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We study the problem of synthesizing lockdown policies-schedules of maximum capacities for different types of activity sites-to minimize the number of deceased individuals due to a pandemic within a given metropolitan statistical area (MSA) while controlling the severity of the imposed lockdown. To synthesize and evaluate lockdown policies, we develop a multiscale susceptible, infected, recovered, and deceased model that partitions a given MSA into geographic subregions, and that incorporates data on the behaviors of the populations of these subregions. This modeling approach allows for the analysis of heterogeneous lockdown policies that vary across the different types of activity sites within each subregion of the MSA. We formulate the synthesis of optimal lockdown policies as a nonconvex optimization problem and we develop an iterative algorithm that addresses this nonconvexity through sequential convex programming. We empirically demonstrate the effectiveness of the developed approach by applying it to six of the largest MSAs in the United States. The developed heterogeneous lockdown policies not only reduce the number of deceased individuals by up to 45 percent over a 100 day period in comparison with three baseline lockdown policies that are less heterogeneous, but they also impose lockdowns that are less severe., (© 2022. The Author(s).)

The vector assignment p-median problem (VAPMP) (Weaver and Church in Transp Sci 19(1):58-74, ) was one of the first location-allocation models developed to handle split assignment of a demand to multiple facilities. The underlying construct of the VAPMP has been subsequently used in a number of reliable facility location and backup location models. Although in many applications the chance that a facility fails may vary substantially with locations, many existing models have assumed a uniform failure probability across all sites. As an improvement, this paper proposes a new model, the expected p-median problem as a generalization of existing approaches by explicitly considering site-dependent failure probabilities. Multi-level closest assignment constraints and two efficient integer linear programming (ILP) formulations are introduced. While prior research generally concludes that similar problems are not integer-friendly and cannot be solved by ILP software, computational results show that our model can be used to solve medium-sized location problems optimally using existing ILP software. Moreover, the new model can be used to formulate other reliable or expected location problems with consideration of site-dependent failure probabilities. [ABSTRACT FROM AUTHOR]

Achieving the greatest coverage using limited resources has long been a concern for regional planners. Since the 1970s, a variety of models have been studied and relied upon. Finding ways to best represent geographical space remains a challenge to many researchers. Solutions suggested by models vary greatly with different space representation schemes. For example, in the past, points have been widely adopted to represent spatial demand for coverage. However, this simple abstraction of geographical space could bring about inaccuracies and uncertainties, and often compromises its solution quality. Considering that demand can be area based, which is beyond points, objects of different shapes have been proposed as an alternative for representation. With advances in geographic information systems ( GISs), the new representation scheme using objects has recently received much attention. Compared with the straightforward point-based abstraction, spatial object representation poses considerable challenges to both model formulation and computation capability. This article revisits model development for the problem of regional coverage maximization and proposes a new formulation where coverage of spatial demand is implicitly modeled. Model testing is conducted through an application to warning siren siting in Dublin, Ohio, which has been studied by other researchers. Results demonstrate the effectiveness of the new model when compared with the existing models. Uno de los objetivos comunes en la planificación regional es lograr la máxima cobertura de un servicio con recursos limitados. Desde la década de los 70s se vienen utilizado una serie de modelos conocidos. Sin embargo, la representación adecuada del espacio geográfico de dichos modelos sigue siendo un problemática para muchos investigadores. Las soluciones derivadas de los modelos varían considerablemente de acuerdo a los diferentes esquemas de representación utilizados. El uso de puntos por ejemplo, ha sido ampliamente utilizado en el pasado como esquema de representación espacial de la demanda a ser cubierta por el servicio. Sin embargo, esta simple abstracción del espacio geográfico puede provocar imprecisiones e incertidumbres que a menudo afectan la calidad de la solución matemática del modelo. En contraste, si la demanda se define como un área que abarca una extensión que va más allá de los puntos es posible proponer-como lo han hecho varios recientemente- el uso de objetos espaciales (de formas variadas) como una alternativa sensata de representación. Con los avances en los sistemas de información geográfica (SIG), este nuevo esquema de representación -que usa objetos especiales- han recibido considerable atención. En contraste con esquemas sencillos como el basado en puntos, la representación de objetos espaciales presenta varios desafíos en cuanto a la formulación y computación del modelo. El presente artículo reseña el desarrollo del modelamiento del problema de máxima cobertura regional ( problem of regional coverage maximization) y propone una nueva formulación en la cual la cobertura de la demanda en el espacio es modelada de manera implícita. La evaluación del modelo se realiza a través de una aplicación que usa datos de la ubicación sirenas de alarma en Dublín, Ohio. Los resultados demuestran la eficacia del nuevo modelo en comparación con los modelos existentes. 利用有限资源实现最大覆盖一直广受区域规划者关注。自20世纪70年代以来，发展了大量针对这一问题的模型研究。寻找最佳的地理空间表达方式仍是研究者面临的一大挑战。不同模型对于不同的空间表达模式变化很大。比如过去空间覆盖需求多采用点集表达。然而，这种简单的地理空间抽象方法可能会引起不精确性和不确定性，通常也会导致解决方案质量下降。考虑到需求可能是基于区域而非基于点，不同形状的对象已经被当作空间表达可替代的方式。随着GIS技术的进步，基于对象空间表达的新方案近来备受关注。较之于直接基于点的空间抽象，空间对象表达在模型的形式化表达和计算性能上均面临相当大的挑战。本文回顾了区域最大覆盖问题模型研究的发展历程，提出了一个新的蕴含空间覆盖建模需求的模型。以曾被诸多学者研究过的俄亥俄州都柏林的报警器选址问题为例对模型进行检验，结果显示新模型较现有模型更为有效。 [ABSTRACT FROM AUTHOR]

Abstract: It is not uncommon to see maps and more advanced statistical or spatial analysis reported in the media. Geographical information systems (GIS) have no doubt facilitated access to and analysis of spatial information. This article is the outgrowth of contact by the Boston Globe and subsequent published articles examining structure fires and the location of fire stations in Massachusetts. The questions asked by the Boston Globe are important geographical ones regarding location specific urban/rural service provision issues, and to answer these questions requires the use of spatial analysis. This article focuses on the use of methods for answering the questions raised in the context of applying academic research, an issue that continues to be a challenge. [Copyright &y& Elsevier]