Design Of A Min-Sum Arborescence With Outage Costs

We present an integer programming formulation of the min-sum arborescence with node outage costs problem. The solution to the problem consists of selecting links to connect a set of terminal nodes to a root node with minimal expected annual cost, where the annual cost is the sum of annual links costs and annual outage costs. The links in the network are prone to failure and each terminal node has an associated outage cost, which is the economic cost incurred by the network user whenever that node is disabled from the central node due to failure of a link. We suggest a Lagrangian-based heuristic to get a good solution to this problem. This solution procedure also gives lower bounds to the optimal solution and is used to assess the quality of the heuristic solution. Numerical experiments taken from instances with up to 100 nodes are used to evaluate the performance of the proposed heuristic.