Probabilistic Weights in the One-Dimensional Facility Location Problem

This note deals with the one-dimensional facility location model in which the weights, which can represent either demand volumes or demands and costs combined, are known only probabilistically. The demand points themselves, or at least the “feeder” routes to the demand points, for the facility are located on a straight line which represents a road or some other transportation route. It is assumed that the weights of the demand points have a multivariate normal distribution. The probability of the facility being optimally located at any point on the route is derived; it is shown that only the demand points have non-zero probabilities. In addition, the expected value of perfect information (EVPI) is found. In this problem, the EVPI is the expected difference in costs between the actual best location and the optimum location obtained by using expected weights. The EVPI, therefore, is the maximum amount the decision maker should pay for information about weights if expected values are acceptable as a decision criterion.