Analysis of Errors Due to Demand Data Aggregation in the Set Covering and Maximal Covering Location Problems

In this paper, we extend the concepts of demand data aggregation error to location problems involving coverage. These errors, which arise from losses in locational information, may lead to suboptimal location patterns. They are potentially more significant in covering problems than in p-median problems because the distance metric is binary in covering problems. We examine the Hillsman and Rhoda (1978) Source A, B, and C errors, identify their coverage counterparts, and relate them to the cost and optimality errors that may result. Three rules are then presented which, when applied during data aggregation, will reduce these errors. The third rule will, in fact, eliminate all loss of locational information, but may also limit the amount of aggregation possible. Results of computational tests on a large-scale problem are presented to demonstrate the performance of rule 3.     

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.     

The Aggregation Problem in Location-Allocation

Location-allocation solutions based on aggregate estimates of demand are subject to error because of a loss of locational information during aggregation. It is shown that any method to remove or reduce uncertainty must be solution-specific and therefore impractical, for both median and center classes of problems. The significance of the error is illustrated by simulation of solutions to a number of artificial and real problems. It is suggested that aggregation problems be specifically addressed in applications of location-allocation models, and possible methods are proposed.     

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.     

A Study of the Role of Regionalization in the Generation of Aggregation Error in Regional Input –Output Models

Although the need for aggregation in input –output modelling has diminished with the increases in computing power, an alarming number of regional studies continue to use the procedure. The rationales for doing so typically are grounded in data problems at the regional level. As a result many regional analysts use aggregated national input –output models and trade –adjust them at this aggregated level. In this paper, we point out why this approach can be inappropriate. We do so by noting that it creates a possible source of model misapplication (i.e., a direct effect could appear for a sector where one does not exist) and also by finding that a large amount of error (on the order of 100 percent) can be induced into the impact results as a result of improper aggregation. In simulations, we find that average aggregation error tends to peak at 81 sectors after rising from 492 to 365 sectors. Perversely, error then diminishes somewhat as the model size decreases further to 11 and 6 sectors. We also find that while region – and sector –specific attributes influence aggregation error in a statistically significantly manner, their influence on the amount of error generally does not appear to be large.     

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.     

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.     

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.     

The Role of Interactive Learning to Close the “Innovation Gap” in SME-Based Local Economies: A Furniture Cluster in the Basque Country and its Key Policy Implications

This paper identifies an “innovation gap” in the (in)efficient relation between innovation structures and production systems in SME-based economies and, by elucidating an implicit aspect of key theoretical contributions from Lundvall and Cooke, among others, sets the basis for a policy focus that may help reducing those margins of inefficiency. In this work, we identify three interdependent drivers of innovation: the “critical mass” of firms in a specific geographical location; the formation of “organizations” devoted to the creation and diffusion of knowledge and innovations; the ignition of “learning processes” within the production system that help catalyse significant innovations within the local economy. We suggest that the importance of processes of codified knowledge flows needs to be complemented by interactive flows of tacit knowledge that help overcoming the “innovation gap” that often exists between firms and knowledge institutions. Since this gap represents the inefficiency of the innovation structures, we suggest that it should be targeted by policy-makers and business associations as a central issue for innovation promotion through actions that intensify interactions and learning processes through bottom-up initiatives. These elements are analysed in a furniture cluster in the Basque Country and are highlighted on the basis of successful micro-territorial experiences.     

Explorations and Syntheses of Linear Programming And Spatial Interaction Models of Residential Location

Various “linear programming” models of residential location are explored in some detail. It is then shown that entropy maximizing “sub-optimal” versions of these can be developed, which may be more realistic at typical levels of resolution used for analysis but can still be given some of the interpretations of the programming models. Further, any programming model can be seen as a limiting case of some entropy maximizing model in which some of the parameters tend to infinity. Some empirical tests of both kinds of models are presented, and the limiting relationships are discussed.     

MEDIAN,MEAN, AND OPTIMUM AS FACILITY LOCATIONS*

ABSTRACT The mean and the median are both measures of centrality. In one dimension, the median minimizes the average absolute distance from a facility to a set of customers {x_i}, and the mean minimizes the average squared distance. In two dimensions, the median minimizes the average rectangular distance, and the mean minimizes the average squared distance. This paper investigates the “location penalty” when a nonoptimal location is substituted for the optimal location. In one dimension, the average absolute distance at the mean is never more than twice the average absolute distance at the median. Surprisingly, this happens when the median and mean are close together. In two dimensions, the ratio of the average Euclidean distance at the median to the average Euclidean distance at the optimum is never more than . However, this upper bound depends on an unlikely scenario with just two customers. With three equal-sized customers, this ratio is never more than 1.12. However, if the triangle formed by the customers is rotated relative to the rectangular grid, the ratio never exceeds 1.028.     

Representation and Agenda Setting

We develop a new approach to the study of representation based on agenda setting and attention allocation. We ask the fundamental question: do the policy priorities of the public and of the government correspond across time? To assess the policy priorities of the mass public, we have coded the Most Important Problem data from Gallup polls across the postwar period into the policy content categories developed by the Policy Agendas Project ( Baumgartner & Jones, 2002 ). Congressional priorities were assessed by the proportion of total hearings in a given year focusing on those same policy categories, also from the Agendas Project. We then conducted similar analyses on public laws and most important laws, similarly coded. Finally we analyzed the spatial structure of public and congressional agendas using the Shepard‐Kruskal non‐metric multidimensional scaling algorithm. Findings may be summarized as follows: First, there is an impressive congruence between the priorities of the public and the priorities of Congress across time. Second, there is substantial evidence of congruence between the priorities of the public and lawmaking in the national government, but the correspondence is attenuated in comparison to agendas. Third, although the priorities of the public and Congress are structurally similar, the location of issues within the structure differs between Congress and the general public. The public “lumps” its evaluation of the nations most important problems into a small number of categories. Congress “splits” issues out, handling multiple issues simultaneously. Finally, the public tends to focus on a very constrained set of issues, but Congress juggles many more issues. The article has strong implications for the study of positional representation as well, because for traditional representation to occur, there must be correspondence between the issue‐priorities of the public and the government. We find substantial evidence for such attention congruence here.     

The Goldilocks Solution: Exploring the Relationship between Trust and Participation in Resource Management within the New Zealand Commercial Rock Lobster Fishery

Our understanding of the role natural resource users, and the governing institutions they create, has grown considerably in recent years. At the same time, our understanding of the role of trust in human interactions continues to grow. We use the case of New Zealand rock lobster (jasus edwardsii and Jasus verrauxi) to ask the question “What is the role of trust in an individual's decision to participate in natural resource management institutions?” Using data from a survey of constituents of the commercial rock lobster fishery, our analysis shows an inverted “U” relationship between trust and participation. We suggest that this may be described as a “Goldilocks solution” in which having both too much and too little trust is problematic; but a healthy level of is “just right.” Theoretical and policy implications of these findings and directions for future research are explored.     

“To This Day”: Aetiology,Rhetoric, or Literary Motif?

ABSTRACT

Many biblical stories exhibit an intentional association between “subjective facts” deriving from the narrative and “objective facts” belonging to external historical reality. This article examines stories belonging to the “departure on a journey” pattern which contain references to objective facts which follow a virtually fixed formula and occur at a standard location in the narrative. Both the frequency with which these facts are adduced and their formulaic nature make it difficult to adopt external criteria such as those proposed by either of the two conventional models (aetiological and communication), suggesting rather an inner—literary—link between the two sets of facts.     

Passion and compassion of god in the old testament

Abstract

The point of departure is the Kitamorian “Pain of God Theology”. However, the present survey is that of exegesis and of biblical theology. We pose the question whether the concept of the “immutability of God” is that of the OT? We believe our focal texts (Hos 11,8; Jer 31,20; Isa 63, 9+15) do challenge that notion. The righteous God of Israel is not presented as a vindictive god, who delights in judgement. Rather, the glimpses of God's “emotions”, read “passions”, suggest a more complex God‐image. The righteousness of God demands judgement, whereas his compassion finds another solution. We find that female and masculine imagery in connection with God's attitude and feelings toward his people, are frequently interchangeable. The all‐embracing motherly love of God may be seen as an expression of God's heart in tension between inevitable judgement and compassionate love. But the same aspect may also be expressed in the father/son relationship. The passion of God in OT is not a static or inherent condition of God's being. Rather, the anthropomorphic (or, anthropopatic) expressions may be glimpses of a rare “I‐You” relationship between God and his people Israel. The passion of God then becomes the most profound expression of God's dynamic response to man's fatal situation.     

生计与风水:清代湘南地区的矿业开发与生态环境

湘南地区毗邻赣、粤、桂三省,地理位置特殊,是一个复杂的地理单元。及至清代,湘南地区已是湖南省乃至全国铜、铅、银等矿业生产的主要区域。长达数百年的矿产开采与冶炼,促进了地方社会的经济发展,也给当地的生态环境带来深远影响。由此,湘南官绅民各界对矿业开发引发的环境问题亦有因应,“坑冶十害论”和“九嶷山封禁案”即为其集中体现。开矿采砂本为解决贫民生计而采取的措施,但因破坏风水、污染水土等一系列影响环境的后果,以致出现开矿与禁矿之争,使得湘南地区矿业开发一度出现波折。这两例个案亦折射出在“重本抑末”的传统社会中地方官绅士民在生计与风水之间的离合关系。地方社会以保护风水为由严禁矿冶,在一定程度上遏止了生态环境的破坏与恶化,不过,其在环保方面发挥的作用也不宜被高估。     

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.     

Das Treffen in Telgte

Transcendental consciousness is described by Kant as “the one single thing” in which “as in the transcendental subject, our perceptions must be encountered.” The unity of that subject depends on intellectual functions. I argue that its singularity is just the same as that of Kant's pre-intellectual “form” of spatiotemporal “intuition.” This may seem excluded by Kant's claim that it is through intellect that “space or time are first given as intuitions.” But while pre-intellectual form is insufficient for space and time as distinct “things,” it is sufficient for the constitution of a “single thing” indifferently construable as both. Contrary to what are typically seen as the main differences between Kant and Hume on identity of “self,” there is thus already a difference in play below the level of either's concern with the sorts of connections available for the combining, or illusion of combining, of manifolds of “impressions” or “ideas.”     

(Education for) Sustainable Development in Geography Education: review and outlook from a perspective of Germany

Nearly 15 years after the Rio Conference and 10 years after the Lucerne Declaration on Geographical Education for Sustainable Development we are interested to what extent the goals of this declaration have been implemented? What role does Geography play in Education for Sustainable Development in higher education? We analyzed the modules of 107 degree programs with Geography as a degree major or as a teacher training subject at 55 German universities, technical colleges and universities of education. We conducted a quantitative text analysis in which we searched the key words “Sustainability”, “Sustainable Development”, “Education for Sustainable Development” and “Nature-Society Studies” in the Module Regulations. Our data indicate great heterogeneity between the degree programs. The key words were predominantly found in majors in “Human Geography”, “Geography” and teacher training programs for “academic high schools”. Aspects of the results considered in the paper include: (a) differences in the orientation of degree programs, (b) varying degree of implementation in the modules, (c) different conceptual understanding of the principles of sustainability, (d) the extent to which concepts of Environmental Education and Education for Sustainable Development are mixed, (e) heterogeneity between mandatory courses and electives.