Evasive flow capture: A multi-period stochastic facility location problem with independent demand

We introduce the problem of locating facilities over a finite time horizon with the goal of intercepting stochastic traffic flows that exhibit evasive behavior, which arises when locating weigh-in-motion systems, tollbooths, vehicle inspection stations, or other fixed flow-capturing facilities used for law enforcement. The problem can be formulated as a multi-stage, mixed-integer stochastic program; however, under certain independence assumptions, this can be reformulated as a large two-stage stochastic program, enabling us to solve much larger instances. We additionally propose an algorithm based on Lagrangian relaxation that separates the reformulated stochastic program into a variant of a deterministic knapsack problem and a sum of time-decoupled single-period stochastic programs that can be solved independently. The model and algorithm are tested on instances involving road networks of Nevada and Vermont. A comparison with the previously studied single-period stochastic programming approach shows that the newly proposed multi-period model substantially reduces the expected cost.