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.     

Multiple Facilities Location in the Plane Using the Gravity Model

Two problems are considered in this article. Both problems seek the location of p facilities. The first problem is the p median where the total distance traveled by customers is minimized. The second problem focuses on equalizing demand across facilities by minimizing the variance of total demand attracted to each facility. These models are unique in that the gravity rule is used for the allocation of demand among facilities rather than assuming that each customer selects the closest facility. In addition, we also consider a multiobjective approach, which combines the two objectives. We propose heuristic solution procedures for the problem in the plane. Extensive computational results are presented.     

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.     

LOCATING A SINGLE NEW FACILITY AMONG EXISTING,UNEQUALLY ATTRACTIVE FACILITIES*

ABSTRACT. The location of a new facility in a competitive environment is investigated. It is assumed that customers patronize the facility with the highest utility value rather than the closest facility. Simulations show that the new approach yields a superior location in terms of market size captured. Sensitivity analyses of the problem parameters illustrate the sensitivity of the location and the sensitivity of the market size captured to the facility's quality.     

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.     

Designing Reliable Center Systems: A Vector Assignment Center Location Problem

The p‐center problem is one of the most important models in location theory. Its objective is to place a fixed number of facilities so that the maximum service distance for all customers is as small as possible. This article develops a reliable p‐center problem that can account for system vulnerability and facility failure. A basic assumption is that located centers can fail with a given probability and a customer will fall back to the closest nonfailing center for service. The proposed model seeks to minimize the expected value of the maximum service distance for a service system. In addition, the proposed model is general and can be used to solve other fault‐tolerant center location problems such as the (p, q)‐center problem using appropriate assignment vectors. I present an integer programming formulation of the model and computational experiments, and then conclude with a summary of findings and point out possible future work.     

SPATIAL ASYMMETRIC DUOPOLY WITH AN APPLICATION TO BRUSSELS' AIRPORTS*

ABSTRACT In this paper, the problem of a city with access to two firms or facilities (shopping malls, airports, commercial districts) selling a differentiated product (shopping, flights) and/or offering a differentiated workplace is studied. Transport connections to one facility are congested. A model is presented for this asymmetric duopoly game that can be solved for a Nash equilibrium in prices and wages. A comparative statics analysis is used to illustrate the properties of the equilibrium. A numerical model is then applied to the two Brussels airports. Three stylized policies are implemented to address the congestion problem: expansion of transport capacity, congestion pricing, and a direct subsidy to the uncongested facility. Our results indicate that the degree of intrinsic differentiation between the two firms is crucial in determining the difference in profit and market share. Price and wage differences also depend on trip frequency and consumer preferences for diversity. Congestion pricing is the most effective policy tool but all three options are shown to have attractive attributes.     

SPATIAL COMPETITION AND THE JOINT CONSUMPTION OF SERVICES*

In Hotelling location models, an implicit assumption has been made that a customer uses the service provided by the firm, independent of other customers. However, for firms that supply meeting rooms, wedding halls, tennis courts, and golf links it is essential to incorporate the fact that the customer only uses the service in conjunction with other customers. The objective of this paper is to formulate the Hotelling location model n consideration of the interdependence among customers in one-dimensional space, and to characterize the state of equilibrium. In our model, each group of members within a given distance enjoys a fixed amount of service of the firms, under the assumption that the travel cost incurred by each group is defined as the travel cost of the farthest customer in the group.     

旅行社顾客教育、顾客的心理受权及消费价值之间的关系

本文在文献研究的基础上,提出一个包含顾客教育、顾客心理受权及消费价值的研究模型,并利用作者在旅行社收集的数据,对模型进行了实证检验。数据分析结果表明:顾客教育对顾客心理受权有显著的直接正向影响;顾客心理受权对顾客感知的风险有显著的直接负向影响,对顾客感知的消费价值有显著的直接正向影响。本次研究结果丰富了学术界在顾客教育、顾客受权的研究成果,对旅行社通过顾客教育增强顾客心理受权感,进而提高顾客感知的消费价值有一定的参考价值。     

A Cost-Benefit Location-Allocation Model for Public Facilities: An Econometric Approach

This research develops and operationalizes a facility location-allocation model based on cost-benefit principles derived from welfare economics. Despite the theoretical advantages of cost-benefit location-allocation models, the difficulties associated with estimating household preferences for public facilities have heretofore prevented their application. This research demonstrates that the hedonic-pricing methodology can be effectively used to estimate preferences for public facilities. Specifically, household preferences for Baltimore public middle schools were estimated from the spatial variation in housing prices using the random bidding model. To provide an example of the methodology, the cost-benefit location-allocation objective function was maximized to simultaneously determine the optimal number, quality, and locations of Baltimore middle schools. The cost-benefit approach to facility location constitutes a major improvement over existing methods because it directly incorporates user preferences into the objective function and because the number and quality of facilities can be determined endogenously rather than being specified as a constraint a priori.     

Maximizing Accessibility on Congested Networks

The problem of locating facilities to maximize their accessibility on networks where costs are functions of flow volume is considered. In particular, an accessibility model developed by Leonardi is extended to bipartite and tree networks whose arc costs are determined by a flow-dependent congestion function. The resultant nonseparable equilibrium problem is solved heuristically, and numerical simulations are used to explore the model's behavior under varying conditions.     

Competitive Multifacility Location on Networks: the (r∣Xp)‐Medianoid Problem

Abstract.  We investigate the ( r ∣ X _p )‐medianoid problem for networks. This is a competitive location problem that consists of determining the locations of r facilities belonging to a firm in order to maximize its market share in a space where a competitor is already operating with p facilities. We consider six scenarios resulting from the combination of three customer choice rules (binary, partially binary, and proportional) with two types of services (essential and unessential).
Known discretization results about the existence of a solution for the set of nodes are extended. Some examples and computational experience using heuristic algorithms are presented.     

A Family of Location Models for Multiple-Type Discrete Dispersion

One of the defining objectives in location science is to maximize dispersion. Facilities can be dispersed for a wide variety of purposes, including attempts to optimize competitive market advantage, disperse negative impacts, and optimize security. With one exception, all of the extant dispersion models consider only one type of facility, and ignore problems where multiple types of facilities must be located. We provide examples where multiple-type dispersion is appropriate and based on this develop a general class of facility location problems that optimize multiple-type dispersion. This family of models expands on the previously formulated definitions of dispersion for single types of facilities, by allowing the interactions among different types of facilities to determine the extent to which they will be spatially dispersed. We provide a set of integer-linear programming formulations for the principal models of this class and suggest a methodology for intelligent constraint elimination. We also present results of solving a range of multiple-type dispersion problems optimally and demonstrate that only the smallest versions of such problems can be solved in a reasonable amount of computer time using general-purpose optimization software. We conclude that the family of multiple-type dispersion models provides a more comprehensive, flexible, and realistic framework for locating facilities where weighted distances should be maximized, when compared with the special case of locating only a single type of facility.     

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.     

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.     

基于旅游生产线的景区容量算法

现行的风景区空间日容量的计算方法往往大大高估了景区容量。本文以游客在景区中的移动行为为出发点,将景区旅游线路类比为旅游生产线,其中游客为工件、景点为工序。利用旅游生产线的平行移动特征,推导出在景区日开放时间内能够完成景区游玩的游客批数。然后,以景区线路中的瓶颈景点容量为批量,该批量与批数相乘即得到了景区容量。旅游生产线理论填补了景区容量计算理论支撑的空白,并使景区容量计算真正的科学化、合理化。     

城市设施环境对初中学生体质健康的影响——以大连市主城区为例

青少年学生体质下降,身体形态肥胖化。论文以BMI指数衡量学生体质健康,通过地理加权回归模型分析了校内、通学以及社区服务设施对初中学生体质健康的异质性影响。发现:(1)初中学生体质健康社区分异明显,超重低风险和未超重高风险社区围绕超重高风险社区集聚。(2)能量摄入型设施分布从中心向边缘逐渐减少,能量消耗型设施表现出相反的特征,道路网密度向中心集聚,医疗设施呈离散分布。(3)学校人均绿地面积,通学距离、道路网密度,公交站、西餐厅、休憩设施、零售设施、医疗设施可达性对学生体质健康的影响在中心区与边缘区具有异质性。     

旅游服务顾客满意度模型实证研究

作者在文献研究的基础上,构建旅游服务顾客满意度模型,并在广州某餐馆和某宾馆向顾客收集数据,对模型进行实证检验。数据分析结果表明：服务公平性和顾客的消费情感是旅游服务顾客满意程度的重要决定因素;对不同的服务质量属性,实绩和期望与实绩之差对顾客满意度的作用过程不同;顾客的期望对顾客满意度并没有直接影响。     

Bi‐objective Model for Optimal Number and Size of Circular Facilities

This article presents a bi‐objective model for determining the number and size of finite size facilities. The objectives are to minimize both the average closest distance to facilities and the probability that a random line intersects facilities. The former represents the accessibility of customers, whereas the latter represents the interference to travelers. The average closest distance and the probability of intersecting facilities are derived for circular facilities randomly distributed in a circular city. The analytical expressions for the average closest distance and the probability of intersecting facilities demonstrate how the number and size of facilities affect the accessibility of customers and the interference to travelers. The model focuses on the tradeoff between the accessibility and interference, and the tradeoff curve provides planners with alternatives for the number and size of facilities.     

GENERAL EQUILIBRIUM OF SPATIAL PRODUCT AND LABOR MARKETS*

ABSTRACT A simple general equilibrium model relates spatial product markets and spatial labor markets. The firm is treated as being a spatial monopolist or as a Löschian competitor in the output market and as a spatial monopsonist in the labor market. Derived free spatial demand and free regional labor supply are defined, and their properties examined. The model provides the framework for analyzing the impact of a technological improvement in labor productivity on the structure of the spatial markets. The impact of entry on spatial labor supply is an important determinant of whether or not entry lowers wages and raises output prices. Unlike the spaceless competitive paradigm, zero-profit long-run equilibrium can occur in a space economy under conditions of increasing returns to scale.