The generalized Weber problem with expected distances

In this paper the authors study a generalized Weber problem where both demand locations and the facility to be located may be regions and are assumed to be distributed according to some probability measures inside each region. A general notation is proposed to describe these location problems and several properties are proved which enable the resolution of the problem using existing algorithms. In some special cases the gradient of the objective function is evaluated, leading to the resolution of a wide range of problems even when the exact expression for the objective function is unknown. This methodology is applied to some cases.