Optimum Location Probabilities in the l_p Distance Weber Problem

In this paper it is assumed that the weights which summarize cost and volume parameters in the Weber problem are known only probabilistically. In general, the object is to find the probability that the facility will be optimally located at any given point or in any region. We assume that the weights have a truncated (no negative values) multivariate normal distribution with known means, variances and covariances. An efficient computational procedure is given in the p = 1 case (rectangular distances) for finding the desired probabilities approximately. An efficient method is also given for finding the approximate probability that a facility will be optimally located at any given demand point in the general l_p case.