Modeling interdependencies in infrastructure systems using multi-layered network flows

•A compact interdependent network flow model that has the capability to capture many common interdependence classifications.•The capability to incorporate non-uniform dependency across the network layers.•The capability to incorporate dependency within a single layer.•A solution method that exploits a high degree of integrality in LP relaxation solutions. We consider the problem of optimizing the operations of interdependent infrastructure systems in a resource-constrained environment. In this problem, decisions consist of determining the set of components that will be operational and how services from different infrastructures will be delivered to operational components. We propose an interdependent multi-layered network flow (IMN) model to solve this problem. In this model, interdependent infrastructures are represented by networks and movement of commodities or services by flows. We seek to maximize the reward obtained from operational components minus the cost of routing flows. We show that IMN is NP-hard in the strong sense even in the case of a single-layer network. We further propose families of valid inequalities for the integer programming formulation of IMN, which are then utilized to develop a solution approach for the problem. The solution approach is tested on synthesized data sets of interdependent infrastructure systems. Our computational results demonstrate that our solution approach can obtain high-quality solutions in less computational time when compared to the mixed integer programming (MIP) formulation solved with standard software for most of the instances. We also show the capability of IMN over the previous models in the literature on interdependent infrastructures’ operations.