AbstractWe study a problem in which a facility has to be located in a given area to serve a given number of customers. The position of the customers is not known. The service to the customers is carried out by several traveling salesmen. Each of them has a capacity in terms of the maximum number of customers that can be served in any tour. The aim is to determine the service zone (in a shape of a circle) that minimizes the expected cost of the traveled routes. The center of the circle is the location of the facility. Once the position of the customers is revealed, the customers located outside the service zone are served with a recourse action at a greater unit cost. For this problem, we compare the performance of two different approaches. The first is a solution based on a heuristic proposed for a similar well known problem and the second is a solution based on a stochastic second–order cone model. An illustrative example on a United States instance with 13509 nodes shows the different solutions and expected costs obtained by the two approaches.