Location-Allocation Models of Some Traffic Facilities

The objective of this paper is to formulate location-allocation models of linear facilities, such as bridges, railroad crossings, and staircases. The location-allocation models in this paper differ from existing location-allocation models in that the service provided by the facilities is consumed by trips, with associated origins and destinations. The first part of the paper shows the formulation of these location-allocation problems in one-dimensional space. It is demonstrated that these problems can also be formulated by the use of a rectilinear Voronoi diagram in two-dimensional space. The second part of the paper demonstrates fundamental relationships between the number of facilities and the total length of indirect trips and between the number of facilities and the total number of indirect trips for uniformly and independently distributed origins and destinations.     

The Zone Definition Problem in Location-Allocation Modeling

Location-allocation modeling is a frequently used set of techniques for solving a variety of locational problems, some of which can be politically sensitive. The typical application of a location-allocation model involves locating facilities by selecting a set of sites from a larger set of candidate sites, with the selection procedure being a function of “optimality” in terms of the allocation of demand to the selected sites. In this paper we examine the sensitivity of one particular type of location-allocation model, the p-median procedure, to the definition of spatial units for which demand is measured. We show that a p-median solution is optimal only for a particular definition of spatial units and that variations in the definition of spatial units can cause large deviations in optimal facility locations. The broad implication of these findings is that the outcome of any location-allocation procedure using aggregate data should not be relied upon for planning purposes. This has important implications for a large variety of applications.     

上海市日常体育生活圈的公共体育设施配置研究

运用"都市生活圈"和"时间地理学"的理论与方法,对上海城市日常体育生活圈进行了划分与构建,提出了由基础体育生活圈、基本体育生活圈和机会体育生活圈所构成的日常体育生活圈层体系,并以上海日常体育生活圈层体系为基础,依据"中心地理论"和上海公共体育设施建设与发展的实际状况,提出了上海日常体育生活圈的公共体育设施配置模式和公共体育设施配置体系。根据上海日常体育生活圈建设与发展的要求及实际状况,提出了相应的公共体育设施建设与配置的建议。     

A Location-Allocation Model of Lösch's Central Place Theory: Testing on a Uniform Lattice Network

This paper develops a location-allocation model of Lösch's central place theory that maximizes the number of firms that can coexist in the market, subject to range, threshold, hierarchy, and other constraints. F.o.b. costs, economies of scale, and elastic demand are included. Consumer behavior postulates concerning the “nearest center hypothesis” and the “indifference principle” are formulated as nonlinear constraints but not used during solution. Methods are developed for simulating the continuous, infinite plain with a discrete, bounded network by use of an outer overflow network and a symmetrical market area constraint. The model is tested by applying it to a uniform lattice network and comparing the results to the expected pattern of nested hexagons. Solutions consistent with the k = 3, 4, and 7 patterns are generated by changing threshold values. However, remaining inconsistencies appear to be due to the inability to express the consumer behavior laws as linear constraints, to the bounded and discrete nature of the network, and to the objective function being the sum of integer variables. The long-run purpose of developing and validating a location-allocation model of a location theory is to use it to relax the theory's restrictive assumptions and to apply the theory to nonuniform regions.     

基于弱势群体需求的北京服务设施可达性集成研究

关注人群属性和需求,探讨服务设施供给的社会公平是新时代服务设施研究的重要议题,对于人口总量巨大、社会构成多元、社会空间分异凸显的大城市尤其如此。尽管研究某一弱势群体对单项服务设施需求的文献不断涌现,但是结合居民主观的服务设施需求偏好的可达性集成研究尚不多见。本文以北京作为案例城市,首先采用居民主观调查数据分析四类弱势群体对于公共服务设施的需求结构,然后基于POI数据,借助GIS分析这四类弱势群体服务设施需求偏好下的北京市公共服务设施综合可达性情况,且对综合可达性较差的区域进行了空间识别。本研究综合定性与定量方法,探讨主观与客观数据相匹配的可达性集成方法,可以为今后的相关研究提供借鉴,并能够对北京建设国际一流和谐宜居之都提供理论支撑。     

邻避设施国内外研究进展

随着城市化进程的加快,城市规模不断扩大,公共设施水平逐步提高,不可避免地需要布局邻避设施,即NIMBY,Not In My Back Yard,"不要布局在我家后院"的设施。随着人们自我健康和保护意识的增强,邻避设施由于负面外部性的存在而面临着"邻避"的风险。如何减少其负面外部性,实现成本-效益对等,解决邻避冲突是邻避设施布局的关键。本文在总结邻避设施的概念的基础上,从邻避设施的分类入手,分别分析了国内外邻避设施的研究进展,综述了国内外邻避设施的类型、规模、选址、与周围环境的协调、困境、邻避冲突及解决方案等进展与不足,提出了未来研究的新视角,以期从发达国家邻避设施的布局中汲取经验,给我国有益的启示。     

An Interactive Approach to the Central Facility Location Problem: Locating Pediatric Hospitals in Warsaw

Most of the conventional approaches to the central facility location problem neglect the interaction of analyst and decision-maker during the locational choice process. This paper presents a new interactive approach to the central facility location problem. It is assumed that the problem is formulated by an analyst as a multiobjective optimization problem. Then the decision-maker searches for a satisfactory solution working directly with the computer system. The interactive procedure was implemented on IBM-PC XT/AT as the decision support system DINAS (Dynamic Interactive Network Analysis System) which enables the solution of various multiobjective location-allocation problems. DINAS has been successfully used for solving a real-world planning problem, namely for finding locations for pediatric hospitals in the Warsaw region.     

北京应急避难场所的区位优化配置分析

在中国城市快速增长的背景下,城市公共服务设施的空间配置成为社会各界关注的热点问题。本文以北京市中心城区的应急避难场所为例,利用Voronoi多边形算法,研究应急避难场所的空间优化和配置。结论显示,北京市作为人口密集的国际大都市,其应急避难场所的建设存在一定的缺口,在空间上分布也不均衡;根据公共服务设施"均等化"的原则,北京市中心城区至少需要新建40多个大型应急避难场所;从公共服务设施配置的公平和效率原则出发,未来应急避难场所的建设重点不仅要增加数量和扩大规模,还应调整空间配置。     

Interfacility Interaction in Models of Hub and Spoke Networks

Providers of transportation services may reduce their average unit costs by bundling flows and channeling them between hubs (also known as concentrators or routers). The resulting facility locations are interdependent because of the flows between them. This paper analyzes mathematical models of hub systems in an effort to enhance understanding of the optimal location of interactive facilities. The paper examines the behavior of solutions to several alternative models that require the location of a hub at either of two similar locations. A model employing a concave cost function favors the assembly of flows, penalizes fractional facility locations, and produces local minima that have integer facilities.     

Optimal Number of Hierarchical Facilities with Failures

This article proposes a continuous approximation model for determining the number of hierarchical facilities when lower level facilities are subject to failures. The average distance from customers to the nearest open facility is derived for two types of customer behavior. The optimal number of facilities that minimizes the average distance is then obtained. The analytical expression for the optimal number of facilities demonstrates how the location of facilities, the failure probability, and the customer behavior affect the optimal hierarchy and the average distance. The result shows that introducing the hierarchy can reduce the average distance if the failure probability is small and the penalty for failing to use facilities is large. The model provides a fundamental understanding of the optimal hierarchy and is useful for designing hierarchical facility systems.     

On the Logit Approach to Competitive Facility Location

The random utility model in competitive facility location is one approach for estimating the market share captured by a retail facility in a competitive environment. However, it requires extensive computational effort for finding the optimal location for a new facility because its objective function is based on a k -dimensional integral. In this paper we show that the random utility model can be approximated by a logit model. The proportion of the buying power at a demand point that is attracted to the new facility can be approximated by a logit function of the distance to it. This approximation demonstrates that using the logit function of the distance for estimating the market share is theoretically founded in the random utility model. A simplified random utility model is defined and approximated by a logit function. An iterative Weiszfeld-type algorithm is designed to find the best location for a new facility using the logit model. Computational experiments show that the logit approximation yields a good location solution to the random utility model.     

广州市中心城区休闲服务设施区位类型特征的研究

以广州市中心城区为研究地域,以城市常住人口密度作为地域划分标准,引入基尼系数、带间差异系数、带别特化系数对广州市中心城区的休闲服务设施的区位类型进行划分,区分出城区均匀分布、弱城心均匀分布、城区核心集聚和城区局部集聚四类休闲服务设施的区位类型,进而对广州市中心城区的休闲服务设施的分布和微区位特征有一个初步的解读。     

On the Finite Optimality Set of the Vector Assignment p‐Median Problem

The vector assignment p‐median problem (VAPMP) is one of the first discrete location problems to account for the service of a demand by multiple facilities, and has been used to model a variety of location problems in addressing issues such as system vulnerability and reliability. Specifically, it involves the location of a fixed number of facilities when the assumption is that each demand point is served a certain fraction of the time by its closest facility, a certain fraction of the time by its second closest facility, and so on. The assignment vector represents the fraction of the time a facility of a given closeness order serves a specific demand point. Weaver and Church showed that when the fractions of assignment to closer facilities are greater than more distant facilities, an optimal all‐node solution always exists. However, the general form of the VAPMP does not have this property. Hooker and Garfinkel provided a counterexample of this property for the nonmonotonic VAPMP. However, they do not conjecture as to what a finite set may be in general. The question of whether there exists a finite set of locations that contains an optimal solution has remained open to conjecture. In this article, we prove that a finite optimality set for the VAPMP consisting of “equidistant points” does exist. We also show a stronger result when the underlying network is a tree graph.     

Location Modeling Utilizing Maximum Service Distance Criteria

The location set-covering problem (LSCP) and the maximal covering location problem (MCLP) have been the subject of considerable interest. As originally defined, both problems allowed facility placement only at nodes. This paper deals with both problems for the case when facility placement is allowed anywhere on the network. Two theorems are presented that show that when facility placement is unrestricted, for either the LSCP or MCLP at least one optimal solution exists that is composed entirely of points belonging to a finite set of points called the network intersect point set (NIPS). Optimal solution approaches to the unrestricted site LSCP and MCLP problems that utilize the NIPS and previously developed solution methodologies are presented. Example solutions show that considerable improvement in the amount of coverage or the number of facilities needed to insure total coverage can be achieved by allowing facility placement along arcs of the network. In addition, extensions to the arc-covering model and the ambulance-hospital model of ReVelle, Toregas, and Falkson are developed and solved.     

Fearing Food: The Influence of Risk Perceptions on Public Preferences for Uniform and Centralized Risk Regulation

Public opinion features prominently in policy research because it sets bounds on the definition of policy problems and acceptable policy solutions. We contend that public opinion is also important for setting bounds on the level of government at which policy hazards are regulated by shaping preferences for uniformity of regulation and, relatedly, preferences for centralization. We offer a theoretical argument for why risk creates pressures for uniform standards and examine the extent to which preferences for uniformity and centralization are the product of fairly stable individual-level predispositions (e.g. partisanship and ideology) versus more fluid attitudes like perceptions of risk, which vary in response to crises, new information, and issue framing. We test our argument using survey data in the policy domain of food safety and find that individuals who anticipate greater risk from food-borne illness prefer more uniform food safety regulation, which translates into preferences for federal-level policymaking. Our results imply that contextual circumstances and strategic communications that influence risk perceptions can create not only generalized public demand for more regulatory policy but specific demand for uniform, centralized regulation.     

Determining Market Areas Captured by Competitive Facilities: A Continuous Equilibrium Modeling Approach

Many existing models concerning locations and market areas of competitive facilities assume that customers patronize a facility based on distance to that facility, or perhaps on a function of distances between the customer and the different facilities available. Customers are generally assumed to be located at certain discrete demand points in a two-dimensional space, or continuously distributed over a one-dimensional line segment. In this paper these assumptions are relaxed by employment of a continuum optimization model to characterize the equilibrium choice behavior of customers for a given set of competitive facilities over a heterogeneous two-dimensional space. Customers are assumed to be scattered continuously over the space and each customer is assumed to choose a facility based on both congested travel time to the facility and on the attributes of the facility. The model is formulated as a calculus of variations problem and its optimality conditions are shown to be equivalent to the spatial customer-choice equilibrium conditions. An efficient numerical method using finite element technique is proposed and illustrated with a numerical example.     

MARKET CAPTURE BY TWO COMPETITORS: THE PREEMPTIVE LOCATION PROBLEM*

ABSTRACT. We consider a location and allocation game for two competitor firms, A and B, that each seek to locate p facilities in a network. A market is captured by a particular firm if that market's closest facility belongs to that firm rather than a competitor. The question is as follows: Firm A wants to locate its p facilities so that B, which enters also with p facilities after Firm A has located its facilities, will capture the minimum market value possible. That is, Firm A wishes to preempt Firm B in its bid to capture market share to the maximum extent possible. A model is presented that addresses this issue, together with solution methods and computing times.     

On Covering Problems and the Central Facilities Location Problem

A number of variations of facilities location problems have appeared in the research literature in the past decade. Among these are problems involving the location of multiple new facilities in a discrete solution space, with the new facilities located relative to a set of existing facilities having known locations. In this paper a number of discrete solution space location problems are treated. Specifically, the covering problem and the central facilities location problem are shown to be related. The covering problem involves the location of the minimum number of new facilities among a finite number of sites such that all existing facilities (customers) are covered by at least one new facility. The central facilities location problem consists of the location of a given number of new facilities among a finite number of sites such that the sum of the weighted distances between existing facilities and new facilities is minimized. Computational experience in using the same heuristic solution procedure to solve both problems is provided and compared with other existing solution procedures.     

THE MINIMAX-MIN LOCATION PROBLEM*

We consider a new objective function for the placement of a public facility with reference to variations in accessibility : the minimization of the range between the maximal and the minimal distances to users. Some properties of the solution are given; algorithms for the Euclidean and rectilinear distance cases are presented.     

THE OPTIMAL LOCATIONS OF BRANCH FACILITIES AND MAIN FACILITIES WITH CONSUMER SEARCH*

ABSTRACT. This paper examines the socially optimal locations of branch facilities (or small stores) and main facilities (or large stores) on a finite linear market that is uniformly populated from position 0 to position 1. Each consumer has a probability w of finding the desired service (or product) at a branch facility, and a probability 1 of finding the desired service (or product) at a main facility. Two types of consumer search are considered: phone search and visit search. Different assumptions are made about the numbers of branch facilities and main facilities (each involving one or two facilities of each type). Under visit search, the socially optimal locations of branch facilities tend to be closer to main facilities than under phone search, and this tendency is more pronounced for smaller values of w.