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.     

Designs for Detecting Spatial Dependence

The aim of this article is to find optimal or nearly optimal designs for experiments to detect spatial dependence that might be in the data. The questions to be answered are: how to optimally select predictor values to detect the spatial structure (if it is existent) and how to avoid to spuriously detect spatial dependence if there is no such structure. The starting point of this analysis involves two different linear regression models: (1) an ordinary linear regression model with i.i.d. error terms—the nonspatial case and (2) a regression model with a spatially autocorrelated error term, a so-called simultaneous spatial autoregressive error model. The procedure can be divided into two main parts: The first is use of an exchange algorithm to find the optimal design for the respective data collection process; for its evaluation an artificial data set was generated and used. The second is estimation of the parameters of the regression model and calculation of Moran's I , which is used as an indicator for spatial dependence in the data set. The method is illustrated by applying it to a well-known case study in spatial analysis.     

Application of LASSO to the Eigenvector Selection Problem in Eigenvector‐based Spatial Filtering

Eigenvector‐based spatial filtering is one of the often used approaches to model spatial autocorrelation among the observations or errors in a regression model. In this approach, a subset of eigenvectors extracted from a modified spatial weight matrix is added to the model as explanatory variables. The subset is typically specified via the selection procedure of the forward stepwise model, but it is disappointingly slow when the observations n take a large number. Hence, as a complement or alternative, the present article proposes the use of the least absolute shrinkage and selection operator (LASSO) to select the eigenvectors. The LASSO model selection procedure was applied to the well‐known Boston housing data set and simulation data set, and its performance was compared with the stepwise procedure. The obtained results suggest that the LASSO procedure is fairly fast compared with the stepwise procedure, and can select eigenvectors effectively even if the data set is relatively large (n = 10⁴), to which the forward stepwise procedure is not easy to apply.     

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.     

Using an Evolutionary Algorithm in Multiobjective Geographic Analysis for Land Use Allocation and Decision Supporting

Usually, allocation of resources is an optimization problem which involves a variety of conflicting economic, social, and ecological objectives. In such a process, advanced geographic analyst tool for manipulation of spatial data and satisfaction of multiple objectives is essential to the success of decision‐making. The present research intends to demonstrate the application of a multiobjective optimization method based on NSGA‐II 1 (we call it HNSGA‐II), along with Geographical Information System (GIS) 2 to select suitable sites for the establishment of large industrial units. Having defined the elements of HNSGA‐II for the site selection of industrial units, the method is tested on the data of Zanjan province, Iran, as the case study. The results showed that the proposed approach can easily find a variety of optimized solutions, giving the decision‐makers the possibility to opt for the most propitious solution. Using this method, the achievement level regarding each objective function can be studied for any of the nondominated solutions.     

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.     

Estimating Spatial Models Within A Disequilibrium Framework

Modeling demand in a spatial context requires careful handling of regional interactions. In situations where there are constraints in some markets that lead to spillovers to others it is useful to build this explicitly into the model. In this paper I present a theoretical model that is related to the disequilibrium and the spatial econometric literature. Under certain conditions the model may be estimable and an appropriate estimation technique that uses the EM algorithm, is put forward. A data set from the U.K. market for secondary school places provides a test for the procedure.     

A Dynamic Location-Allocation Model for Evaluating the Spatial Impacts for Just-in-Time Planning

This paper presents an interperiod network storage location-allocation (INSLA) model to solve the just-in-time production planning problem. The model is extended to a multiobjective problem in which trade-offs between delivery time and transportation costs are analyzed. The results for a hypothetical problem show that in an attempt to reduce inventories on the part of the primary purchaser of raw materials, the possibility exists for less than optimal behavior in the system.     

Using AMOEBA to Create a Spatial Weights Matrix and Identify Spatial Clusters

The creation of a spatial weights matrix by a procedure called AMOEBA, A Multidirectional Optimum Ecotope-Based Algorithm , is dependent on the use of a local spatial autocorrelation statistic. The result is (1) a vector that identifies those spatial units that are related and unrelated to contiguous spatial units and (2) a matrix of weights whose values are a function of the relationship of the ith spatial unit with all other nearby spatial units for which there is a spatial association. In addition, the AMOEBA procedure aids in the demarcation of clusters, called ecotopes, of related spatial units. Experimentation reveals that AMOEBA is an effective tool for the identification of clusters. A comparison with a scan statistic procedure (SaTScan) gives evidence of the value of AMOEBA. Total fertility rates in enumeration districts in Amman, Jordan, are used to show a real-world example of the use of AMOEBA for the construction of a spatial weights matrix and for the identification of clusters. Again, comparisons reveal the effectiveness of the AMOEBA procedure.     

An Efficient Search Strategy for Site-Selection Decisions in an Expert System

This paper describes an algorithm for spatial search, which is used in an expert system for site selection. The algorithm, named ProfMat, is able to find the best site in the area of interest even when the number of possible sites is large and many decision criteria are involved. Compared to commonly used search procedures, ProfMat improves the efficiency of spatial search in two ways. First, the best site is identified through an iterative rather than a linear process of selection and evaluation of optional sites. Second, an area is searched by narrowing down the focus to increasingly smaller areas and, thus, sites are evaluated as much as possible groupwise. The ProfMat procedure is illustrated by analyzing the problem of retail site selection. A comparison with alternative search procedures shows that ProfMat considerably reduces the evaluation costs needed to find the best site. The implementation of the algorithm in an expert system shows how ProfMat can be used in combination with specialist's knowledge to solve site-selection problems. The efficiency of the procedure allows considering large sets of optional sites, so that it may improve the quality of the outcome.     

Location-Allocation Models for Control of Forest Fires by Air Tankers

Four air tanker location-allocation models are considered as tools for suppression of forest fires. The models are tested and compared using forest fire data for Alberta. The results show that fire location patterns can vary considerably over the short term and that not responding to such variation by optimally relocating air tanker groups could be very costly in terms of losses to fire. We argue that an improved location-allocation model can serve as the heart of an optimal air tanker relocation system and suggest the basic requirements for developing such a model.
Quatre modèles localisation-allocation pour avions-citerne sont considérés comme des outils servant dans la lutte contre les incendies forestiers. Les différents modèles sont mis a l'tpreuve et comparts utilisant des données recuillies lors d'incendies forestiers survenus en Alberta. Les rtsultats obtenus montrent que les modèles de localisation de feu peuvent varier considérablement B court terme et que de ne pas se soucier de telles variations par une relocalisation optimale des groupes d'avions-citerne pourait s'avérer trts couteux en terme de pertes dues aux incendies forestiers. Nous soutenons qu'un modtle localisation-allocation amtliort peut constituer le coeur d'un systtme de relocalisation optimal pour avions-citerne et suggérons les conditions fondamentales requises pour le dèveloppement d'un tel modèle.     

The Effect on Attribute Prediction of Location Uncertainty in Spatial Data

A datum is considered spatial if it contains location information. Typically, there is also attribute information, whose distribution depends on its location. Thus, error in location information can lead to error in attribute information, which is reflected ultimately in the inference drawn from the data. We propose a statistical model for incorporating location error into spatial data analysis. We investigate the effect of location error on the spatial lag, the covariance function, and optimal spatial linear prediction (that is, kriging). We show that the form of kriging after adjusting for location error is the same as that of kriging without adjusting for location error. However, location error changes entries in the matrix of explanatory variables, the matrix of co‐variances between the sample sites, and the vector of covariances between the sample sites and the prediction location. We investigate, through simulation, the effect that varying trend, measurement error, location error, range of spatial dependence, sample size, and prediction location have on kriging after and without adjusting for location error. When the location error is large, kriging after adjusting for location error performs markedly better than kriging without adjusting for location error, in terms of both the prediction bias and the mean squared prediction error.     

The Majority Theorem for the Single (p = 1) Median Problem and Local Spatial Autocorrelation

Except for about a half dozen papers, virtually all (co)authored by Griffith, the existing literature lacks much content about the interface between spatial optimization, a popular form of geographic analysis, and spatial autocorrelation, a fundamental property of georeferenced data. The popular p-median location-allocation problem highlights this situation: the empirical geographic distribution of demand virtually always exhibits positive spatial autocorrelation. This property of geospatial data offers additional overlooked information for solving such spatial optimization problems when it actually relates to their solutions. With a proof-of-concept outlook, this paper articulates connections between the well-known Majority Theorem of the 1-median minisum problem and local indices of spatial autocorrelation; the LISA statistics appear to be the more useful of these later statistics because they better embrace negative spatial autocorrelation. The relationship articulation outlined here results in the positing of a new proposition labeled the egalitarian theorem.     

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.     

Optimizing the Spatial Structure of the Agricultural Production Function

Important characteristics of spatial agricultural production functions are derived by introducing a non‐negative curvilinear spatial demand function for production input intensities. Given the usual neoclassical rationale assumptions of spatial demand for capital and labor inputs under competitive environment of farming in developing agricultural economies, the optimal production levels are determined by optimizing spatial demand for production inputs. Decreasing price‐to‐transport costs ratio (that is, decrease in the prices of capital goods or increase in freight rates) and increasing wage‐to‐travel costs ratio (that is, increase in labor wages or decrease in the travel rate) expand the limits of the (spatial) optimal boundary of the demand for agricultural capital goods and labor input respectively. These effects occur on account of the operation of (positive) spatial price gradient and (negative) wage‐gradient in the market region. It may be noted that elasticities of demand for production factors are spatially variant and have significant effects on the alterations in the structure of agricultural production. However, the spatial optimal solution of production has a complicated relationship with them. The price elasticity has negative and wage elasticity has positive spatial gradients in the market region. Farmers located in the periphery of the market region are not much affected by the proportionate changes occurring in the prices of agricultural capital goods but are more sensitive to the proportional changes in labor wages. Because of a decreasing trend in capital input demand and increase in labor input with distance from the market, capital‐product diminishes with a decreasing rate and labor‐product increases with an increasing rate in the spatial structure of agricultural production. As a result, capital‐labor ratio falls toward zero, which raises profit rate per unit of capital investment especially in the outer part of the market region. The equilibria of optimal production with price elasticity as well as of capital intensity with labor employment (that is, capital‐labor ratio as unity) determine spatial limits of the optimal production zone which is shifted outward subject to the provision of cheap transportation, stabilizing market prices and/or increasing wage rate at the market center. It will help in extending outwardly the optimal spatial limits of capital investment and will mobilize capital resources of farmers in the periphery for efficient and competitive capital‐dominated farming.     

Can Earthquake Loss Models be Validated Using Field Observations?

The occurrence of a damaging earthquake provides an opportunity to compare observed and estimated damage, provided that detailed observations of the earthquake effects are made in the field. A question that arises is whether such comparisons can provide the basis for validation of an earthquake loss model. In order to explore this issue, a case study loss model for the northern Marmara region has been set up and the losses have been calculated for various ground-motion fields that arise when different assumptions are made about the ground-motion variability. In particular, the influence of removing the inter-event variability for a scenario earthquake and modeling spatial correlation among ground motions is studied. Further analyses are conducted assuming that a number of accelerograms are available within the region and that knowledge of spatial correlations among ground motions can therefore be used to better predict the motions at sites in the vicinity of the recording stations. The results demonstrate that unless one has a dense network of accelerographs (commensurate with the geographical resolution of exposure), then the variability in the losses cannot be sufficiently reduced to allow validation of the loss model.     

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.     

Theory and practice in urban pottery seriation

The paper discusses the principles and a procedure for analysing urban archaeological sequences using pottery seriation. Interpretations of particular shapes of seriation curve are offered and the problem of residuality is confronted. The method is suggested as having direct relevance for the definition of stratigraphic events and historical activities on urban sites.     

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.     

Theoretical and Computational Links between the p-Median,Location Set-covering,and the Maximal Covering Location Problem

It has been shown that the p-median problem, the location set-covering and the maximal covering location problems are important facility location models. This paper gives a historical perspective of the development of these models and identifies the theoretical links between them. It is shown that the maximal covering location problem can be structured and solved as a p-median problem in addition to the several approaches already developed. Computational experience for several maximal covering location problems is given.