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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. 

Motor vehicle accidents are one of the most prevalent causes of traumatic injury in patients needing transport to a trauma center. Arrival at a trauma center within an hour of the accident increases a patient’s chances of survival and recovery. However, not all vehicle accidents in Tennessee are accessible to a trauma center within an hour by ground transportation. This study uses the anti-covering location problem (ACLP) to assess the current placement of trauma centers and explore optimal placements based on the population distribution and spatial pattern of motor vehicle accidents in 2015 through 2019 in Tennessee. The ACLP models seek to offer a method of exploring feasible scenarios for locating trauma centers that intend to provide accessibility to patients in underserved areas who suffer trauma as a result of vehicle accidents. The proposed ACLP approach also seeks to adjust the locations of trauma centers to reduce areas with excessive service coverage while improving coverage for less accessible areas of demand. In this study, three models are prescribed for finding optimal locations for trauma centers: (a) TraCt: ACLP model with a geometric approach and weighted models of population, fatalities, and spatial fatality clusters of vehicle accidents; (b) TraCt-ESC: an extended ACLP model mitigating excessive service supply among trauma center candidates, while expanding services to less served areas for more beneficiaries using fewer facilities; and (c) TraCt-ESCr: another extended ACLP model exploring the optimal location of additional trauma centers. 

Both historically and in terms of practiced academic organization, the anticipation should be that a flourishing synergistic interface exists between statistics and operations research in general, and between spatial statistics/econometrics and spatial optimization in particular. Unfortunately, for the most part, this expectation is false. The purpose of this paper is to address this existential missing link by focusing on the beneficial contributions of spatial statistics to spatial optimization, via spatial autocorrelation (i.e., dis/similar attribute values tend to cluster together on a map), in order to encourage considerably more future collaboration and interaction between contributors to their two parent bodies of knowledge. The key basic statistical concept in this pursuit is the median in its bivariate form, with special reference to the global and to sets of regional spatial medians. One-dimensional examples illustrate situations that the narrative then extends to two-dimensional illustrations, which, in turn, connects these treatments to the spatial statistics centrography theme. Because of computational time constraints (reported results include some for timing experiments), the summarized analysis restricts attention to problems involving one global and two or three regional spatial medians. The fundamental and foundational spatial, statistical, conceptual tool employed here is spatial autocorrelation: geographically informed sampling designs—which acknowledge a non-random mixture of geographic demand weight values that manifests itself as local, homogeneous, spatial clusters of these values—can help spatial optimization techniques determine the spatial optima, at least for location-allocation problems. A valuable discovery by this study is that existing but ignored spatial autocorrelation latent in georeferenced demand point weights undermines spatial optimization algorithms. All in all, this paper should help initiate a dissipation of the existing isolation between statistics and operations research, hopefully inspiring substantially more collaborative work by their professionals in the future.