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.     

HOTELLING'S “MAIN STREET” WITH MORE THAN TWO COMPETITORS*

ABSTRACT. I analyze oligopolistic competition among three or more firms located on Hotelling's (1929) Main Street and show that in contrast with Hotelling's duopoly, the symmetric locational structure supports a noncooperative equilibrium in prices. However, in a two-stage game of location choice in the first stage, and price choice in the second stage, there exists no subgame-perfect equilibrium where the whole market is served. This is because, starting from any locational pattern, firms have incentives to move toward the central firm. This strong version of the Principle of Minimum Differentiation destroys the possibility of a locational equilibrium. The results are a direct consequence of the existence of boundaries in the space of location. The sharp difference between these results and those of the standard circular model (whose product space lacks boundaries) shows that the general use of the circular model as an approximation to the line interval model may be unwarranted.     

Elimination of Source A and B Errors in p-Median Location Problems

The p-median problem is a powerful tool in analyzing facility location options when the goal of the location scheme is to minimize the average distance that demand must traverse to reach its nearest facility. It may be used to determine the number of facilities to site, as well as the actual facility locations. Demand data are frequently aggregated in p-median location problems to reduce the computational complexity of the problem. Demand data aggregation, however, results in the loss of locational information. This loss may lead to suboptimal facility location configurations (optimality errors) and inaccurate measures of the resulting travel distances (cost errors). Hillsman and Rhoda (1978) have identified three error components: Source A, B, and C errors, which may result from demand data aggregation. In this article, a method to measure weighted travel distances in p-median problems which eliminates Source A and B errors is proposed. Test problem results indicate that the proposed measurement scheme yields solutions with lower optimality and cost errors than does the traditional distance measurement scheme.     

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.     

EXPLORING LOCATIONAL EQUILIBRIA IN A COMPETITIVE BROADBAND ACCESS MARKET: THEORETICAL MODELING APPROACH

ABSTRACT Due to strong local competition in the broadband access market, strategic locational planning is very important for service providers. In this paper, we explore locational equilibria in a competitive broadband market under several situations: with and without customer loyalty and under different initial market conditions. To do this, we propose a competitive broadband location model based on probabilistic patronage behavior, explicitly considering the characteristics of the broadband market and competitive structures. Also, we suggest iterative algorithms to identify spatial equilibria. We show that competing location strategies may lead to a stable spatial configuration of market share.     

DISCRETE SPATIAL CHOICE MODELS FOR AGGREGATE DESTINATIONS*

ABSTRACT. In problems of spatial choice, the choice set is typically more aggregated than the one considered by decision-makers, often because choice data are available only at the aggregate level. These aggregate choice units will exhibit heterogeneity in utility and in size. To be consistent with utility maximization, a choice model must estimate choice probabilities on the basis of the maximum utility within heterogeneous aggregates. The ordinary multinomial logit model applied to aggregate choice units fails this criterion as it is estimated on the basis of average utility. In this paper, we derive and discuss a model which utilizes the theory underlying the nested logit model to estimate the appropriate maximum utilities of aggregates. We also demonstrate that the aggregate alternative error terms are asymptotically Gumbel, thereby relaxing the assumption of extreme value distributed error terms. This is accomplished with help from the asymptotic theory of extremes.     

Net migration,unemployment, and the business cycle

"An empirical test of the effects of exogenous shocks upon a region's population size is conducted in the framework of an equilibrium locational model. The model emphasizes the separation of endogenous from exogenous factors, a point omitted in most empirical studies of aggregate migration. Exogenous changes are manifested in the local relative cost of living and the local relative unemployment rate. Hypotheses are tested using a national sample of youth, in addition to census, data [for the United States]. Surprisingly, a simple measure of the size of shock to a regional economy has the greatest explanatory power compared to more sophisticated measures based on prior business cycles."     

An ethnoarchaeological inductive model for predicting archaeological site location: A case-study of pastoral settlement patterns in the Val di Fiemme and Val di Sole (Trentino,Italian Alps)

In this paper I propose a novel integration of inductive predictive modelling and ethnoarchaeology. The case study concerns seasonal upland pastoral settlement patterns in the eastern Italian Alps. A sample of modern pastoral sites has been selected, and their relationships with environmental variables have been analyzed in order to create a model to predict the location of archaeological upland pastoral sites. The model has been tested with modern and archaeological control samples. It has proved to be useful for predicting the location of specific site categories. Ethnoarchaeological fieldwork has been carried out in the same alpine sample area, which has enhanced the interpretative potential of the proposed model, suggesting that the spatial of the analyzed sites could well be related to their dairying function. The creation of ethnoarchaeological locational models with a predictive potential may be very important not only in helping to tackle some theoretical and methodological problems in predictive modelling, but also in enhancing the importance of ethnoarchaeology in landscape archaeology projects.     

美国大都市区尺度上的工业区位研究

工业化和城市化之间的互动关系体现在都市区尺度上的工业区位上。本文在新经济地理学和城市地理学所揭示的产品差异化和城市集聚效应相互关系的基础上,通过区位熵分析、赫芬达尔-赫希曼指数,对美国工业区位与大都市区间的耦合关系进行实证研究。结果显示:集聚于大都市区核心区的往往是产品个性化和定制化程度较高的行业;位于大都市区外围区的大都是产品依赖于城市市场,但标准化程度较高的行业;传统制造业则往往位于非大都市区。多数都市工业的市场集中度较低,而大部分传统工业的市场集中度较高。这不仅印证了新经济地理学的理论推演和城市地理学的行业分析,而且对包括中国在内的转型国家城市及其产业发展具有重要的参考意义。     

A Synthesis of Aggregation Methods for Multifacility Location Problems: Strategies for Containing Error

When solving a location problem using aggregated units to represent demand, it is well known that the process of aggregation introduces error. Research has focussed on individual components of error, with little work on identifying and controlling total error. We provide a focussed review of some of this literature and suggest a strategy for controlling total error. Consideration of alternative criteria for evaluating aggregation schemes shows that the method selected should be compatible with the objectives of the analyses in which it is used. Experiments are described that show that two different measures of error are related in a nonlinear way to the number of aggregate demand points (q), for any value of the number of facilities (p). We focus on the parameter q/p and show that it is critical for determining the expected severity of the error. Many practical implementations of location algorithms operate within the range of q/p where the rate of change of error with respect to q/p is highest.     

基于GIS的农村医疗设施空间可达性分析——以河南省兰考县为例

针对农村医疗设施空间分布的公平性问题,提出了使用GIS技术和空间可达性指标评估医疗设施的区域分布特征。以兰考县乡级以上卫生院为例,建立人口分布、医疗设施位置、行政区域等地理数据库,选择人均医疗资源分配、就医的最近距离、选择医院的机会、重力模型及改进的重力模型5个空间可达性模型,计算了各乡镇、各行政村的医疗设施可达性指标,并制作了相应的专题地图;在此基础上对医疗设施的空间布局进行了分析。空间可达性指标全面地反映医疗设施的空间分布特征,鉴别出资源分配较薄弱的区位,是农村医疗改革中设施规划和资源分配的重要依据。     

Cognitive Maps and Spatial Behavior Of Consumers

Two multidimensional scaling algorithms are used to externally measure cognitive maps of supermarket locations for a sample of sixty-one supermarket shoppers. Issues raised in the construction of the cognitive maps are discussed. The relationship between the derived cognitive maps and consumer behavior is compared to the relationship between physical maps and consumer behavior. Behavior is shown to be more closely related to cognitive maps. Differences in cognitive maps are defined and canonically correlated with consumers' socioeconomic and locational attributes. While aggregate cognitive maps are closely associated with physical maps, there is substantial variation between individual maps. This variation is related to shopping behavior and selected socioeconomic and locational characteristics of consumers.     

Errors Caused by Rounded Data in Two Simple Facility Location Problems

As a rule, data to be used in locational analysis are either rounded up or rounded down. Therefore, error is incurred if such location data are used. The objective of this paper is to examine location error and cost error due to rounding in unweighted minisum and minimax problems in one-dimensional continuous space. Several conclusions on rounding effects are obtained by examining the respective mean-squared errors. First, rounding tends to exert more serious influence on the minisum problem than on the minimax problem. Second, in both location problems, the location error shows a pattern that is the inverse of that of the cost error.     

A Geostatistical Linear Regression Model for Small Area Data. 一种适用于小区域数据的地统计线性回归模型

We present a new linear regression model for use with aggregated, small area data that are spatially autocorrelated. Because these data are aggregates of individual‐level data, we choose to model the spatial autocorrelation using a geostatistical model specified at the scale of the individual. The autocovariance of observed small area data is determined via the natural aggregation over the population. Unlike lattice‐based autoregressive approaches, the geostatistical approach is invariant to the scale of data aggregation. We establish that this geostatistical approach also is a valid autoregressive model; thus, we call this approach the geostatistical autoregressive (GAR) model. An asymptotically consistent and efficient maximum likelihood estimator is derived for the GAR model. Finite sample evidence from simulation experiments demonstrates the relative efficiency properties of the GAR model. Furthermore, while aggregation results in less efficient estimates than disaggregated data, the GAR model provides the most efficient estimates from the data that are available. These results suggest that the GAR model should be considered as part of a spatial analyst's toolbox when aggregated, small area data are analyzed. More important, we believe that the GAR model's attention to the individual‐level scale allows for a more flexible and theory‐informed specification than the existing autoregressive approaches based on an area‐level spatial weights matrix. Because many spatial process models, both in geography and in other disciplines, are specified at the individual level, we hope that the GAR covariance specification will provide a vehicle for a better informed and more interdisciplinary use of spatial regression models with area‐aggregated data.     

A GENERAL FRAMEWORK FOR THE INTEGRATION OF A LAND-USE MODEL WITH A TRANSPORTATION MODEL COMPONENT

Integrated land-use—transportation models are characterized as models in which the redistributive effects of one subsystem upon the other are explicitly defined and incorporated into the model's structure. At the core of integrated models is a linking procedure whose function is to transform the outputs of one model component into inputs for the other. Despite major efforts made in the past to build operational large scale integrated models, the structural properties of such models remain largely unexplored. This paper describes a general framework for an integrated model consisting of prototype model components. These are an iterative activity allocation model of the Garin-Lowry type, an equilibrium-assignment transportation network model, and a linking procedure. Given the level of analysis, this framework is shown useful for exploring the analytics of integrated models and, in particular, their equilibrium properties. By means of many simulation experiments based on an hypothetical numerical example, the operation of the model is demonstrated with an emphasis on the locational interpretation of the integration procedure. On the basis of the empirical results and considering the model's intrinsic assumptions, the following major findings can be cited. First, the effects of nontravel factors (such as basic employment and zonal attractions) upon activity distribution are stronger than effects caused by changes in the transportation system. The latter effects were found to yield nonlinear and, spatially, nonuniform changes in activity location which also tended to be larger in peripheral regions. Second, implicit in the specification of the integration procedure are behavioral assumptions regarding time-lags in locational adjustments made by activities in reaction to rising cost of travel. The present formulation implies that once located, activities do not revise their locational decisions despite substantial increases in travel costs. At the other extreme, all activities are permitted to readjust their locational preferences after the final interzonal travel costs are derived. The effect upon activity distribution of the latter specification is, of course, larger than that of the former, although less than the effect yielded by changes in nontravel factors. Regarding the equilibrium properties of the integrated system, both the theoretical and empirical analyses show that the entire model will converge into an equilibrium solution and that the corresponding trip patterns are also at equilibrium. These results will hold as long as the operation of the integrated models is completely controlled by the generation functions of the land-use model and the transportation model component only affects the spatial distribution of activities. Finally, the results from the simulation experiments indicate that the computed mean travel cost parameter tends to stabilize around a certain value as the level of demand for travel, within the system, rises. There is evidence that compensating changes in the location and composition of this demand are the main causes of this phenomenon. In light of these findings, it is possible to point to three key problems whose resolution could largely improve the predictive power of integrated models. First, it would be useful to define activity models in which the generation of activities is, among other things, a function of travel conditions. Second, currently formulated integrated models do not contain trip demand functions and, thus, demand for travel by an activity unit is regarded as completely inelastic. Third, different locating activities respond differently—over time and space—to changíng travel conditions, and models should, therefore, reflect explicitly such differences in activity behavior. A recent paper by Los [14], is an important contribution to the analysis of this issue.     

MIGRATION AS A WAY TO DIVERSIFY: EVIDENCE FROM RURAL TO URBAN MIGRATION IN THE U.S.

This paper extends the utility maximization model of migration by introducing income and unemployment‐related uncertainties as determinants of utility, and analyzes the effects of the informational advantages of migrants. The paper maintains that migration would expand an individual's economic choices and opportunities and allow diversification. Consequently, diversification advantages influence the location decisions of migrants, an effect captured by the correlation of incomes at the origin and potential destinations. We use the discrete choice model based on random utility maximization as the framework for our empirical investigation of migration from the United States rural to urban counties. This paper takes advantage of an equivalent relation between the conditional logit model and Poisson regression to study the migration decisions using aggregate data among a large set of spatial alternatives. The results show that the diversification concerns have significant effects on location decisions of the rural‐urban migrants in the United States.     

New patterns in the locational choice of immigrants in Spain

During recent years, Spain has experienced an important revolution in its migration flows. With the 2008–2013 Spanish financial crisis, the model of economic growth that attracted a large number of foreign people disappeared, and the entry of immigrants for reasons other than economic issues gained relevance. Linked with this phenomenon are the new patterns of locational choice across provinces and the variation in the nature of immigrants. In this paper, we examine the differential patterns and drivers of immigration across Spanish regions before and after the financial crisis. Special attention is paid to the question of how the characteristics of individual migrants influence their locational preferences. To answer this question, we use the Dirichlet multinomial regression model. The results obtained show a sharp change in the locational patterns of Spanish immigrants after the economic recession, confirming that traditional economic incentives are less relevant, while non-economic factors linked with a better lifestyle gain importance. They also reveal that, regardless of the economic conditions, network effects are strong. Finally, and what is probably more important for us, our estimates support the hypothesis that the locational preferences rely on the interaction between the immigrants’ characteristics and the underlying locational features.     

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.     

Microeconomic Formulation and Estimation of a Residential Location Choice Model: Implications for the Value of Time

Abstract We formulate a microeconomic model of residential location choice behavior as an aggregate of the individual behaviors of household members, subject to individual time constraints and a common income budget. A simplified version of the model is estimated from stated preference rank‐order data, yielding a function that may be interpretated as a conditional indirect utility function. We consider Box‐Tukey transformations, segmentation by income class, and a consistent treatment of data at different rank depths using the simultaneous mixed‐estimation method. Measures of the household's willingness‐to‐pay (through rents) for reducing travel times to work and study in the short run, are interpreted as subjective values of time and compared with such values derived from mode choice models. Our results are plausible, and consistent with recent findings showing that the short‐run benefits of transport projects derived by transport models are larger than benefits measured at the land use system.     

Management cultures and regional development: High performance management and the location of new manufacturing plants

In-depth case studies of new manufacturing plants are used to motivate a new business location model that incorporates management practices and cultures as location factors. This model is tested using US data on the location of new manufacturing plants. It is found that plants that adopt high performance management practices and cultures rely on different criteria when making their location decisions from those plants that are managed in more traditional ways. Omitting management culture from studies of business location may result in biased estimates of the importance of various traditional location factors. By demonstrating that location decisions are differentiated according to the management practices of firms, it is argued that regional development planning should pay more attention to specific business characteristics and that regional development policy include programmes that strengthen complementarities between management practices and the regional economic environment.