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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. 

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. 

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. 

Payments for Ecosystem Services (PES) programs have been implemented in both developing and developed countries to conserve ecosystems and the vital services they provide. These programs also often seek to maintain or improve the economic wellbeing of the populations living in the corresponding (usually rural) areas. Previous studies suggest that PES policy design, presence or absence of concurrent PES programs, and a variety of socioeconomic and demographic factors can influence decisions of households to participate or not in the PES program. However, neighborhood impacts on household participation in PES have rarely been addressed. This study explores potential neighborhood effects on villagers’ enrollment in the Grain-to-Green Program (GTGP), one of the largest PES programs in the world, using data from China’s Fanjingshan National Nature Reserve. We utilize a fixed effects logistic regression model in combination with the eigenvector spatial filtering (ESF) method to explore whether neighborhood size affects household enrollment in GTGP. By comparing the results with and without ESF, we find that the ESF method can help account for spatial autocorrelation properly and reveal neighborhood impacts that are otherwise hidden, including the effects of area of forest enrolled in a concurrent PES program, gender and household size. The method can thus uncover mechanisms previously undetected due to not taking into account neighborhood impacts and thus provides an additional way to account for neighborhood impacts in PES programs and other studies. 

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.