Network disruption recovery for multiple pairs of shortest paths

For an arc-disrupted network, we investigate the problem of partially recovering this network by given budget resource such that the total weighted transportation cost for all the origin-destination pairs is minimized. To obtain the solutions, we propose two heuristic algorithms based on Lagrangian relaxation, which both can generate good feasible solutions for the network disruption recovery problem. Accordingly, we are able to study how the marginal efficiency changes of providing additional resource and then decide the appropriate amount of budget resource to achieve the optimal social welfare.