The β‐reliable minimax and maximin location problems on a network with probabilistic weights

We study the β‐reliable minimax and maximin location problems on a network when the weights associated with the nodal points are random variables. In the β‐reliable minimax (maximin) problem, we locate a single facility so as to minimize (maximize) the upper (lower) bound on the maximum (minimum) weighted distance from the nodes to the facility with a probability greater than or equal to a pre‐specified level β. It is shown that under some conditions the two probabilistic models are equivalent to their deterministic counterparts. Solution procedures are developed to solve the problems with weights of continuous and discrete probability distributions.