Determination of optimal MR&R policies for retaining life-cycle connectivity of bridge networks

Bridge management problems are computationally difficult to solve when considering network connectivity, because all bridges must be analyzed together. Past research has usually adopted simulation-based numerical methods, which are inaccurate and time-consuming. In this paper, an analytical and efficient approach is presented to determine the optimal maintenance, rehabilitation, and replacement (MR&R) plan. The objective is to ensure an adequate level of network reliability at the lowest possible life-cycle maintenance cost. Instead of considering the evolution of network reliability over the whole life cycle, the optimization is formulated with a constraint on the lower bound of network reliability, which reduces the network-level problem to one of optimizing the set of reliability levels for individual bridges. For simple decomposable networks, the network-level optimization can be tackled with standard techniques in polynomial time. For complex networks that are nondecomposable, an algorithm is provided to transform the nonlinear integer programming problem into binary integer linear programming. Finally, the framework is extended to networks with multiple origin-destination pairs. The contribution of this paper is a novel approach to solve the network connectivity problem, which makes it possible to use standard optimization tools (with guaranteed convergence to optimality), as opposed to the heuristic algorithms used in related literature.