Maximal Covering Location Model Research Articles

A GIS-Based Spatial Decision Support System for Facility Location Planning in Nigeria

Abstract
 Public facilities are to be located optimally in the interest of society. In Nigeria, public facilities' locations are largely influenced by administrative constraints and politics, rather than efficiency and equity. This practice limits access, most especially, in rural communities where the population is dispersed. Studies on efficiency and equity in access to public health facilities focused on urban centres. The aim of this study, therefore, is to advance the understanding of the application of the spatial decision support system (SDSS) to evaluate efficiency and equity in access to public facilities in rural regions. The study used Ogun State, Nigeria as a case. The data used include the population and coordinates of the location of the settlements, coordinates of the location of health facilities and the transport networks. This study showed that 38.5% of settlements do not have access to primary care and the application of the p-median model showed that the efficiency of the existing location of health facilities can be improved by 40.6%. Application of the maximal covering location model showed that the existing maximum travel distance of 26.3km can be reduced. It can be reduced for the sake of equity to 9.9 km. This study demonstrated ways to develop evaluative tools for analyzing the distribution of public facilities in Nigeria. It is suggested that planners in rural regions of other developing countries can adopt these techniques and tools to make their location decisions more logical.
 Keywords: Geographic Information System, Public Health Facilities, Spatial Decision Support System, Location Efficiency, Location Equity.

Fire stations siting with multiple objectives and geospatial big data

In recent years, with the rapid development of urbanization, the urban public emergency management faces increasing challenges, and the number of fire incidents has increased largely. For mitigating injury risk and reducing property loss, fire station locations need to be optimized to provide efficient fire emergency services. However, the locations of fire facilities in China are mainly determined according to administrative divisions, lacking effective data-driven applications. In addition, existing location models are designed for general purpose, and few have taken into account the unique characteristics of fire services with multiple objectives, i.e., maximum coverage, minimum overlapping coverage and balanced workloads. With the recent development of geospatial big data, lots of fire risk related data (e.g. fire incidents data and travel time data) can be obtained, which provides an unprecedented opportunity for urban fire emergency facilities planning. In this paper, we propose to establish the multi-objective maximal covering location model by accurately estimating fire rescuing demands and travel cost from geospatial big data. A case study was carried out in Nanjing, China, and the result shows that our method is effective in optimizing the locations of fire stations.

Distance restricted maximal covering model for pharmacy duty scheduling problem

Pharmacies are considered as an integral part of health care systems for supplying medicine to patients. In order to access medicine with ease, pharmacies locations in the context of distance and demand are important for patients. In the case of a few numbers of pharmacies may be on duty at nights or during holidays, pharmacies duty scheduling problem occur and can be associated with location models. In contrast to widely used p-median model which aims to minimize the demand-weighted distance, we maximize the demand covered over the distance between the patients and the pharmacies on duty. Main contribution of the proposed model is the restriction constraint for the distance between pharmacies on duty in order to ensure fairness in an organizational view of point. We propose a distance restricted maximal covering location model (DR-MCLM) in this study. This mathematical model is a mixed integer linear programming model and solved by Lingo optimization software. The distances between the pharmacies and the sites are obtained using Geographic Information Systems (GIS). The model is applied for the case in Adana, one of the biggest cities in Turkey. The results are given on the maps of the city, including the pharmacies on duty and their assignments to sites in each day of the period.

การกำหนดที่ตั้งสถานีช่วยเหลือฉุกเฉินที่เหมาะสมบนทางหลวงโดยตัวแบบครอบคลุมความต้องการสูงสุด: กรณีศึกษาจังหวัดนครปฐม

การกำหนดที่ตั้งสถานีช่วยเหลือฉุกเฉินที่เหมาะสมบนทางหลวงโดยตัวแบบครอบคลุมความต้องการสูงสุด: กรณีศึกษาจังหวัดนครปฐม

Analysis of maximal covering location-allocation model for congested healthcare systems in user choice environment

This paper attempts to shed light onto the formulation and the solution of a probabilistic maximal covering location model for determining the optimal location of facilities in congested healthcare systems with referral hierarchical structure. We will address healthcare systems operating in a competitive setting and when the customers choose the facilities they patronise, by the travel time to the hospitals and service costs at each hospital. The hospitals have several low-level sections for offering low level services (such as primary services) and several high-level sections for offering high level services (such as professional services) and the patients will refer to different sections of hospitals according to their requirements and their physical conditions. Our objective is to minimise the total amount of demand that is lost in the system. To solve the model, two meta-heuristic algorithms, including population-based simulated annealing (PBSA) and ant colony optimisation (ACO) have been executed and analysed using statistical test and TOPSIS method to determine which algorithm works better.

Analysis of maximal covering location-allocation model for congested healthcare systems in user choice environment

This paper attempts to shed light onto the formulation and the solution of a probabilistic maximal covering location model for determining the optimal location of facilities in congested healthcare systems with referral hierarchical structure. We will address healthcare systems operating in a competitive setting and when the customers choose the facilities they patronise, by the travel time to the hospitals and service costs at each hospital. The hospitals have several low-level sections for offering low level services (such as primary services) and several high-level sections for offering high level services (such as professional services) and the patients will refer to different sections of hospitals according to their requirements and their physical conditions. Our objective is to minimise the total amount of demand that is lost in the system. To solve the model, two meta-heuristic algorithms, including population-based simulated annealing (PBSA) and ant colony optimisation (ACO) have been executed and analysed using statistical test and TOPSIS method to determine which algorithm works better.

Covering location problem of emergency service facilities in an uncertain environment

• Three models are proposed for uncertain covering location problem. • The crisp equivalences of the models are discussed. • Uncertainty distribution of the covered demand is studied. In practical location problems on networks, the response time between any pair of vertices and the demands of vertices are usually indeterminate. This paper employs uncertainty theory to address the location problem of emergency service facilities under uncertainty. We first model the location set covering problem in an uncertain environment, which is called the uncertain location set covering model. Using the inverse uncertainty distribution, the uncertain location set covering model can be transformed into an equivalent deterministic location model. Based on this equivalence relation, the uncertain location set covering model can be solved. Second, the maximal covering location problem is investigated in an uncertain environment. This paper first studies the uncertainty distribution of the covered demand that is associated with the covering constraint confidence level α . In addition, we model the maximal covering location problem in an uncertain environment using different modelling ideas, namely, the ( α, β )-maximal covering location model and the α -chance maximal covering location model. It is also proved that the ( α, β )-maximal covering location model can be transformed into an equivalent deterministic location model, and then, it can be solved. We also point out that there exists an equivalence relation between the ( α, β )-maximal covering location model and the α -chance maximal covering location model, which leads to a method for solving the α -chance maximal covering location model. Finally, the ideas of uncertain models are illustrated by a case study.

Location Optimization of Urban Mining Facilities with Maximal Covering Model in GIS: A Case of China

SummaryUrban mining offers an efficient supply of resources because of rich mines and low environmental impacts. Location selection and optimization for urban mining facilities is more complicated than for natural mines, given that it may vary according to the urban population, consumption habits, and economic development. China initiated the National Urban Mining Pilot Bases program in 2010 that targeted 50 national urban mining pilot bases, but unfortunately neglected the location planning issue. Twenty‐eight bases have already been selected, which are concentrated in the central and eastern areas of China. This article combines the use of analytic hierarchy process, maximal covering location model, and geographical information systems (GIS) software to optimize locations for China's urban mining pilot bases. Primary findings show that, theoretically, 40 urban mining pilot bases can sufficiently provide maximum gross domestic product (GDP) and population coverage service for China. Taking the current 28 bases as a precondition and 50 bases as the remaining policy target, our second optimization results in a list of 22 cities for the location selection of future urban mining pilot bases. In total, the optimized 22 cities, together with the selected 28 bases, can provide a maximum 97.5% of GDP and 95.1% of population coverage in China. This study illustrates the optimization process for urban mining recycling facilities in general and provides policy advice for China in a specific case.

A new partial coverage locating model for cooperative fire services

The location and allocation of fire service facilities, especially for those facilities expecting high demand and severe conditions, require consideration of the cooperative behavior of multi-type fire vehicles in different fire station locations, the gradual decline of coverage with increasing distance, and the sufficient number of fire vehicles given specific requirements of the Urban Fire Rescue Specification (UFRS) of China. This paper presents a mixed integer nonlinear program (MINLP) model that integrates a cooperative mechanism of multi-type vehicles, partial distance coverage of single-type vehicle (PDC-S), and partial quantity coverage of single-type vehicle (PQC-S) into an integrated maximal covering location model for cooperative fire services, therein offering partial distance and quantity coverage of multi-type vehicles (PDQC-M). Numerical experiments with a testing example validate our model and demonstrate that the BARON algorithms can be used to effectively solve the problem. An empirical case study of Harbin (China) and a series of sensitivity analyses are conducted to illustrate the effects of station size and total budget on PDQC-M provided by cooperative fire services.

Incorporating institutional and spatial factors in the selection of the optimal locations of public electric vehicle charging facilities: A case study of Beijing, China

In this paper, we present a case study on planning the locations of public electric vehicle (EV) charging stations in Beijing, China. Our objectives are to incorporate the local constraints of supply and demand on public EV charging stations into facility location models and to compare the optimal locations from three different location models. On the supply side, we analyse the institutional and spatial constraints in public charging infrastructure construction to select the potential sites. On the demand side, interviews with stakeholders are conducted and the ranking-type Delphi method is used when estimating the EV demand with aggregate data from municipal statistical yearbooks and the national census. With the estimated EV demand, we compare three classic facility location models – the set covering model, the maximal covering location model, and the p-median model – and we aim to provide policy-makers with a comprehensive analysis to better understand the effectiveness of these traditional models for locating EV charging facilities. Our results show that the p-median solutions are more effective than the other two models in the sense that the charging stations are closer to the communities with higher EV demand, and, therefore, the majority of EV users have more convenient access to the charging facilities. From the experiments of comparing only the p-median and the maximal covering location models, our results suggest that (1) the p-median model outperforms the maximal covering location model in terms of satisfying the other’s objective, and (2) when the number of charging stations to be built is large, or when minor change is required, the solutions to both models are more stable as p increases.

Optimizing precipitation station location: a case study of the Jinsha River Basin

ABSTRACTPrecipitation stations are important components of a hydrological monitoring network. Given their critical role in rainfall forecasting and flood warnings, along with limited observation resources, determining the optimal locations to deploy precipitation stations presents an important problem. In this paper, we use a maximal covering location problem to identify the best precipitation station sites. Considering the terrain conditions and the characteristics of a rainfall network, the original maximal covering location model is modified with the introduction of a set of additional constraints. The minimum density requirement is used to determine a precipitation station’s coverage range, and three weighting schemes are used to evaluate each demand object’s covering priority. As a typical mountainous watershed with high annual precipitation, the Jinsha River Basin is selected as the study area to test the applicability of the proposed method. Results show that the proposed method is effective for precipitation station configuration optimization, and the model solution achieves higher coverage than the real-world deployment. Compared with the commercial solver CPLEX, a genetic algorithm-based heuristic can significantly reduce the computation time when the problem size is large. Several deployment strategies are also discussed for establishing the optimal configuration of precipitation stations.

Improving Accessibility and Efficiency of Service Facility through Location-Based Approach: A Case Study at Narvik University College

Location problem of service facility has never lost its appeal to both academics and practitioners due to the complexity in balancing availability, responsiveness and efficiency. In this paper, a location-based study is performed in order to improve the accessibility of service facility in terms of availability and responsiveness for customers as well as the efficiency for service providers. This study employs two well-known location models for service facility: Maximal covering location model which aims to maximize the coverage of customer demands with limited number of facilities (efficiency) and p-median location model which aims to minimize the overall distance travelled from customs to service facilities (accessibility), and location-based comparison of the two solutions in a case study at the 3rd floor of the main building of Narvik University College (NUC) for improving the overall performance of printing service is conducted so as to illustrates a deep insight of real-world application. The optimal solutions for maximizing the overall performance are obtained under different scenarios, and Lingo software is applied for resolving the computational optimization problems.

Maximal Covering Location Model for Doctor-Helicopter Systems with Two Types of Coverage Criteria

Maximal Covering Location Model for Doctor-Helicopter Systems with Two Types of Coverage Criteria

Research on Maintenance Force Location Model

To optimize to allocation of maintenance force in warfare, this paper extended the application of the maximal covering location problem. As the priority function being defined, a maximal covering location model based on the priority of requirement nodes was set up and a lagrangean relaxation algorithm was applied to solve the problem. A case study was given at last, which verified the model.

Facility location in humanitarian relief

In this study, we consider facility location decisions for a humanitarian relief chain responding to quick-onset disasters. In particular, we develop a model that determines the number and locations of distribution centres in a relief network and the amount of relief supplies to be stocked at each distribution centre to meet the needs of people affected by the disasters. Our model, which is a variant of the maximal covering location model, integrates facility location and inventory decisions, considers multiple item types, and captures budgetary constraints and capacity restrictions. We conduct computational experiments to illustrate how the proposed model works on a realistic problem. Results show the effects of pre- and post-disaster relief funding on relief system's performance, specifically on response time and the proportion of demand satisfied. Finally, we discuss the managerial implications of the proposed model.

Provisional breeding zone determination modeled as a maximal covering location problem

This study was a first attempt to model the problem of delineating breeding zones as a maximal covering location problem. The method involves two steps. First, a comprehensive set of candidate breeding zones is generated for a region using the focal point seed zone method. This method allows for control over the adaptive difference of genetic material within each zone. A grid of points is used to create the set of candidate breeding zones: one zone per point. Next, candidate zones are entered into a maximal covering location model formulated to suit this problem. The objective of this model is to select a subset of candidate zones that maximally covers the area of the region, given a limit on the number of zones to be selected and on the adaptive dissimilarity allowed within zones. Through use of this method, decision-makers can gain insight into how many breeding zones are needed to cover the region. Using different inputs from the focal point seed zone method, it is also possible to explore the trade-offs between the quantity and the quality of breeding zones. The method was tested on data from a series of jack pine (Pinus banksiana Lamb.) common garden trials of 102 seed sources from northwestern Ontario.

A fuzzy multi-objective covering-based vehicle location model for emergency services

Timeliness is one of the most important objectives that reflect the quality of emergency services such as ambulance and firefighting systems. To provide timeliness, system administrators may increase the number of service vehicles available. Unfortunately, increasing the number of vehicles is generally impossible due to capital constraints. In such a case, the efficient deployment of emergency service vehicles becomes a crucial issue. In this paper, a multi-objective covering-based emergency vehicle location model is proposed. The objectives considered in the model are maximization of the population covered by one vehicle, maximization of the population with backup coverage and increasing the service level by minimizing the total travel distance from locations at a distance bigger than a prespecified distance standard for all zones. Model applications with different solution approaches such as lexicographic linear programming and fuzzy goal programming (FGP) are provided through numerical illustrations to demonstrate the applicability of the model. Numerical results indicate that the model generates satisfactory solutions at an acceptable achievement level of desired goals. Scope and purpose This paper considers the emergency service vehicles location problem. A multi-objective maximal covering location model is proposed in this paper. The model addresses the issue of determining the best base locations for a limited number of vehicles so that the service level objectives are optimized. Three of the important surrogates that reflect the quality of emergency service systems are considered as objectives in the model: maximization of the population covered by one vehicle, maximization of the population with backup coverage and minimization of the total travel distance from locations at a distance bigger than a prespecified distance standard for all zones. The proposed model allows the incorporation of decision maker's imprecise aspiration levels for the goals by means of FGP approach. Thus, the solution efficiency inherent in the FGP approaches is also included into the model. To demonstrate the applicability of the model, numerical examples are provided using different solution approaches.

A maximal covering location model in the presence of partial coverage

The maximal covering location problem (MCLP) addresses the issue of locating a predefined number of facilities in order to maximize the number of demand points that can be covered. In a classical sense, a demand point is assumed to be covered completely if located within the critical distance of the facility and not covered at all outside of the critical distance. Since the optimal solution to a MCLP is likely sensitive to the choice of the critical distance, determining a critical distance value when the coverage does not change in a crisp way from “fully covered” to “not covered” at a specific distance may lead to erroneous results. We allow the coverage to change from “covered” to “not-covered” within a distance range instead of a single critical distance and call this intermediate coverage level partial coverage. In this paper, we formulate the MCLP in the presence of partial coverage, develop a solution procedure based on Lagrangean relaxation and show the effect of the approach on the optimal solution by comparing it with the classical approach.

Reserve selection as a maximal covering location problem

Many alternative approaches have been proposed for setting conservation priorities from a database of species (or communities) by site. We present a model based on the premise that reserve selection or site prioritization can be structured as a classic covering problem commonly used in many location problems. Specifically, we utilize a form of the maximal covering location model to identify sets of sites which represent the maximum possible representation of specific species. An example application is given for vertebrate data of Southwestern California, which is then compared to an iterative solution process used in previous studies. It is shown that the maximal covering model can quickly meet or exceed iterative models in terms of the coverage objective and automatically satisfies a complementarity objective. Refinements to the basic model are also proposed to address additional objectives such as irreplaceability and flexibility.