COMPETITIVE FACILITIES: MARKET SHARE AND LOCATION WITH RANDOM UTILITY*

ABSTRACT. A new approach is proposed for calculating the expected market share. It is assumed that consumers patronize a facility according to a utility function, selecting the facility with the highest utility value. However, consumers'ratings of the utility components are stochastic by some random distribution. Therefore, the buying power of customers located at the same point is divided among several facilities. A probability that a consumer patronizes a certain facility can be calculated. Consequently, the expected market share by competing facilities can be estimated. This calculation is more than 1,000 times faster than repeating a simulation enough times to achieve a reasonable accuracy. The distance decay calculated using the new approach is approximately exponential. A procedure for finding the optimal location anywhere in the plane for a new facility that maximizes the market share is also introduced.     

A NOTE ON THE LOCATION OF MEDICAL FACILITIES

In this note, I present a method to estimate the desired distance between medical facilities. The survival rate of patients improves when the facility is larger, however larger facilities result in a longer driving distance to the facility which decreases the survival rate. I identify the desired distance between facilities for which the survival rate is maximized.     

LOCATION OF PUBLIC FACILITIES WITH SPILLOVER EFFECTS: VARIABLE LOCATION AND PARAMETRIC SCALE*

ABSTRACT This paper studies the location of public facilities of two neighboring local governments which consider not only the influence of the land market but also the spillover effects that each jurisdiction may have on the other. We obtain the following results: (1) in most cases, one of the cities behaves as an isolated city in choosing the facility location while the other enjoys the spillover effect as a free rider; (2) we also find that the equilibrium location in the two noncooperative city case is not socially optimal except for a special case.     

THE OPTIMAL LOCATIONS OF MULTIPLE BRIDGES,CONNECTING FACILITIES,OR PRODUCT VARIETIES*

ABSTRACT This paper considers the optimal locations of two or more facilities, and the optimal number of facilities, when trips are made in pairs. The results are the same as standard models of spatial competition when there is perfect matching, but not when there is random matching. The first interpretation is bridges across a river, with residential locations on one side matched perfectly or randomly to jobs on the other side. The second interpretation is connecting facilities, such as tennis courts or restaurants where pairs of consumers meet. The third interpretation is product differentiation, with husbands and wives jointly choosing from among varieties.     

LOCATION AND SPATIAL PRICING FOR PUBLIC FACILITIES

ABSTRACT. Past analysis of public facility location has generally assumed a single goal, such as cost minimization or welfare maximization, and exogenous spatial pricing. This paper considers optimal facility location under a variety of goals. Furthermore, the facility manager is allowed to engage in freight absorption so that the delivered price to consumers need not reflect actual transportation costs. A systematic interaction among management goals, freight absorption, and the optimal size and spacing of public facilities is found.     

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。     

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。     

Adaptive Cell Tower Location Using Geostatistics. 基于地统计学的适应性基站发射塔选址研究

In this article, we address the problem of allocating an additional cell tower (or a set of towers) to an existing cellular network, maximizing the call completion probability. Our approach is derived from the adaptive spatial sampling problem using kriging, capitalizing on spatial correlation between cell phone signal strength data points and accounting for terrain morphology. Cell phone demand is reflected by population counts in the form of weights. The objective function, which is the weighted call completion probability, is highly nonlinear and complex (nondifferentiable and discontinuous). Sequential and simultaneous discrete optimization techniques are presented, and heuristics such as simulated annealing and Nelder–Mead are suggested to solve our problem. The adaptive spatial sampling problem is defined and related to the additional facility location problem. The approach is illustrated using data on cell phone call completion probability in a rural region of Erie County in western New York, and accounts for terrain variation using a line‐of‐sight approach. Finally, the computational results of sequential and simultaneous approaches are compared. Our model is also applicable to other facility location problems that aim to minimize the uncertainty associated with a customer visiting a new facility that has been added to an existing set of facilities.     

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。     

北京市公共服务设施供需协调发展的时空演化特征——以教育医疗设施为例

公共服务设施的优化配置是构建和谐社会、改善民生的内在要求。本文通过构建协调发展度模型,对北京市2001年和2012年16个区县教育医疗设施供需关系及二者协调发展的时空演化特征进行研究。研究认为:①教育设施"供不应需",供需差距增大;协调发展等级总体较低且有下降趋势;协调发展水平由"东高西低"向"南高北低"格局演变,空间差异增大。②医疗设施"供不应需",供需差距缩小;供需协调发展等级较低但有上升趋势,空间格局由"中心集聚"向"南高北低"演变,空间差异减小。     

线上和线下生活服务设施可达性及其协调关系——以生鲜果蔬店铺为例

作为智慧城市的重要组成部分,“新零售”得到蓬勃发展,提供当日配送服务的“新零售”深刻影响了城市生活服务的可获取性和时空可达性。本文以南京中心城区为例,运用两步移动搜索法、耦合协调度模型等方法,探究提供当日配送生鲜果蔬服务的店铺和传统生鲜果蔬实体店空间分布特征,分析线上和线下生鲜果蔬店铺的可达性及空间协调关系。研究发现,线上生活服务遵循技术扩散假说,强化了中心城区的生活服务集聚,同时线上生活服务集聚和可达性仍受实体地理空间约束;线上生活服务有悖于效率假说,对传统生活服务的空间分异具有加强作用,整体上没有提高生活服务的供给效率和空间公平性。研究结果可为新零售影响下城市生活服务设施的配置优化提供科学依据。     

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.     

Dispersion of Nodes Added to a Network

For location problems in which optimal locations can be at nodes or along arcs but no finite dominating set has been identified, researchers may desire a method for dispersing p additional discrete candidate sites along the m arcs of a network. This article develops and tests minimax and maximin models for solving this continuous network location problem, which we call the added-node dispersion problem (ANDP). Adding nodes to an arc subdivides it into subarcs. The minimax model minimizes the maximum subarc length, while the maximin model maximizes the minimum subarc length. Like most worst-case objectives, the minimax and maximin objectives are plagued by poorly behaved alternate optima. Therefore, a secondary MinSumMax objective is used to select the best-dispersed alternate optima. We prove that equal spacing of added nodes along arcs is optimal to the MinSumMax objective. Using this fact we develop greedy heuristic algorithms that are simple, optimal, and efficient (O( mp )). Empirical results show how the maximum subarc, minimum subarc, and sum of longest subarcs change as the number of added nodes increases. Further empirical results show how using the ANDP to locate additional nodes can improve the solutions of another location problem. Using the p-dispersion problem as a case study, we show how much adding ANDP sites to the network vertices improves the p-dispersion objective function compared with (a) network vertices only and (b) vertices plus randomly added nodes. The ANDP can also be used by itself to disperse facilities such as stores, refueling stations, cell phone towers, or relay facilities along the arcs of a network, assuming that such facilities already exist at all nodes of the network.     

The Optimal Nodal Location of Public Facilities With Price-Sensitive Demand

The purpose of this paper is to present some models for the location of public facilities in nodal networks that explicitly maximize social welfare by accounting for price-elastic demand functions. The models presented here are general; yet they are mathematically equivalent to the plant location problem and are therefore amenable to solution procedures developed for the plant location problem. The models presented here distinguish between two institutional environments that reflect the degree of power of the consumer to choose which facility to patronize. If consumers can be assigned arbitrarily to facilities and can be denied service, then the environment is one of public fiat. If consumers must be served at the facility of their choice, then a “serve-allcomers” environment exists. Separate models for each environment are specified, and the relationship between optimal assignments and pricing policies is developed.     

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.     

上海市主城区公共服务设施网点分布的空间异质性

城市内部格局与过程空间异质性的复杂性规律成为当前人文地理研究的难点和热点。以上海市主城区为例,从结构与功能视角刻画公共服务设施的空间异质性并发现有趣现象：上海市公共服务网点呈典型“核心-边缘”圈层特点;由于占地面积、租金、服务性质等因素五大设施形成类似金融类网点的强邻近性群集聚与类似科教类网点的弱向心集聚（逆增长点）两种模式;弱向心集聚呈现空间差异扩大、空间集聚增强的新特征,与多中心空间结构会促进设施均衡化布局的构想相反;主城区边缘地带交通发展未受重视导致其运输功能空间差异增强。     

The Probabilistic Minisum Flow Interception Problem: Minimizing the Expected Travel Distance until Intercept under Probabilistic Interception

We develop a variant of the flow interception problem (FIP) in which it is more desirable for travelers to be intercepted as early as possible in their trips. In addition, we consider flows being intercepted probabilistically instead of the deterministic view of coverage assumed in the FIP literature. We call the proposed model the probabilistic minisum FIP (PMFIP); it involves minimizing the sum of the expected distance that each flow travels until intercepted at a facility among placed facilities. This extension allows us to evaluate the effect of facility location under any given value of the interception probability and to apply the model to a variety of situations. We apply the proposed model to an example network by assuming a hypothetical situation in which people gather at a stadium from various nodes on the network, and receive some goods or services on the way to the stadium. We analyze optimal solutions obtained by varying the number of facilities and interception probability. It is shown that the expected travel distance until intercept is greatly reduced by means of a few optimally located facilities under a moderate interception probability.     

REPORT ON DAMAGE TO INDUSTRIAL FACILITIES IN THE 1999 KOCAELI EARTHQUAKE,TURKEY

The author got a chance to visit Turkey for investigating the damage of industrial facilities in the 1999 Kocaeli Earthquake which occurred on 17 August 1999 in the Kocaeli province of Turkey.

This report provides a brief investigation obtained through the seismic damage survey, particularly, focused on the damages to industrial facilities. The epicentral area in the Kocaeli province is the most industrial region of Turkey. Severe excitation attacked this region and industrial plants and structures were more or less damaged. Since the author could only visit a few sites, the report mainly describes the damages of two plants; TÜPRA? oil refinery where big fire occurred and TOYOTA-SA car manufacturing factory where no significant damage appeared.     

Order Distance in Regular Point Patterns

This article examines the k th nearest neighbor distance for three regular point patterns: square, triangular, and hexagonal lattices. The probability density functions of the k th nearest distance and the average k th nearest distances are theoretically derived for k =1, 2, …, 7. As an application of the k th nearest distance, we consider a facility location problem with closing of facilities. The problem is to find the optimal regular pattern that minimizes the average distance to the nearest open facility. Assuming that facilities are closed independently and at random, we show that the triangular lattice is optimal if at least 68% of facilities are open by comparing the upper and lower bounds of the average distances.