A two-stage stochastic programming model for transportation network protection

Network protection against natural and human-caused hazards has become a topical research theme in engineering and social sciences. This paper focuses on the problem of allocating limited retrofit resources over multiple highway bridges to improve the resilience and robustness of the entire transportation system in question. The main modeling challenges in network retrofit problems are to capture the interdependencies among individual transportation facilities and to cope with the extremely high uncertainty in the decision environment. In this paper, we model the network retrofit problem as a two-stage stochastic programming problem that optimizes a mean-risk objective of the system loss. This formulation hedges well against uncertainty, but also imposes computational challenges due to involvement of integer decision variables and increased dimension of the problem. An efficient algorithm is developed, via extending the well-known L-shaped method using generalized benders decomposition, to efficiently handle the binary integer variables in the first stage and the nonlinear recourse in the second stage of the model formulation. The proposed modeling and solution methods are general and can be applied to other network design problems as well.