Network interdiction to minimize the maximum probability of evasion with synergy between applied resources

In this paper, we model and solve the network interdiction problem of minimizing the maximum probability of evasion by an entity traversing a network from a given source to a designated terminus, while incorporating novel forms of superadditive synergy between resources applied to arcs in the network. Inspired primarily by operations to coordinate Iraqi and U.S. security forces seeking to interdict an evader attempting to avoid detection while transiting part of the nearly rectilinear street network in East Baghdad, this study motivates and examines either linear or concave (nonlinear) synergy relationships between the applied resources within our formulations. We also propose an alternative model for sequential overt and covert deployment of subsets of interdiction resources, and conduct theoretical as well as empirical comparative analyses between models for purely overt (with or without synergy) and composite overt-covert strategies to provide insights into absolute and relative threshold criteria for recommended resource utilization. Our empirical results confirm the value of tactical patience regarding decisions on the covert utilization of resources for network interdiction. Furthermore, considering non-integral and integral resource allocations, we identify (theoretically and empirically) parametric characteristics of instances that exhibit the relative worth of employing partially covert operations. Under the relatively more practical scenario involving integral resource allocations, we demonstrate that the composite overt-covert strategy of deploying resources has a greater potential to improve over a purely overt resource deployment strategy, both with and without synergy, particularly when costs are positively correlated, resources are plentiful, and a sufficiently high ratio of covert to overt resources exists. Moreover, should an interdictor be able to ascertain an optimal evader path, the potential and magnitude of this relative improvement for the overt-covert resource allocation strategy is significantly greater.