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The existing quantitative geography literature contains a dearth of articles that span spatial autocorrelation (SA), a fundamental property of georeferenced data, and spatial optimization, a popular form of geographic analysis. The well-known location–allocation problem illustrates this state of affairs, although its empirical geographic distribution of demand virtually always exhibits positive SA. This latent redundant attribute information alludes to other tools that may well help to solve such spatial optimization problems in an improved, if not better than, heuristic way. Within a proof-of-concept perspective, this paper articulates connections between extensions of the renowned Majority Theorem of the minisum problem and especially the local indices of SA (LISA). The relationship articulation outlined here extends to the p = 2 setting linkages already established for the p = 1 spatial median problem. In addition, this paper presents the foundation for a novel extremely efficient p = 2 algorithm whose formulation demonstratively exploits spatial autocorrelation. 

Police patrolling intends to enhance traffic safety by mitigating the risks associated with vehicle crashes and accidents. From a view of operations, patrolling requires an effective distribution of resources and often involves area delineations for this distribution purpose. Given constraints such as budget and human resources for traffic safety, delineating geographic areas optimally for police patrol areas is an important agenda item. This paper considers two p-median location models using segments on a street network as observational units on which traffic issues such as vehicle crashes occur. It also uses two weight sets to construct an enhanced delineation of police patrol areas in the City of Plano, Texas. The first model for the standard p-median formulation gives attention to the cumulative number of motor vehicle crashes from 2011 to 2021 on the major transportation networks in Plano. The second model, an extension of this first p-median one, uses balancing constraints to achieve balanced spatial coverage across patrol areas. These two models are also solved with network kernel density count estimates (NKDCE) instead of crash counts. These smoothed densities on a network enable consideration of uncertainty affiliated with this aggregation. The analysis results of this paper suggest that the p-median models provide effective specifications, including their capability to define patrol areas that encompass the entire study region while minimizing distance costs. The inclusion of balancing constraints ensures a more equitable distribution of workloads among patrol areas, improving overall efficiency. Additionally, the model with NKDCE results in an improved workload balance among delineated areas for police patrolling activities, thus supporting more informed spatial decision-making processes for public safety. 

Thep‐dispersion problem is a spatial optimization problem that aims to maximize the minimum separation distance among all assigned nodes. This problem is characterized by an innate spatial structure based on distance attributes. This research proposes a novel approach, named thedistance‐based spatially informed property(D‐SIP) method to reduce the problem size of thep‐dispersion instances, facilitating a more efficient solution while maintaining optimality in nearly all cases. The D‐SIP is derived from investigating the underlying spatial characteristics from the behaviors of thep‐dispersion problem in determining the optimal location of nodes. To define the D‐SIP, this research applies Ripley'sK‐function to the different types of point patterns, given that the optimal solutions of thep‐dispersion problem are strongly associated with the spatial proximity among points discovered by Ripley'sK‐function. The results demonstrate that the D‐SIP identifies collective dominances of optimal solutions, leading to buildingthe spatially informed p‐dispersion model. The simulation‐based experiments show that the proposed method significantly diminishes the size of problems, improves computational performance, and secures optimal solutions for 99.9% of instances (999 out of 1,000 instances) under diverse conditions. 

This research employs a spatial optimization approach customized for addressing equitable emergency medical facility location problems through the p-dispersed-median problem (p-DIME). The p-DIME integrates two conflicting classes of spatial optimization problems, dispersion and median problems, aiming to identify the optimal locations for emergency medical facilities to achieve an equitable spatial distribution of emergency medical services (EMS) while effectively serving demand. To demonstrate the utility of the p-DIME model, we selected Gyeongsangbuk-do in South Korea, recognized as one of the most challenging areas for providing EMS to the elderly population (aged 65 and over). This challenge arises from the significant spatial disparity in the distribution of emergency medical facilities. The results of the model assessment gauge the spatial disparity of EMS, provide significantly enhanced solutions for a more equitable EMS distribution in terms of service coverage, and offer policy implications for future EMS location planning. In addition, to address the computational challenges posed by p-DIME’s inherent complexity, involving mixed-integer programming, this study introduces a solution technique through constraint formulations aimed at tightening the lower bounds of the problem’s solution space. The computational results confirm the effectiveness of this approach in ensuring reliable computational performance, with significant reductions in solution times, while still producing optimal solutions. 

Accessibility to trauma centers is vital for the patients of severe motor vehicle crashes. Many vehicle crash fatalities failed to reach the proper emergency medical services since the accident location was far away from trauma centers. The spatial discordance between the service coverage area of trauma centers and actual locations of motor vehicle accidents delays the definitive medical care and results in death or disability. Many fatalities would have been prevented if the patients had a chance to get proper treatment in time at Southeastern region of the U.S. Also, the accessibility to trauma centers from the actual locations of motor vehicle accidents is different in the Southeastern region. This research aimed to facilitate the accessibility to trauma centers for severe motor vehicle crash patients in the Southeastern region. The analyses are conducted to assess current trauma center accessibility and suggest the optimal locations of future trauma centers using the Anti-covering location model for trauma centers (TraCtmodel). This study found that existing trauma centers failed to serve many demands, and the actual coverages of the current locations of trauma centers over potential demands are highly different in each Southeastern state.TraCtmodel is applied to each Southeastern state, and its solutions provide better coverage for demand locations. However, theTraCtmodel for each state tends to choose too many facilities, with excessively supplied facilities across the Southeastern region. The excessive service supply issue is addressed by applying theTraCtModel to a broader spatial extent.TraCtmodel applied to the entire Southeastern region and most of the demand, over 98% covered by the service coverage of optimal facility locations with 15 additional facilities. This research proves that the GIS andTraCtmodel applied to the broader spatial extent works well with increasing trauma medical service beneficiaries while providing a minimum number of additional facilities. 

Except for about a half dozen papers, virtually all (co)authored by Griffith, the existing literature lacks much content about the interface between spatial optimization, a popular form of geographic analysis, and spatial autocorrelation, a fundamental property of georeferenced data. The popularp‐median location‐allocation problem highlights this situation: the empirical geographic distribution of demand virtually always exhibits positive spatial autocorrelation. This property of geospatial data offers additional overlooked information for solving such spatial optimization problems when it actually relates to their solutions. With a proof‐of‐concept outlook, this paper articulates connections between the well‐known Majority Theorem of the 1‐median minisum problem and local indices of spatial autocorrelation; the LISA statistics appear to be the more useful of these later statistics because they better embrace negative spatial autocorrelation. The relationship articulation outlined here results in the positing of a new proposition labeled the egalitarian theorem.