Entropy Maximization and Inferred Ideal Weights in Public Facility Location

It is assumed that a planner entrusted with the decision to choose a site for a public service facility attempts to find that location which minimizes the summed weighted distances from the facility to each resident in the service area. An observer may be able to infer the set of relative weights assigned by the planner to the residents by observing the actual site choice and then solving an inverse Weber problem. However, in general, there can be many weighting schemes which are consistent with any given locational choice. This paper uses an entropy model to select the maximally least biased set of weights consistent with the limited information available and examines some of the properties of such a model.