The hazardous orienteering problem

This article studies the Hazardous Orienteering Problem (HOP), a variant of the more famous Orienteering Problem (OP). In the OP, a vehicle earns a profit for each customer it visits (e.g., to pick up a parcel) subject to an upper bound on the tour time. In the HOP, the parcels picked up at some customers have a probability of triggering a catastrophic event. The probability depends on how long the parcels travel on the vehicle. If any catastrophic event triggers, the entire collected profit is lost. The goal is to determine the tour that maximizes the expected profit. The problem has interesting applications in routing of hazardous material, cash-in-transit, and law enforcement. We propose a mixed-integer nonlinear formulation and techniques both to obtain dual bounds and to produce primal solutions. Computational tests investigate the efficacy of the methods proposed and allow to gain insights into solution features.