The internal complexity of lifeline systems and their interdependencies amplify the vulnerability of external disruptions. We consider lifeline infrastructures as a network system with supply, transshipment, demand nodes and arcs constructed between node-pair for conveying service flows. The complex interactive network system can be modeled as multi-layered graphs, whereby the power network depends on the gas network linked through the gasified power plants. Similarly, the water network depends on both quality and quantity of power supply. A successful emergency rescue can make lifeline infrastructures more resilient against natural disasters and unexpected accidents. This study focuses on a resource allocation and schedule problem to restore the most critical components quickly in the multiple interdependent lifeline infrastructures under disruptions. The key objectives of quick response model include reducing the overall losses caused by the accidents, and restoring system functions as quickly as possible. The Resource Allocation Model (RAM) for rescue was formulated as a two-stage mixed-integer programming, in which the first stage problem aims to minimize the total losses, while the second stage problem is to optimize resource allocation for rescue service within the rescue time horizon using the proposed heuristic algorithm in polynomial complexity. In the meantime, those tasks/components to be repaired are selected by the proposed vulnerability analysis method to guarantee the optimal whole network efficiency, and then put them into the Resource Allocation Model. The simulation results demonstrate that the proposed approaches are both efficient and effective to solve the real-life post-disaster resource allocation problem. 
A two-stage resource allocation model for lifeline systems quick response with vulnerability analysis