Analysing the police patrol routing problem : a review

Police patrol is a complex process. While on patrol, police officers must balance many intersecting responsibilities. Most notably, police must proactively patrol and prevent offenders from committing crimes but must also reactively respond to real-time incidents. Efficient patrol strategies are crucial to manage scarce police resources and minimize emergency response times. The objective of this review paper is to discuss solution methods that can be used to solve the so-called police patrol routing problem (PPRP). The starting point of the review is the existing literature on the dynamic vehicle routing problem (DVRP). A keyword search resulted in 30 articles that focus on the DVRP with a link to police. Although the articles refer to policing, there is no specific focus on the PPRP; hence, there is a knowledge gap. A diversity of approaches is put forward ranging from more convenient solution methods such as a (hybrid) Genetic Algorithm (GA), linear programming and routing policies, to more complex Markov Decision Processes and Online Stochastic Combinatorial Optimization. Given the objectives, characteristics, advantages and limitations, the (hybrid) GA, routing policies and local search seem the most valuable solution methods for solving the PPRP

A Proposed Bi-layer Crime Prevention Framework Using Big Data Analytics

The future of science and technology sounds very promising. The need to adopt new technologies while navigating towards industry 4.0 has changed the perceptions of law enforcement agency to contend against criminal minds. It is sad but true that the conventional crime prevention system followed by government agencies is not effective for long-term implications. With advanced technologies that constantly generate and exchange data, big data analytics can be applied to predict and prevent crime from happening. However, dealing with the overwhelming amount of complex and heterogeneous crime-related data is never an easy task. Additionally, there are many data analytical techniques and each of them has its own strengths and weaknesses. In order to identify the most efficient techniques, recent literature is reviewed to spotlight the trend as well as to shed light on the research gaps and challenges in various areas. The areas include crime data collection and preprocessing, crime data analysis, crime prediction and crime prevention. These techniques are further analyzed by considering the advantages and disadvantages which then provides insight to propose a bi-layer crime prevention framework. The first layer intends to support the law enforcement agency’s daily operation while the second layer serves as a countermeasure for first layer. Both layers aim to reduce the crime rate by involving law enforcement agency through the utilization of various big data sources and techniques effectively. The proposed crime prevention framework will progressively collect data to deter criminal behavior for city’s environmental design. Ultimately, a safe and secure city is molded in the near future

A Balanced Route Design for Min-Max Multiple-Depot Rural Postman Problem (MMMDRPP): a police patrolling case

Providing distributed services on road networks is an essential concern for many applications, such as mail delivery, logistics and police patrolling. Designing effective and balanced routes for these applications is challenging, especially when involving multiple postmen from distinct depots. In this research, we formulate this routing problem as a Min-Max Multiple-Depot Rural Postman Problem (MMMDRPP). To solve this routing problem, we develop an efficient tabu-search-based algorithm and propose three novel lower bounds to evaluate the routes. To demonstrate its practical usefulness, we show how to formulate the route design for police patrolling in London as an MMMDRPP and generate balanced routes using the proposed algorithm. Furthermore, the algorithm is tested on multiple adapted benchmark problems. The results demonstrate the efficiency of the algorithm in generating balanced routes

Predictive police patrolling to target hotspots and cover response demand

Police forces are constantly competing to provide adequate service whilst faced with major funding cuts. The funding cuts result in limited resources hence methods of improving resource efficiency are vital to public safety. One area where improving the efficiency could drastically improve service is the planning of patrol routes for incident response officers. Current methods of patrolling lack direction and do not consider response demand. Police patrols have the potential to deter crime when directed to the right areas. Patrols also have the ability to position officers with access to high demand areas by pre-empting where response demand will arise. The algorithm developed in this work directs patrol routes in real-time by targeting high crime areas whilst maximising demand coverage. Methods used include kernel density estimation for hotspot identification and maximum coverage location problems for positioning. These methods result in more effective daily patrolling which reduces response times and accurately targets problem areas. Though applied in this instance to daily patrol operations, the methodology could help to reduce the need for disaster relief operations whilst also positioning proactively to allow quick response when disaster relief operations are required

Police officer dynamic positioning for incident response and community presence

Police Forces are under a constant struggle to provide the best service possible with limited and decreasing resources. One area where service cannot be compromised is incident response. Resources which are assigned to incident response must provide attendance to the scene of an incident in a timely manner to protect the public . To ensure the possible demand is met maximum coverage location planning can be used so response officers are located in the most effective position for incident response. This is not the only concern of response officer positioning. Location planning must also consider targeting high crime areas, hotspots, as an officer presence in these areas can reduce crime levels and hence reduce future demand on the response officers. In this work hotspots are found using quadratic kernel density estimation with historical crime data. These are then used to produce optimal dynamic patrol routes for response officers to follow. Dynamic patrol routes result in reduced response times and reduced crime levels in hotspot areas resulting in a lower demand on response officers

Essays on Shipment Consolidation Scheduling and Decision Making in the Context of Flexible Demand

This dissertation contains three essays related to shipment consolidation scheduling and decision making in the presence of flexible demand. The first essay is presented in Section 1. This essay introduces a new mathematical model for shipment consolidation scheduling for a two-echelon supply chain. The problem addresses shipment coordination and consolidation decisions that are made by a manufacturer who provides inventory replenishments to multiple downstream distribution centers. Unlike previous studies, the consolidation activities in this problem are not restricted to specific policies such as aggregation of shipments at regular times or consolidating when a predetermined quantity has accumulated. Rather, we consider the construction of a detailed shipment consolidation schedule over a planning horizon. We develop a mixed-integer quadratic optimization model to identify the shipment consolidation schedule that minimizes total cost. A genetic algorithm is developed to handle large problem instances. The other two essays explore the concept of flexible demand. In Section 2, we introduce a new variant of the vehicle routing problem (VRP): the vehicle routing problem with flexible repeat visits (VRP-FRV). This problem considers a set of customers at certain locations with certain maximum inter-visit time requirements. However, they are flexible in their visit times. The VRP-FRV has several real-world applications. One scenario is that of caretakers who provide service to elderly people at home. Each caretaker is assigned a number of elderly people to visit one or more times per day. Elderly people differ in their requirements and the minimum frequency at which they need to be visited every day. The VRP-FRV can also be imagined as a police patrol routing problem where the customers are various locations in the city that require frequent observations. Such locations could include known high-crime areas, high-profile residences, and/or safe houses. We develop a math model to minimize the total number of vehicles needed to cover the customer demands and determine the optimal customer visit schedules and vehicle routes. A heuristic method is developed to handle large problem instances. In the third study, presented in Section 3, we consider a single-item cyclic coordinated order fulfillment problem with batch supplies and flexible demands. The system in this study consists of multiple suppliers who each deliver a single item to a central node from which multiple demanders are then replenished. Importantly, demand is flexible and is a control action that the decision maker applies to optimize the system. The objective is to minimize total system cost subject to several operational constraints. The decisions include the timing and sizes of batches delivered by the suppliers to the central node and the timing and amounts by which demanders are replenished. We develop an integer programing model, provide several theoretical insights related to the model, and solve the math model for different problem sizes

Determining optimal police patrol deployments: a simulation-based optimisation approach combining agent-based modelling and genetic algorithms

One of the most important tasks faced by police agencies concerns the strategic deployment of patrols in order to respond to calls whilst also deterring crime. Current deployment strategies typically lack robustness as they are often based on tradition. As police agencies are encouraged to improve the effectiveness and efficiency of their services, it is essential to devise advanced patrol deployments that are based on recent scientific evidence. Most existing models of patrol deployments are too simplistic, and are thus unable to provide a realistic representation of the complexity of patrol activities. Furthermore, past studies have tended to focus on individual aspects of patrol deployment such as efficiency, reactive effectiveness or proactive effectiveness, rather than consider them all together as part of the same problem. This thesis proposes to develop a decision-support tool for informing better patrol deployment designs. This tool consists of a simulation-based optimisation approach combining two key components: (1) an agent-based model (ABM) of patrol activities used to evaluate the performance of the system under a given deployment configuration and (2) a genetic algorithm (GA) which seeks to speed up the search for optimal deployments. While the developed framework is designed to be applicable to any police force, a case study is provided for the city of Detroit in order to demonstrate its potential. The developed decision-support tool shows considerable potential in informing more cost-effective patrol deployments. First, the ABM of patrol activities allows for exploration of the impact of various deployment decisions that police agencies are unable to experiment with in the real world. Second, the GA makes it possible to optimise patrol deployments by identifying 'good' solutions, which provide faster responses to incidents and deter crime in key areas, in reasonable time

Developing Police Patrol Strategies Based on the Urban Street Network

In urban areas, crime and disorder have been long-lasting problems that spoil the economic and emotional well-being of residents. A significant way to deter crime, and maintain public safety is through police patrolling. So far, the deployment of police forces in patrolling has relied mainly on expert knowledge, and is usually based on two-dimensional spatial units, giving insufficient consideration to the underlying urban structure and collaboration among patrol officers. This approach has led to impractical and inefficient police patrol strategies, as well as a workload imbalance among officers. Therefore, it is of essential importance to devise advanced police patrol strategies that incorporate urban structure, the collaboration of the patrol officers, and a workload balance. This study aims to develop police patrol strategies that would make intelligent use of the street network layout in urban areas. The street network is a key component in urban structure and is the domain in which crime and policing take place. By explicitly considering street network configurations in their operations, police forces are enabled to provide timely responses to emergency calls and essential coverage to crime hotspots. Although some models have considered street networks in patrolling to some extent, challenges remain. First, most existing methods for the design of police districts use two-dimensional units, such as grid cells, as basic units, but using streets as basic units would lead to districts that are more accessible and usable. Second, the routing problem in police patrolling has several unique characteristics, such as patrollers potentially starting from different stations, but most existing routing strategies have failed to consider these. Third, police patrolling strategies should be validated using real-world scenarios, whilst most existing strategies in the literature have only been tested in small hypothetical instances without realistic settings. In this thesis, a framework for developing police patrol strategies based on the urban street network is proposed, to effectively cover crime hotspots, as well as the rest of the territory. This framework consists of three strategies, including a districting model, a patrol routing strategy for repeated coverage, and a patrol routing strategy for infrequent coverage. Various relevant factors have been considered in the strategy design, including the underlying structure of the street network and the collaboration among patrollers belonging to different stations. Moreover, these strategies have been validated by the patrolling scenarios in London. The results demonstrate that these strategies outperform the current corresponding benchmark strategies, which indicates that they may have considerable potential in future police operations