Optimal Resource Allocation Strategies to Protect Network-structured Systems

Protection of critical national infrastructure has received significant attention in the past recent years. As a result, researchers have developed methods to preserve and maintain critical infrastructure systems and minimize their vulnerability to disasters and disruptions. However, these models are often customized to meet the characteristics and functionality requirements for a particular system, and are computationally intensive and require simplifying assumptions. In this study, we first develop a tractable and relatively comprehensive model for optimizing maintenance planning of generic network-structured systems. We considered both linear and nonlinear objective functions for our problems. We then reformulate the model in order to enhance its computational effectiveness for large scale complex problems. The proposed modeling framework inherently captures the network topography, the stochastic nature of disruptions, and can be applied to network-structured systems for which performance is assessed based on network flow efficiency and mobility.

A hypothetical small-sized network is used to illustrate the developed models, and the pro- posed models are also applied to analyze a larger scale real network in order to assess their relative computational effectiveness and robustness. We selected the Istanbul highway net- work for the latter purpose because of its critical location and also because it has been considered in previous studies, which enables us to compare the effectiveness of our models with an existing model in the literature. We designed several test cases (considering single and multiple treatment types, and linear and nonlinear objectives), and solved them on the NEOS server using different available software. The results demonstrate that our models are capable of attaining optimal solutions within a very short time. Furthermore, the linear model is shown to yield a good approximation to the nonlinear model (it determined solutions within 0.3% of optimality, on average). Moreover, in both cases (our hypothetical illustrative example and the Istanbul highway network), the optimal policies obtained appear to favor the selection of fewer links and to apply a higher quality treatment to them.