Police districting problem: literature review and annotated bibliography

The police districting problem concerns the efficient and effective design of patrol sectors in terms of performance attributes. Effectiveness is particularly important as it directly influences the ability of police agencies to stop and prevent crime. However, in this problem, a homogeneous distribution of workload is also desirable to guarantee fairness to the police agents and an increase in their satisfaction. This chapter provides a systematic review of the literature related to the police districting problem, whose history dates back to almost 50 years ago. Contributions are categorized in terms of attributes and solution methodology adopted. Also, an annotated bibliography that presents the most relevant elements of each research is given

Investigación de casos de optimización para servicios de seguridad y emergencias

El presente trabajo tiene como objetivo presentar un conjunto de casos relacionados, principalmente, a las diversas formas de optimización de los servicios de seguridad, así como de los servicios de emergencias. Para un mejor entendimiento del estudio se optó por presentar los aspectos teóricos en el primer capítulo, el cual abarca los conceptos de las herramientas que se emplearon en la investigación. Hay presente un mayor énfasis en el uso de herramientas de investigación de operaciones ya que son una de las más usadas para temas de optimización en lo que respecta a este tipo de servicios; sin embargo, también se presenta una base conceptual de otros métodos empleados. En el segundo capítulo se muestran los diversos casos de optimización que resolvieron varios problemas encontrados para los servicios mencionados anteriormente en diferentes partes del mundo. Dentro de cada caso se encuentra una descripción del problema que se resolvió, el procedimiento empleado por cada autor para solucionarlo, explicado mediante la base teórica vista en el primer capítulo, y las conclusiones a las que se llegaron una vez se obtuvieron los resultados. En la mayoría de casos se podrá observar que se hace uso de más de una herramienta para la optimización del servicio. Finalmente, en el último capítulo se presentan las conclusiones encontradas sobre los resultados encontrados en cada caso mostrado a lo largo del estudio y también sobre la variedad de herramientas empleadas en cada problema, principalmente para mostrar mayor énfasis en los diferentes métodos de optimización que se han utilizado en la actualidad.Trabajo de investigació

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

Mathematical Methods and Operation Research in Logistics, Project Planning, and Scheduling

In the last decade, the Industrial Revolution 4.0 brought flexible supply chains and flexible design projects to the forefront. Nevertheless, the recent pandemic, the accompanying economic problems, and the resulting supply problems have further increased the role of logistics and supply chains. Therefore, planning and scheduling procedures that can respond flexibly to changed circumstances have become more valuable both in logistics and projects. There are already several competing criteria of project and logistic process planning and scheduling that need to be reconciled. At the same time, the COVID-19 pandemic has shown that even more emphasis needs to be placed on taking potential risks into account. Flexibility and resilience are emphasized in all decision-making processes, including the scheduling of logistic processes, activities, and projects

Effect of Hot Spot Policing on Reducing Officer Stress

Police officers endure various threats ranging from verbal abuse to physical attacks, which can escalate and lead to police officer stress. Despite the abundant research exploring the relationship between high-stress occupations and environmental health, adequate exploration of the relationship between officer stress and hot spot policing (HSP; area with an above-average level of crime) has yet to occur. The purpose of this correlational study was to use Cohen and McKay\u27s conceptualization of the stress-buffering hypothesis to explore whether HSP mitigates the negative impact of job stress, leading to improved officer performance and ultimately improved relationships between the police and communities as well as lower crime rates. Posting of a SurveyMonkey link in law enforcement only, social-media communities (with administrator permission) facilitated data collection for the 151 respondents. Findings indicated that the overall regression model was significant; however, the simple correlation between HSP and officer stress (.118) indicated that HSP alone does not account for unique variance (there was a value of .014 or 1.4% of the variation in officer stress). The social change implications of this study include recommendations to police department administrations to continue to explore efforts to reduce officer stress, which could lead to improved officer performance and police and community relationships

Reliable design of interdependent service facility systems under correlated disruption risks

Facility location decisions lie at the center of planning many infrastructure systems. In many practice, public agencies (e.g., governments) and private companies (e.g., retailers) need to locate facilities to serve spatially distributed demands. For example, governments locate public facilities, e.g., hospitals, schools, fire stations, to provide public services; retail companies determine the locations of their warehouses and stores to provide business. The design of such facility systems involves considerations of investment of facility construction and transportation cost of serving demands, so as to maximize the system operational efficiency and profit. Recently, devastating infrastructure damages observed in real world show that infrastructure facilities may be subject to disruptions that compromise individual facility functionality as well as overall system performance. This emphasizes the necessity of taking facility disruptions into consideration during planning to balance between system efficiency and reliability. Furthermore, facility systems often exhibit complex interdependence when: (1) facilities are spatially correlated due to physical connections/interrelations, and (2) facilities provide combinatorial service under cooperation, competition and/or restrictions. These further complicate the facility location design. Therefore, facility location models need to be extended to tackle all these challenges and design a reliable interdependent facility system. This dissertation aims at investigating several important and challenging topics in the reliable facility location context, including facility correlations, facility combinations, and facility districting. The main work of this PhD research consist of: (1) establishing a new systematic methodological framework based on supporting stations and quasi-probabilities to describe and decompose facility correlations into succinct mathematical representations, which allows compact mathematical formulations to be developed for planning facility locations under correlated facility disruptions; (2) expanding the modeling framework to allow facilities to provide combinatorial service; e.g., in the context of sensor deployment problems, where sensors work in combinations to provide positioning/surveillance service via trilateration procedure; and (3) incorporating the concepts of spatial districting into the reliable facility location context, with the criteria of spatial contiguity, compactness, and demand balance being ensured. First, in many real-world facility systems, facility disruptions exhibit spatial correlations, which have strong impacts on the system performance, but are difficult to be described with succinct mathematical models. We first investigate facility systems with correlations caused by facilities’ share of network access points (e.g., bridges, railway crossings), which are required to be passed through by customers to visit facilities. We incorporate these network access points and their probabilistic failures into a joint optimization framework. A layer of supporting stations are added to represent the network access points, and are connected to facilities to indicate their real-world relationships. We then develop a compact mixed-integer mathematical model to optimize the facility location and customer assignment decisions. Lagrangian relaxation based algorithms are designed to effectively solve the model. Multiple case studies are constructed to test the model and algorithm, and to demonstrate their performance and applicability. Next, when there exists no real access points, facilities could also be correlated if they are exposed to shared hazards. We develop a virtual station structure framework to decompose these types of facility correlations. First, we define three probabilistic representations of correlated facility disruptions (i.e., with scenario, marginal, and conditional probabilities), derive pairwise transformations between them, and theoretically prove their equivalence. We then provide detailed formulas to transform these probabilistic representations into an equivalent virtual station structure, which enables the decomposition of any correlated facility disruptions into a compact network structure with only independent failures, and helps avoid enumerating an exponential number of disruption scenarios. Based on the augmented system, we propose a compact mixed-integer optimization program, and design several customized solution approaches based on Lagrangian relaxation to efficiently solve the model. We demonstrate our methodology on a series of numerical examples involving different correlation patterns and varying network and parameter settings. We then apply the reliable location modeling framework to sensor deployment problems, where multiple sensors work in combinations to provide combinatorial coverage service to customers via trilateration procedure. Since various sensor combinations may share common sensors, one combination is typically interrelated with some other combinations, which leads to internal correlations among the functionality of sensors and sensor combinations. We address the problem of where to deploy sensors, which sensor combinations are selected to use, and in what sequence and probability to use these combinations in case of disruptions. A compact mixed-integer mathematical model is developed to formulate the problem, by combining and extending the ideas of assigning back-up sensors and correlation decomposition via supporting stations. A customized solution algorithm based on Lagrangian relaxation and branch-and-bound is developed, together with several embedded approximation subroutines for solving subproblems. A series of numerical examples are investigated to illustrate the performance of the proposed methodology and to draw managerial insights. Finally, we develop an innovative reliable network districting framework to incorporate districting concepts into the reliable facility location context. Districting criteria including spatial contiguity, compactness, and demand balance are enforced for location design and extended in considerations of facility disruptions. The problem is modeled into a reliable network districting problem, in the form of a location-assignment based model. We develop customized solution approaches, including heuristics (i.e., constructive heuristic and neighborhood search) and set-cover based algorithms (e.g., district generation, lower bound estimation) to provide near-optimum solution with optimality gap. A series of hypothetical cases and an empirical full-scale application are presented to demonstrate the performance of our methodology for different network and parameter settings

Efficient Decision Support Systems

This series is directed to diverse managerial professionals who are leading the transformation of individual domains by using expert information and domain knowledge to drive decision support systems (DSSs). The series offers a broad range of subjects addressed in specific areas such as health care, business management, banking, agriculture, environmental improvement, natural resource and spatial management, aviation administration, and hybrid applications of information technology aimed to interdisciplinary issues. This book series is composed of three volumes: Volume 1 consists of general concepts and methodology of DSSs; Volume 2 consists of applications of DSSs in the biomedical domain; Volume 3 consists of hybrid applications of DSSs in multidisciplinary domains. The book is shaped decision support strategies in the new infrastructure that assists the readers in full use of the creative technology to manipulate input data and to transform information into useful decisions for decision makers