Two New Location Covering Problems: The Partial P-Center Problem and the Partial Set Covering Problem

Two new covering problems are introduced. The partial covering P-center problem minimizes a coverage distance in such a way that a given fraction of the population is covered. The partial set covering problem seeks the minimum number of facilities needed to cover an exogenously specified fraction of the population within a given coverage distance. The problems are formulated as integer linear programming problems. Bisection search algorithms are outlined for the two problems. The search algorithm repeatedly solves a Lagrangian relaxation of the maximal covering problem. Computational results for the Lagrangian relaxation of the maximal covering problem and for the bisection search algorithms are presented on problems with up to 150 nodes.     

Two New Location Covering Problems: The Partial P-Center Problem and the Partial Set Covering Problem

Two new covering problems are introduced. The partial covering P-center problem minimizes a coverage distance in such a way that a given fraction of the population is covered. The partial set covering problem seeks the minimum number of facilities needed to cover an exogenously specified fraction of the population within a given coverage distance. The problems are formulated as integer linear programming problems. Bisection search algorithms are outlined for the two problems. The search algorithm repeatedly solves a Lagrangian relaxation of the maximal covering problem. Computational results for the Lagrangian relaxation of the maximal covering problem and for the bisection search algorithms are presented on problems with up to 150 nodes.     

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.     

Computational Comparison of Five Maximal Covering Models for Locating Ambulances

This article categorizes existing maximum coverage optimization models for locating ambulances based on whether the models incorporate uncertainty about (1) ambulance availability and (2) response times. Data from Edmonton, Alberta, Canada are used to test five different models, using the approximate hypercube model to compare solution quality between models. The basic maximum covering model, which ignores these two sources of uncertainty, generates solutions that perform far worse than those generated by more sophisticated models. For a specified number of ambulances, a model that incorporates both sources of uncertainty generates a configuration that covers up to 26% more of the demand than the configuration produced by the basic model.     

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.     

Probabilistic, Maximal Covering Location—Allocation Models forCongested Systems

When dealing with the design of service networks, such as health andemergency medical services, banking or distributed ticket-selling services, the location of servicecenters has a strong influence on the congestion at each of them, and, consequently, on thequality of service. In this paper, several probabilistic maximal coveringlocation—allocation models with constrained waiting time for queue length are presentedto consider service congestion. The first model considers the location of a given number ofsingle-server centers such that the maximum population is served within a standard distance, andnobody stands in line for longer than a given time or with more than a predetermined number ofother users. Several maximal coverage models are then formulated with one or more servers perservice center. A new heuristic is developed to solve the models and tested in a 30-node network.     

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.     

p‐Functional Clusters Location Problem for Detecting Spatial Clusters with Covering Approach

Regionalization or districting problems commonly require each individual spatial unit to participate exclusively in a single region or district. Although this assumption is appropriate for some regionalization problems, it is less realistic for delineating functional clusters, such as metropolitan areas and trade areas where a region does not necessarily have exclusive coverage with other regions. This paper develops a spatial optimization model for detecting functional spatial clusters, named the p‐functional clusters location problem (p‐FCLP), which has been developed based on the Covering Location Problem. By relaxing the complete and exhaustive assignment requirement, a functional cluster is delineated with the selective spatial units that have substantial spatial interaction. This model is demonstrated with applications for a functional regionalization problem using three journey‐to‐work flow datasets: (1) among the 46 counties in South Carolina, (2) the counties in the East North Central division of the US Census, and (3) all counties in the US. The computational efficiency of p‐FCLP is compared with other regionalization problems. The computational results show that detecting functional spatial clusters with contiguity constraints effectively solves problems with optimality in a mixed integer programming (MIP) approach, suggesting the ability to solve large instance applications of regionalization problems.     

The Multi‐level Location Set Covering Model

The classical Location Set Covering Problem involves finding the smallest number of facilities and their locations so that each demand is covered by at least one facility. It was first introduced by Toregas in 1970. This problem can represent several different application settings including the location of emergency services and the selection of conservation sites. The Location Set Covering Problem can be formulated as a 0–1 integer‐programming model. Roth (1969) and Toregas and ReVelle (1973) developed reduction approaches that can systematically eliminate redundant columns and rows as well as identify essential sites. Such approaches can often reduce a problem to a size that is considerably smaller and easily solved by linear programming using branch and bound. Extensions to the Location Set Covering Model have been proposed so that additional levels of coverage are either encouraged or required. This paper focuses on one of the extended model forms called the Multi‐level Location Set Covering Model. The reduction rules of Roth and of Toregas and ReVelle violate properties found in the multi‐level model. This paper proposes a new set of reduction rules that can be used for the multi‐level model as well as the classic single‐level model. A demonstration of these new reduction rules is presented which indicates that such problems may be subject to significant reductions in both the numbers of demands as well as sites.     

The Sahelian Problem

Abstract

Philosophy of engineering is an area of study that is still in its infancy – attracting a growing number of researchers but still far behind the established field of philosophy of science. This essay reports on a series of seminars held on the topic at the Royal Academy of Engineering which have demonstrated that it is an area rich with problems for both philosophers and engineers to tackle. These problems can shed light on existing philosophical questions, raise new ones and even have practical value for the engineer.     

The Postmodern Problem

Abstract

Mormon political theology must reconcile two distinct projects: the care for the Church's concrete, temporal existence in the World, and the welcoming of the future Kingdom of God on earth. Because of this duality, political theology finds itself highlighting the distinction between the World and the Kingdom of God and at the same time pointing out common ground and attempting to establish peace between the Church and the World. The alleged contradictions of Mormon political thought are, according to this conception, to be understood not as confrontations between idealism and brute reality (or “utopianism” and “assimilation”), but rather as the bringing together of the two goals of Mormon political reflection, pursued by two sides of political theology. These two sides, apologetic and prophetic political theology, are distinguished not by their political content, but rather by their particular kinds of political rhetoric.     

Protecting Critical Assets: The r-Interdiction Median Problem with Fortification

Many systems contain bottlenecks, critical linkages, and key facilities. Such components, when lost due to a man-made or natural disaster, may imperil a system in performing its intended function. This article focuses on reducing the impact of an intentional strike against a supply system where supply facilities can be fortified in order to prevent such events. It is assumed that fortification resources are limited and must be used in the most efficient manner. In a recent article, Church, Scaparra, and Middleton (2004) introduced the r-interdiction median problem, which can be used to identify the most important facilities in a supply system. In this article, we extend that model to address the option of fortifying such sites against possible interdiction. We present a new integer-linear programming model that optimally allocates fortification resources in order to minimize the impact of interdiction. Computational results are presented in using this model for several hypothetical problems. We also discuss the general properties of fortification and demonstrate that the presence of fortification can impact which system elements are considered critical.     

The Negative Effects of Insufficient Support Systems on Kuwaiti Mothers of Children with Disabilities

Parents raising a child with a physical or cognitive disability are often faced with the negative stigma against disabilities that exist in several Arab countries. This puts extra pressure on the parents and can lead to negative outcomes for the children. The purpose of this study was to investigate the effects of parenting stress and varying levels of support for mothers of children with disabilities and the effects of these pressures on their relationship with their disabled child. We surveyed 85 Kuwaiti mothers of children with disabilities. The participants filled out an online survey with questions regarding parenting related stress, perceived social support, feelings of social isolation, self‐efficacy, and attachment to their child. Results indicate that mothers who feel unsupported by their families, community, and government experience more parenting stress and greater social isolation. These in turn lead them to feel less competent in their parenting abilities, and ultimately they feel less emotionally connected to their child. Implications of these findings are discussed.     

Stuck in a Rut: The Problem with Australia's Electoral Apparatus

The origins of the distinguishing features of the Australian Electoral Commission can be found in nineteenth-century South Australia, when that colony led the world in electoral administration. It was the first jurisdiction to develop a professional, permanent, independent election management body, with salaried electoral officials, and to pursue continuous, State-initiated enrolment. South Australia evolved this way because, to extend path dependence terminology, it was ‘locked out’ of inefficient British practices. After Federation in 1901, the new Australian Electoral Office, largely based on the South Australian model, continued the tradition. One unique and defining feature was the strong, permanent role of divisional returning officers –‘Electoral Kings’, in the words of the first Australian Chief Electoral Officer. The ‘Kings’ were an integral component of much that was good about Australia's way of running elections. However, this structure is no longer the most appropriate for an organisation such as the AEC. It has long outlived its usefulness and is holding the Commission back. And, perhaps ironically for an organisation with a long record of resistance to political interference, it is House of Representatives politicians, of all major parties, who are restraining the AEC from adopting sensible arrangements. The AEC is now, in path dependence terms, ‘locked in’ to inefficient practices.     

加蓬资源经济的负面效应

加蓬,濒临大西洋彼岸,方圆近27万平方公里,人口约120万,自然资源丰富,石油、木材、铀、锰为四大经济支柱,人均国民收入4000美元左右,在中部非洲乃至整个非洲令人刮目相看。然而,随着世界经济一体化进程的加快,特别是亚洲金融危机的冲击,加蓬资源经济的脆弱性暴露无遗：石油、木材出口(价)锐减,财政入不敷出,社会、政治矛盾迭起。本文以世界经济全球化为经、加蓬石油与木材出口为纬。剖析近几年来加蓬资源经济的负面效应,力图说明,像加蓬这样的非洲小国,只有调整产业结构。才能在世界经济一体化的大潮中趋利避害,立于不败之地。     

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.     

The Regionally Constrained p-Median Problem

In many applications involving the location of public facilities, the activity that is being located is added to the landscape of existing public facilities and services. Further, there also exists a political and behavioral landscape of differing jurisdictions, representations, and perceptions. This paper presents a new form of the p-median problem which addresses two types of “regional” constraints that can arise in public facilities planning. A formulation is given for this specially constrained median problem along with a solution approach. Several examples are presented with computational results which indicate that this type of constrained problem could lead to better facilities planning.