Extensions to the Hub Location Problem: Formulations and Numerical Examples

Although a tremendous amount of analytical research is being conducted on the hub location problem, few models exist that extend the number of characteristics found in actual hub-and-spoke networks. Four extensions are presented in this paper: (1) a capacitated network model; (2) a minimum threshold model; (3) a model that endogenously determines the number of open hubs for the network; and (4) a model that incorporates a flow-dependent cost function for the spokes as well as the interhub links. Both the capacitated and the minimum threshold models drop the assumption of a completely interconnected network commonly found in hub location models. Numerical results show that total network costs are often minimized by closing a few interhub links. The third extension is the first known hub location model to determine the optimal number of hubs based on the needs of the network. In this model, the number of open hubs depends on the distribution of flows in the network and how cost effectively the flows can be moved across the network. Previous models that endogenously determined the number of open hubs utilized a fixed cost for establishing each hub in order to limit the number of hubs in the network. The final extension recognizes the potential of all links to amalgamate flows and includes a separate flow-dependent cost function for the spokes in addition to the one for the interhub links. Numerical results are shown for all four models.     

Reliable p-Hub Location Problems in Telecommunication Networks

Hubs are critical elements of telecommunication and transportation networks because they play a vital role in mass traffic movement. The design of more reliable networks in hub-and-spoke systems is a critical issue because current networks, particularly many commercial Internet backbones, are quite vulnerable. In hub-and-spoke-type topologies, any malfunction at a hub may cause degradation of the entire network's ability to transfer flows. This article presents a new hub location problem, termed the reliable p-hub location problem , which focuses on maximizing network performance in terms of reliability by locating hubs for delivering flows among city nodes. Two submodels, the p-hub maximum reliability model and the p-hub mandatory dispersion model, are formulated. Based on hypothetical and empirical analyses using telecommunication networks in the United States, the relationship between network performance and hub facility locations is explored. The results from these models could give useful insights into telecommunication network design.     

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.     

Activity Levels at Hub Facilities in Interacting Networks

Hubs are a special type of central facility which are designed to act as switching points for intemodal flows. For instance, a set of ten interacting cities might all be connected to one of two major hubs. All flows between the cities would then be routed via the hubs. There is an obvious saving in the number of routes necessary to interconnect the cities when hubs are utilized, with a concomitant high level of activity at the facilities. This paper takes a heuristic approach to the evaluation of networks and hub locations to find locally optimal designs. It is shown that minimization of transportation costs may require assignment of nodes to a facility other than the nearest. A discount on the interhub transportation costs promotes a wider spacing of facilities. In a system with several hubs, minimization of total hub usage tends to concentrate demand very heavily into one central facility.     

The Pickup Problem: Consumers' Locational Preferences in Flow Interception

This article addresses the pickup problem , wherein patrons briefly interrupt their predetermined journeys to obtain a simple good, such as fast food or a video, and then resume their journeys. This is a problem from the class known as the flow-interception location problems. Traditional flow-interception location models (FILMs) are used to select service locations such that the intercepted flows are maximized. In these traditional models, only flow quantities are considered; these models do not consider where a pickup is made in a journey. However, in the real world, consumers often wish to obtain a product or service at or near a specific location along their trips. The pickup model (PUP) proposed here considers consumers' locational preferences, providing a much broader, more realistic approach than FILM (a special case of PUP) to problems in the private and public sectors. By considering which patrons are served where, PUP transforms the FILM into a flow-interception location-allocation model, providing a fruitful garden for further research. Geographic information systems and optimization engines are integrated to investigate the PUP model in real-world transportation systems. Reported findings demonstrate that the optimal locations identified by traditional models arise solely from network flow structure, whereas the optimal locations identified by PUP result from trade-offs between network flow structure and the importance of proximity to preferred locations. One important discovery is that PUP solutions are superior to those of traditional FILMs if consumers have locational preferences. Up-to-date, real-world transportation networks provide a realistic test-bed for this and other models of the flow-interception type.     

An Integrated Network Equilibrium Model of Urban Location and Travel Choices

This paper develops a mixed, combined, and stochastic user-equilibrium model for urban location and travel choices with variable origin and destination costs. Different types of travelers will be considered explicitly, including: workers with fixed residences seeking jobs, workers with fixed job locations seeking residences, and workers with both fixed residences and jobs. The costs or benefits of residing or working in a zone are described by appropriate location functions. In order to reflect effects of activity congestion the location function includes variables such as the total number of persons residing in a zone and of persons working in a zone. We prove that the proposed model is equivalent to a convex optimization problem that can be solved by a convergent method of successive averages. A numerical example is presented to demonstrate the application of the model and algorithm.     

COMPETITIVE LOCATION UNDER UNCERTAINTY OF COSTS

ABSTRACT. In this paper, we study the centroid problem from competitive location theory for a linear market with uniform demand, assuming that the leader has imperfect information about the follower's fixed and marginal costs. It is shown that the general version of this problem can be formulated as a nonlinear programming problem and the exact solution can be obtained analytically in a special case. A simple strategy is also given for the general problem, and it is proven that this strategy has a guaranteed error bound. It is demonstrated that uncertainty of costs might lead to market failure in the centroid problem, but this disappears if the game is repeated and the firms learn from observing each other's moves. It is also shown that it is possible for the leader to obtain optimal expected profit at a low perceived risk, with only sufficient, and not necessarily perfect, information. These two observations lead to our primary conclusion from the study that although cost uncertainty is a realistic feature of most competitive location models, there are very effective ways of dealing with it.     

Hub Location Problem with Allowed Routing between Nonhub Nodes

In this study, we relax one of the general assumptions in the hub location literature by allowing routed flows between nonhub nodes. In hub networks, different flows are consolidated and routed via collection, interhub, and distribution arcs. Due to consolidation, some flows travel long paths despite closeness of their origin and destination. In this study, we allow direct flows by penalizing by a scalar factor of original cost of transshipment between these arcs. We present mathematical models for median, center, and set covering versions of the problem for single‐ and multi‐allocation cases. We test the models with the CAB and TR data sets. We discuss the properties of established direct connections for different models by using another mathematical model where the number of direct flows is bounded and interpret the effect of changes in problem parameters.     

空铁型综合交通枢纽地区空间演化特征——以上海虹桥枢纽为例

空铁型综合交通枢纽是将航空枢纽和高铁枢纽有机整合而形成的航空高铁一体化综合交通枢纽,具有较强的经济社会带动作用,对区域空间演化产生重要影响。根据复杂适应系统理论,选取上海虹桥综合交通枢纽地区为案例地,分析了空铁型综合交通枢纽地区地域空间演化阶段性特征。结果表明：交通枢纽地区地域系统通过多个适应性主体之间非线性相互作用形成复杂适应系统,该地域系统演化过程可划分为枢纽地区空间形成阶段、枢纽地区空间生长阶段和枢纽地区空间涌现阶段。上海虹桥综合交通枢纽地区在三个阶段特征不同,配套设施建设、要素集聚与流动、城市功能形成与发展、区域品牌形成等方面不断深化。研究有助于认知综合交通枢纽地域系统空间演化规律,为深化研究和实践发展提供科学借鉴。     

A Combined Cluster and Interaction Model: The Hierarchical Assignment Problem

This article presents a new spatial modeling approach that deals with interactions between individual geographic entities. The developed model represents a generalization of the transportation problem and the classical assignment problem and is termed the hierarchical assignment problem (HAP). The HAP optimizes the spatial flow pattern between individual origin and destination locations, given that some grouping, or aggregation of individual origins and destinations is permitted to occur. The level of aggregation is user specified, and the aggregation step is endogenous to the model itself. This allows for the direct accounting of aggregation costs in pursuit of optimal problem solutions. The HAP is formulated and solved with several sample data sets using commercial optimization software. Trials illustrate how HAP solutions respond to changes in levels of aggregation, as well as reveal the diverse network designs and allocation schemes obtainable with the HAP. Connections between the HAP and the literature on the p-median problem, cluster analysis, and hub-and-spoke networks are discussed and suggestions for future research are made.     

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.     

Transportation Networks and the Location of Human Activities

The impact of transportation networks on the location of human activities is a surprisingly neglected topic in economic geography. Using the simple plant location problem, this paper investigates such an impact in the case of a few idealized networks. It is seen that a grid network tends to foster a dispersed pattern of activities, while the center of a radial network acts as an attractor. The case of two economies characterized by different network configurations that form a custom union is then analyzed. It is shown that the structural properties of the networks still hold, though some locations are pulled toward the common border. This suggests that no such relocation should be expected within the European Union if the state members endorse similar fiscal and social policies after the formation of the single market.     

基于网络分析的交通网络评价及其与区域经济发展关系研究

以网络分析为基础,使用节点连通性和可达性等指标,评价研究甘肃省的交通网络以及交通网络与区域经济发展之间的内在关系,提出了平均经济--网络直径概念、功能及其计算方法。研究结果表明,节点连通性和可达性指标与区域经济发展水平具有密切的相关性,且跨区域交通对区域经济发展的贡献率大于仅邻域交通对区域经济发展的贡献率;使用节点连通性和可达性指标可界定出各区域经济之间的空间相互作用范围,为整个区域的交通规划和经济区划提供有力的科学依据;甘肃省交通呈聚团模式,具有空间自相关性。     

京津冀交通路网结构特征及其演变的分形刻画

交通一体化是京津冀协同发展的基础和前提，合理的交通网络结构对提升城市群整体效能意义重大。本文基于1995-2030年多源交通路网数据，运用分形思想，研究京津冀以城市群为节点体系的交通路网空间结构特征及演化趋势。主要结论如下：①京津冀高等级路网仍有一定扩展潜力，交通网络整体等级结构尚不稳定，未达到一种优化的分形递阶状态。②各级路网空间分布具有自仿射特征，但各向异性扩展强度正在逐渐减弱，城镇化和交通一体化战略的实施正在促进各级路网逐渐向自相似的结构一体化方向演化。③交通路网空间结构演化与城镇用地结构不同步，可能与系统所处城镇化发展阶段有关。④高等级路网分维演化服从次数大于1的logistic模型，按照规划预期，各级路网空间发育将相继在2040年前后达到饱和；但按照规划设计高速公路建设将过度饱和，未来应及时调整规划。     

公共交通可达性分析方法进展

公共交通可达性拥有空间属性、时间属性、社会属性和经济属性,它是一种衡量区位价值的综合性指标,不仅可以反映城市空间特征,同时对城市中生活的人的社会经济属性和生活习惯,具有一定的解释力。为了不断适应新形势下的交通发展要求,减少环境负担,早日实现低碳绿色发展,创新公交都市规划与分析方法迫在眉睫。本文对基于个人的、基于效用的、基于基础设施的和基于位置的可达性研究进行了回顾,并归纳了七种公共交通可达性的分析方法,分别为：基于缓冲区的公共交通站点可达性、基于供需模型的公共交通面状可达性、基于网络分析法的公共交通网络可达性、基于成本栅格法的公共交通可达性、基于成本栅格与网络分析的集成法的公共交通可达性、基于高性能图形数据库的公共交通高精度可达性、基于开放地图 API 的公共交通高精度可达性。 以期为我国未来公共交通可达性的分析方法提供指引和借鉴。     

Empirical Analysis of a Travel-Time Forecasting Model

The purpose of this article is to analyze empirically a travel-time forecasting model that estimates link travel times on congested road networks. In separate studies by You and Kim, a nonparametric regression model has been developed as a core forecasting algorithm to reduce computation time and increase forecasting accuracy. In this article, the sensitivity of model parameters is evaluated so that the proposed travel-time forecasting model could be utilized in transportation information and management systems such as location-based services and intelligent transportation systems applications.     

Nonparametric Significance Test for Discovery of Network‐Constrained Spatial Co‐Location Patterns

Spatial co‐location patterns are useful for understanding positive spatial interactions among different geographical phenomena. Existing methods for detecting spatial co‐location patterns are mostly developed based on planar space assumption; however, geographical phenomena related to human activities are strongly constrained by road networks. Although these methods can be simply modified to consider the constraints of networks by using the network distance or network partitioning scheme, user‐specified parameters or priori assumptions for determining prevalent co‐location patterns are still subjective. As a result, some co‐location patterns may be wrongly reported or omitted. Therefore, a nonparametric significance test without priori assumptions about the distributions of the spatial features is proposed in this article. Both point‐dependent and location‐dependent network‐constrained summary statistics are first utilized to model the distribution characteristics of the spatial features. Then, by using these summary statistics, a network‐constrained pattern reconstruction method is developed to construct the null model of the test, and the prevalence degree of co‐location patterns is modeled as the significance level. The significance test is evaluated using the facility points‐of‐interest data sets. Experiments and comparisons show that the significance test can effectively detect network‐constrained spatial co‐location patterns with less priori knowledge and outperforms two state‐of‐the‐art methods in excluding spurious patterns.     

Digitalising sex commerce and sex work: a comparative analysis of French,Greek and Slovenian websites

The aim of this article is to explore the complexity of the online sex trade and work by analysing sexuality-related commercial websites, with reference to three European states, France, Greece and Slovenia. The article compares websites in each specific sociocultural context, in order to provide insights into the various types of networks and services that emerge, and to explore how they operate, how they communicate and how sex is being merchandised. We have conducted a two-tier analysis: The first part discusses results of a quantitative macro-analysis exploring 149 websites, while the second part is a micro-analysis analysing the visualisation of egocentric network of three selected websites. The focus is on understanding how gender relations develop in digital environment and how within cyberspace sectorial and national divides are dealt with. While there is evidence to suggest that in some sectors the Internet has opened avenues for sex workers to work independently of the control networks, there are also many forms of exploitation that arise from new media. We observe that sex commerce online is not particularly attentive to the agency of sex workers but is, to the contrary, oriented to provide opportunities and a forum for businessmen and clients.     

High‐speed railway to success? The effects of high‐speed rail connection on regional economic development in China

We find that high‐speed railway connection in China has led to a reduction in GDP per capita for connected peripheral prefectures. We use the least‐cost path‐spanning tree network to address the nonrandom route placement issue. We find that the reduction of GDP per capita is driven by significant contractions in capital input, industrial output, and skilled labor outflow. We present evidence to support a trade‐based channel in light of falling transportation costs between peripheral and metropolitan regions. Our finding highlights the importance of the cost of human transport.