The Probabilistic Network Design Problem

We analyze the probabilistic variation of the multicommodity discrete network design problem named the probabilistic network design problem in which the commodities are generated probabilistically and the objective is to calculate the expected value of all possible network design instances. We extend the a priori strategy which has been successfully applied to the probabilistic variations of the traveling salesman and mill1mum spanning tree problems. We use the a priori network strategy, which can be seen as an extension of I.he a priori strategy, to calculated the upper bounds of the expectations of the network design costs, and analyze several heuristic methods for constructing the a priori network both in the worse case model and in the probabilistic model. We also derive the lower bounding procedure using the probabilistic extensions of valid inequalities which, by combining the linear programming technique and the cutting plane procedure, induce the lower bounds of the expected network design costs.