Applying ranking and selection procedures to long-term mitigation for improved network restoration

In this paper we consider methods to determine the best single arc mitigation plan for improving rapid recovery of a network with a given level of statistical certainty. This problem is motivated by infrastructure managers interested in increasing the resilience of their systems through costly long-term mitigation procedures. Our problem is two-stage, where we consider a small number of pre-event decisions for mitigation, with a large second-stage integer programming problem to capture the restoration process for each damage scenario and each mitigation plan. We consider a ranking and selection (R&S) procedure and compare its performance against a brute force method using standard statistical testing on problems with low, medium, and high damage levels. These comparisons are made by using the same number of integer programs for each method, and comparing the level of confidence achieved to determine a best single arc mitigation plan. We find that R&S procedures perform as well or better than brute force procedures in all cases, and significantly outperform the brute force procedure in almost all cases (five out of six). Having developed a general framework for determining the best single arc mitigation plan for any network, we conclude with thoughts and challenges on how this framework can be expanded and applied to different problems.