Robust positioning of service units

In this paper, we address the problem of locating mobile service units to cover random incidents. The model does not assume complete knowledge of the probability distribution of the location of the incident to be covered. Instead, only the main value of that distribution is known. We propose the minimization of the maximum expected response time as an effectiveness measure for the model. Thus, the solution obtained is robust with respect to any probability distribution. The cases of one and two service units under the nearest allocation rule are studied in the paper. For both problems, the optimal solutions are shown to be degenerate distributions for the servers.