component

In transport, warehouse and other types of logistics, there is a task of determining the coordinates of the optimal distribution center. In a simple case, this task is reduced to determining the center of mass on the plane in an analytical or graphical way. In general, the neighborhood of points surrounding the likely location of the distribution center and the location of consumers to whom resources are supplied from it, and the points themselves, when linked to a specific map, cannot be located «exactly according to coordinates». In this case, it is useful to introduce the concept of a neighborhood of points, such a neighborhood, the coordinates of points in this neighborhood, can be represented by a distribution of random variables. Such a view will allow you to get additional information about the possibility of placing a distribution center when linking its location to a specific map.