Probabilistic demands and costs in facility location problems.

In this paper, the definition of medians in 'classical' location problems is generalized to the cases: 1) when generated demands and travel costs are random, and 2) when the demand induced at the facilities is random because of competition. Under a particular set of assumptions, the well-known theorems on 'optimality of node locations' hold for the underlying 'probabilistic networks'. For case 1) the model is shown to be a generalization of the probabilistic and deterministic median location problem is also pointed out. For case 2) the 'competitive median location' problem is formulated, and some results presented. For the special structure of probabilistic tree networks some interesting localization properties for both medians are discussed.-from Authors