Application of decision analysis techniques to the Weber facility location problem

A location problem with future uncertainties about the data is considered. Several possible scenarios about the future values of the parameters are postulated. However, it is not clear which of these scenarios will actually happen. We find the location that will best accommodate the possible scenarios. Four rules utilized in decision theory are examined: the expected value rule, the optimistic rule, the pessimistic rule, and the minimax regret rule. The solution for the squared Euclidean distance is explicitly found. Algorithms are suggested for general convex distance metrics. An example problem is solved in detail to illustrate the findings, and computational experiments with randomly generated problems are reported.