Location-coverage models for preventing attacks on interurban transportation networks

Interurban roads are constantly used by transient vehicles. In some places, however, network users are subject to attacks, resulting in assaults to drivers and cargo theft. In an attempt to solve this problem, a binary integer programming model is developed, whose objective is to maximize the expected vehicle coverage across the network. The model dynamically locates patrol units through a fixed time horizon, subject to movement and location constraints, considering a probability of not being able to attend to an attack, due to a distance factor. A chronological decomposition heuristic is developed, and achieves an optimality gap of less than 1 %, in less than 5 min. The problem is also solved by developing a geographical decomposition heuristic. To introduce a measure of equity, two sets of constraints are proposed. Three measures are considered: total vehicle coverage, inequity and network coverage. A trade-off between these three measures is observed and discussed. Finally, scalability of the model is explored, using decomposition in terms of patrolling units, until we obtain subproblems of equal size as the original instance. All of these features are applied to a case study in Northern Israel. In the last section, some adaptations and additions to the model that can be made in further research are discussed.