Mean-Variance Location Problems

In this paper we discuss three mean-variance location problems. Two of them are constrained problems where one performance measure—mean of the weighted distance, or variance, is minimized subject to an upper bound constraint on the value of the other. In the third problem the objective function minimized is given by the mean plus a constant times the variance. The paper includes polynomial time algorithms to solve the three problems. The solutions produced by these algorithms are Pareto optimum solutions (solutions that are strictly better than any other solution in at least one of the two measures: mean and variance).