The escape interdiction problem within the context of attacker activities on a transportation network is addressed in this study. In the absence of traffic within the network, the attacker attempts to flee the city by choosing one of the shortest paths from the crime scene to a randomly selected exit point. However, in the presence of traffic, the attacker strategically selects the optimal route that minimizes his time to reach a randomly selected exit point. On the other side, defenders try to interdict the attacker on his escape route. Defenders face the daunting challenge of interdicting the attacker's escape route while operating under limited resources. Dealing with a real city road network further adds complexity to the scenario. A simulation-based model is proposed for the optimal allocation of resources to tackle this issue. The focus then shifts to the development of an advanced search strategy that involves routing with optimal resource allocation. This paper presents the first comparative study for escape interdiction problems within a simulation environment, explicitly focusing on solution methodologies. An optimal resource allocation approach is proposed in the presence of traffic, constituting a novel contribution that has not been previously implemented in escape interdiction problems. In addition, the paper introduces a Genetic Algorithm (GA)-based meta-heuristic approach within a simulation environment. This approach generates optimal paths for defenders, wherein each node is associated with a fixed time window, representing the defender's waiting time. In this proposed methodology, defenders undertake a tour of the network rather than remaining stationary at a single location. This approach expands the network search capabilities, thereby requiring optimization to ascertain the optimal routes and schedules for the defender vehicles. A case study is conducted using the map of IIT Kharagpur, India, to evaluate the effectiveness of this approach. By employing this approach and conducting in-depth analyses, the aim is to provide valuable insights into the efficiency and practicality of the developed methods on real-world transportation networks.

Containment of dynamic crimes such as kidnapping, bank robbery, hit-and-run, etc., is a challenging issue for law enforcement agencies as the criminal changes his location with time. This type of scenario is generally modelled as an escape interdiction game. We consider two types of players, namely multiple defenders and a single attacker. The defenders choose a sequence of junctions to protect, while the attacker chooses an escape path and the travel time on distinct edges along the path. Hence, both the defender strategy space and the continuous attacker strategy space suffer an exponential growth. This leads to major challenges in the computation of the optimal solution with respect to each player. We develop a double oracle Variable Neighborhood Search (VNS) based meta-heuristic algorithm for finding near-optimal defender and attacker strategies in a time efficient manner. We test the efficiency of this approach against an established exact algorithm named Escape Interdiction Game Solver (EIGS). We use EIGS to generate the benchmark results to check the performance of our heuristic. We also show that the performance of our approach is reasonably good under strict time limitations, as observed in practice.

This correction is published as author missed out critical corrections related with referencing style. The article files have now been corrected.

Police patrol is an effective crime prevention tool and boosts public confidence in urban security. Many interesting decision making problems appear in route design, resource allocation and jurisdiction planning. Many cities across the world have adopted a structured and intelligent method of police patrol due to the presence of a variety of operational and resource constraints. In this paper, we present a comprehensive review of the state-of-the-art in this domain, especially from the practice of operations research (OR) point of view. This is the first-of-its-kind review on police patrol presenting a classification scheme based on the type of problem, objective and modelling approach. In this novel scheme, one can track any paper almost readily to find the specific contribution. The applicability of OR in this domain is set to grow significantly as the governments formulate policies related to smart city planning and urban security. This study reveals many practical challenges in police patrolling for future research.

The dynamic crimes like kidnapping, bank robbery, ATM loot must get special attention from police as the static crime removal techniques are insufficient to contain this type of crime. Here, the criminal changes his location with time. Thus, the decisions should be made rapidly within a certain amount of time. Again, the city road networks are complex, and the police resources are also limited. Therefore, an effective resource allocation strategy for police vehicles needs to be developed to catch the criminal. We propose a simulation-based approach using the Simulation of Urban MObility (SUMO) simulator to develop interdiction strategies. The developed simulation approach is tested with a case study in the IIT Kharagpur road network with 123 nodes and 281 edges.