Location Set Covering Problem Research Articles

The integration of GIS location‐based APIs and urban growth modeling for improved geographic access to hospital services

AbstractThis article aims to present an integration model of GIS with open data sourced from application programming interface (API) as a solution for the location set covering problem (LSCP) with an urban land dynamics model. The development of GIS which is increasingly advanced makes traditional GIS transition in the open data era to become more modern. One of the benefits is to help urban planners in determining the allocation of health facilities such as hospitals. This research takes the case of hospital service coverage during emergencies, especially during the COVID‐19 extraordinary event in Metropolitan Semarang, Indonesia. In addition to utilizing API‐base Location, the model process also uses a Cellular Automata‐based land use prediction model. Thus, the facility location plan not only considers service coverage but also land use growth which is a reflection of population growth. To analyze the problem of inequity of hospital services, this research combined the location‐based APIs‐based service area model with the urban growth model to evaluate the existing condition and predict the future of hospital service demand. It also uses the emergency standard with a maximum service distance of 1500 m and a maximum travel time of 7 min. The model confirmed that there are still critical spots not served by hospitals in Semarang City. According to the concept of health and place, it is essential to recommend adding two hospitals in unserved areas so that services are more evenly distributed in the future, especially in emergencies.

Reliability Computing Methods of Probabilistic Location Set Covering Problem Considering Wireless Network Applications

Reliability Computing Methods of Probabilistic Location Set Covering Problem Considering Wireless Network Applications

Determining the Best Location for COVID-19 Vaccine Distribution in Palembang Using the Set Covering Problem Model and Greedy Heuristic Algorithm

Optimizing the location of public health facilities is crucial to ensure public accessibility. Palembang City uses public health facilities for COVID-19 vaccine distribution and administration. This study identified the best location for COVID-19 vaccine distribution in Palembang City by implementing the Set Covering Problem (SCP) model and solving it with the Greedy Heuristic Algorithm. The SCP model consists of the Set Covering Location Problem (SCLP) model and the p-Centre Location Problem (p-CLP) and considers the separating distance between vaccine distribution sites located in each sub-district of Palembang City. The p-CLP model was formulated, and the Greedy Heuristic Algorithm was executed to determine the optimal distribution location for COVID-19 vaccines. The SCLP model successfully identified 27 optimal COVID-19 vaccine locations in Palembang City. These locations were subsequently used to formulate the p-CLP model. The p-CLP model's solution and the application of the Greedy Heuristic Algorithm yielded 27 optimal vaccine sites, which include Ariodillah Health Centre, Naga Swidak Health Centre, Sako Health Centre, Bukitsangkal Health Centre, Sei Lincah Health Centre, Kenten Health Centre, Kalidoni Health Centre, Pakjo Health Centre, Sei Baung Health Centre, Merdeka Health Centre, OPI Health Centre, Sosial Health Centre, Talang Betutu Health Centre, Myria Hospital, Sukarami Health Centre, Keramasan Health Centre, Karya Jaya Health Centre, 7 Ulu Health Centre, Sabokingking Health Centre, Charitas Hospital, Dr. Mohammad Hasan Hospital, Siti Khadijah Hospital, Bunda Hospital, Bunda Noni Hospital, Pelabuhan Kelas ll Palembang Health Office, Tiara Fatrin Hospital, and Alang-Alang Lebar Health Centre.

Location Optimization of Emergency Bell Based on Coverage Analysis for Crime Prevention

Typically, emergency bells are security facilities that, when activated, trigger an alarm and immediately dispatch a police car to prevent crime. However, there currently exists an ambiguity in the criteria for emergency bell installation. Consequently, this study aims to find an optimal location for emergency bells whilst considering several factors like cumulative crime incidents. In particular, we exploited emergency bell location data, data on five major crimes, and the geographic information of administrative dongs (primary division of districts) in this study. Specifically, we performed correlation analysis, principal component analysis, and K-means clustering for exploratory data analysis. To effectively cover all 17,437 crimes, which are not covered by the existing emergency bells in Gwangju metropolitan city from 2018 to 2021, the results from the implementation of the emergency bell location set-covering problem revealed the need for about 6228 emergency bells. More precisely, the emergency bell maximal covering location problem was employed to derive the coverage percentage for 250, 500, 800, 1000, and 1500 emergency bells. The results showed that 2850 emergency bells were required to cover over 80% of crime occurrence coordinates, saving over half of the budget compared with covering them all. Overall, this study is noteworthy in its potential role as a roadmap for the optimal placement of emergency bells for future crime prevention.

Spatial Layout and Accessibility Evaluation of COVID-19 Vaccination Sites Based on Three Optimization Models: A Case Study of Tianhe District, Guangzhou

The outbreak of COVID-19 poses a serious threat to global public health, and vaccination is an effective means of prevention. Studying the spatial layout and accessibility of COVID-19 vaccination sites is of great significance. The study analyzes the spatial distribution characteristics and accessibility of vaccination sites in the early stage of mass vaccination in Tianhe District, Guangzhou, based on GIS technology and combines three location allocation models: the p-median model, maximum covering location problem (MCLP) model, and location set covering problem (LSCP) model to identify candidate COVID-19 vaccination sites for the proposed public service facilities. The study found that only 47 COVID-19 vaccination sites exist in the early stage, with a small overall number, uneven spatial distribution, and trend of high accessibility in the central but low accessibility in the north and south; after the proposed addition of 31 vaccination sites, the overall distribution showed an even and dense distribution in the central and western regions, sporadic distribution in other regions, consistent with the distribution characteristics of residential communities. The areas where the accessibility of vaccination sites increased by more than 500 m accounted for 41% of the total area, and the area served by vaccination sites increased by 18%. Therefore, using the existing public service facilities to reasonably add the vaccination sites can improve the efficiency of vaccination and safeguard the establishment of a herd immunity barrier.

Efficient presolving methods for solving maximal covering and partial set covering location problems

The maximal covering location problem (MCLP) and the partial set covering location problem (PSCLP) are two fundamental problems in facility location and have widespread applications in practice. The MCLP determines a subset of facilities to open to maximize the demand of covered customers subject to a budget constraint on the cost of open facilities; and the PSCLP aims to minimize the cost of open facilities while requiring a certain amount of customer demand to be covered. Both problems can be modeled as mixed integer programming (MIP) formulations. Due to the intrinsic NP-hardness nature, however, it is a great challenge to solve them to optimality by MIP solvers, especially for large-scale cases. In this paper, we present five customized presolving methods to enhance the capability of employing MIP solvers in solving the two problems. The five presolving methods are designed to reduce the sizes of the problem formulation and the search tree of the branch-and-cut procedure. For planar problems with an extremely huge number of customers under realistic types of facility coverage, we show that the number of customers in the reduced problems can be bounded above by a quadratic polynomial of the number of facilities. By extensive numerical experiments, the five presolving methods are demonstrated to be effective in accelerating the solution process of solving the MCLP and PSCLP. Moreover, they enable to solve problems with billions of customers, which is at least one order of magnitude larger than those that can be tackled by previous approaches.

Greedy Reduction Algorithm as the Heuristic Approach in Determining the Temporary Waste Disposal Sites in Sukarami Sub-District, Palembang, Indonesia

Waste is one of the problems in Palembang, Indonesia. The amount of waste in Palembang increases proportionally to the population yearly and can adversely affect the community. Therefore, we determine the optimal temporary waste disposal site (TWDS) to optimize the problems. The set covering model is the proper model for solving the location and allocation problem. In this study, data on the distance between each TWDS is needed in the set covering modeling. The novelty in this research is developing the p-median problem model, which is formed from the optimal solution of the set covering location problem (SCLP) model. Palembang consists of 18 sub-districts, of which the Sukarami sub-district has the highest population density. This study discussed the determination of strategic TWDS in the Sukarami sub-district using the SCLP model, the p-median problem, and a heuristic approach, namely the greedy reduction algorithm in solving the model. Based on the solution of the p-median problem model with LINGO 18.0 and the p-median problem solved by the greedy reduction algorithm, only three strategic TWDS were found for the Sukarami sub-district. The study results recommend a review of the existing TWDS and particularly the addition of a TWDS in Sukodadi and Talang Betutu villages, respectively.

A multicriteria GIS-based decision-making approach for locating electric vehicle charging stations

Electric vehicles (EVs) will be the next technological leap for urban mobility, however the market penetration rate depends on several factors, including the major hurdle of limited EV charging stations. Equity is also an important factor – ensuring EV charging stations are widespread and available for all segments of the population. This paper outlines an innovative methodology to systematically determine the locations of EV charging stations while considering equity and efficiency to maximize accessibility and usage. The methodology has two levels. First, solving what is known as the Set Covering Location Problem (SCLP) by determining a threshold so that the distance (or travel time) between the consumer and the EV charging station will be less than or equal to a given value. This is a policy-based decision and provides a framework to ensure EV charging stations are ubiquitous and equitable. Second is solving the Maximum Covering Location Problem (MCLP) by considering a series of evaluation criteria to satisfy the demand of the early adopters. Following evaluation of the SCLP and MCLP, selected locations are aggregated by partitions to develop larger scale hubs. These hubs will not only include EV charging stations but will also function as connection points that integrate different modes of transportation.

Set Covering Model Using Greedy Heuristic Algorithm to Determine The Temporary Waste Disposal Sites in Palembang

Optimizing the facility location has a vital role in providing services to the community. This study aims to determine the Temporary Waste Disposal Site (TWDS) in Sako District, Palembang City. The distance data between each TWDS in Sako District is used to formulate the Set Covering model, consisting of the Set Covering Location Problem (SCLP) model and the p-Median Problem model. The classical approach is made by solving both models using Lingo 18.0 software. The Greedy Heuristic algorithm is used as the heuristic approach. Based on the results and discussion, Sako District consists of 4 Villages and 9 TWDS. The SCLP and p-Median Problem models with LINGO 18.0 software and the Greedy Heuristic algorithm show a difference. The study results suggest using the optimal solution resulting from the Greedy Heuristic algorithm because it can meet all requests in Sako District. Research shows that there are six optimal TWDS in Sako District. However, several locations are still not optimal, so it is recommended that there are an additional 14 new TWDS facilities in Sako District to serve all requests.

Probabilistic Set Covering Location Problem in Congested Networks

This paper focuses on designing a facility network, taking into account that the system may be congested. The objective is to minimize the overall fixed and service capacity costs, subject to the constraints that for any demand the disutility from travel and waiting times (measured as the weighted sum of the travel time from a demand to the facility serving that demand and the average waiting time at the facility) cannot exceed a predefined maximum allowed level (measured in units of time). We develop an analytical framework for the problem that determines the optimal set of facilities and assigns each facility a service rate (service capacity). In our setting, the consumers would like to maximize their utility (minimize their disutility) when choosing which facility to patronize. Therefore, the eventual choice of facilities is a user-equilibrium problem, where at equilibrium, consumers do not have any incentive to change their choices. The problem is formulated as a nonlinear mixed-integer program. We show how to linearize the nonlinear constraints and solve instead a mixed-integer linear problem, which can be solved efficiently.

Allocation of Relief Centre for Flood Victims Using Location Set Covering Problem (LSCP)

The frequency of natural disaster has been increasing over the years, resulting in loss of life, damage to properties and destruction of the environment. Compared to other natural disaster, floods are the most significant natural hazard in Malaysia that affect thousands of people. It becomes of great concern especially, during these recent floods, several relief centers were experiencing problems when most of the flood’s victims needed to move to the other relief centers after the existing shelters were also affected by flood water. Furthermore, the relief centers were congested due to the large number of flood evacuees that were over the capacity provided. This study attempts to adapt an advance mathematical location-allocation models in making decision to locate and allocate flood victims during flood event. The Location Set Covering Problem (LSCP), with capacitated constraint is considered and solved using Excel Solver. The determination of safe locations for relief centres with respect to prone area is proposed by adding three new constraints which are the distance from river, elevation from sea level and rainfall amount. A flood case of Kuala Kuantan, Pahang in 2013 was used as the main study area for the analysis as well as the whole Kuantan district. Two scenarios of split and non-split allowed were tested for allocation process and result showed that the percentage allocation and number of relief centers involved increases when the distance increases accordingly. Hence, the model can be considered for better evacuation plan.

Reducing exposure to COVID-19 by improving access to fever clinics: an empirical research of the Shenzhen area of China

BackgroundThe current 2019 coronavirus disease (COVID-19) pandemic is hitting citizen’s life and health like never before, with its significant loss to human life and a huge economic toll. In this case, the fever clinics (FCs) were still preserved as one of the most effective control measures in China, but this work is based on experience and lacks scientific and effective guidance. Here, we use travel time to link facilities and populations at risk of COVID-19 and identify the dynamic allocation of patients’ medical needs, and then propose the optimized allocation scheme of FCs.MethodsWe selected Shenzhen, China, to collect geospatial resources of epidemic communities (ECs) and FCs to determine the ECs’ cumulative opportunities of visiting FCs, as well as evaluate the rationality of medical resources in current ECs. Also, we use the Location Set Covering Problem (LSCP) model to optimize the allocation of FCs and evaluate efficiency.ResultsFirstly, we divide the current ECs into 3 groups based on travel time and cumulative opportunities of visiting FCs within 30 min: Low-need communities (22.06%), medium-need communities (59.8%), and high-need communities (18.14%) with 0,1–2 and no less than 3 opportunities of visiting FCs. Besides, our work proposes two allocation schemes of fever clinics through the LSCP model. Among which, selecting secondary and above hospitals as an alternative in Scheme 1, will increase the coverage rate of hospitals in medium-need and high-need communities from 59.8% to 80.88%. In Scheme 2, selecting primary and above hospitals as an alternative will increase the coverage rate of hospitals in medium-need and high-need communities to 85.29%, with the average travel time reducing from 22.42 min to 17.94 min.ConclusionsThe optimized allocation scheme can achieve two objectives: a. equal access to medical services for different types of communities has improved while reducing the overutilization of high-quality medical resources. b. the travel time for medical treatment in the community has reduced, thus improving medical accessibility. On this basis, during the early screening in prevention and control of the outbreak, the specific suggestions for implementation in developing and less developed countries are made.

Solving Classic Discrete Facility Location Problems Using Excel Spreadsheets

There are a variety of discrete facility location models that have practical relevance for operations management and management science courses. Integer linear programming (ILP) is the standard technique for solving such problems. An alternative approach that is often conceptually appealing to students is to pose the problem as one of finding the best possible subset of p facilities out of n possible candidates. I developed an Excel workbook that allows students to interactively evaluate the quality of different subsets, to run a VBA macro that finds the optimal subset, or to solve an ILP formulation that finds the optimal subset. Spreadsheets are available for five classic discrete location models: (1) the location set-covering problem, (2) the maximal covering location problem, (3) the p-median problem, (4) the p-centers problem, and (5) the simple plant location problem. The results from an assignment in a master’s-level business analytics course indicate that the workbook facilitates a better conceptual understanding of the precise nature of the discrete facility location problems by showing that they can be solved via enumeration of all possible combinations of p subsets that can be drawn from n candidate locations. More important, students directly observe the superiority of ILP as a solution approach as n increases and as p approaches n/2.

Location-allocation modeling for emergency evacuation planning with GIS and remote sensing: A case study of Northeast Bangladesh

This work developed models to identify optimal spatial distribution of emergency evacuation centers (EECs) such as schools, colleges, hospitals, and fire stations to improve flood emergency planning in the Sylhet region of northeastern Bangladesh. The use of location-allocation models (LAMs) for evacuation in regard to flood victims is essential to minimize disaster risk. In the first step, flood susceptibility maps were developed using machine learning models (MLMs), including: Levenberg–Marquardt back propagation (LM-BP) neural network and decision trees (DT) and multi-criteria decision making (MCDM) method. Performance of the MLMs and MCDM techniques were assessed considering the area under the receiver operating characteristic (AUROC) curve. Mathematical approaches in a geographic information system (GIS) for four well-known LAM problems affecting emergency rescue time are proposed: maximal covering location problem (MCLP), the maximize attendance (MA), p-median problem (PMP), and the location set covering problem (LSCP). The results showed that existing EECs were not optimally distributed, and that some areas were not adequately served by EECs (i.e., not all demand points could be reached within a 60-min travel time). We concluded that the proposed models can be used to improve planning of the distribution of EECs, and that application of the models could contribute to reducing human casualties, property losses, and improve emergency operation.

Hybrid Set Covering and Dynamic Modular Covering Location Problem: Application to an Emergency Humanitarian Logistics Problem

This paper presents an extension of the covering location problem as a hybrid covering model that utilizes the set covering and maximal covering location problems. The developed model is a multi-period model that considers strategic and tactical planning decisions. Hybrid covering location problem (HCLP) determines the location of the capacitated facilities by using dynamic set covering location problem as strategic decisions and assigns the constructive units of facilities and allocates the demand points by using dynamic modular capacitated maximal covering location problem as tactical decisions. One of the applications of the proposed model is locating first aid centers in humanitarian logistic services that have been addressed by studying a threat case study in Japan. In addition to validating the developed model, it has been compared to other possible combined problems, and several randomly generated examples have been solved. The results of the case study and model validation tests approve that the main hybrid developed model (HCLP) is capable of providing better coverage percentage compared to conventional covering models and other hybrid variants.

Analysis of Covering Problem Models for Setting the Location of a Ready-Mixed Concrete Plant: Case Study of the Rayong Province, Thailand

Decision makers must prepare good plans when developing large-scale projects. The Thai government has been increasing economic growth in three provinces under the Eastern Economic Corridor Development Program (EEC). The project includes reconstruction and new construction. This paper aims to find locations for several ready-mixed concrete plants to cover all ready-mixed concrete needs in the Rayong province. The plant location problem could be solved using optimization modelling for a set covering location problem (SCLP) and a maximal covering location problem (MCLP). The results show that two ready-mixed concrete plants location in the Mueang Rayong district and Klaeng district could meet the problem solution.

Chance constrained programming models for uncertain hub covering location problems

Hub covering location problem is a typical strategic decision with the purpose of locating hubs and determining the assignments of other nodes to ensure the travel time is not exceeding a specific threshold. Since the parameters such as flows and travel times are difficult to be precisely obtained in advance, a feasible way is to estimate them following the experts’ subjective beliefs. Hence, this paper is devoted to study hub covering location problem by using uncertain measure to characterize the subjective belief and considering the flows and travel times by uncertain variables. The uncertain hub set covering location problem is first discussed under the purpose of covering the flows entirely with the minimum setup cost of hubs. Then the uncertain hub maximal covering problem is studied by maximizing the total flow covered when the number of hubs is confirmed previously. Chance constrained programming models for both problems are constructed, respectively, and their corresponding deterministic forms are derived. A hybrid intelligence algorithm named GA–VNS is proposed by combing the variable neighborhood search with the genetic algorithm. Finally, several numerical experiments are presented to indicate the efficiency of GA–VNS.

Benders decomposition for very large scale partial set covering and maximal covering location problems

Covering problems constitute a fundamental family of facility location problems. This paper introduces a new exact algorithm for two important members of this family: (i) the maximal covering location problem (MCLP), which requires finding a subset of facilities that maximizes the amount of customer demand covered while respecting a budget constraint on the cost of the facilities; and (ii) the partial set covering location problem (PSCLP), which minimizes the cost of the open facilities while forcing a certain amount of customer demand to be covered. We study an effective decomposition approach to the two problems based on the branch-and-Benders-cut reformulation. Our new approach is designed for the realistic case in which the number of customers is much larger than the number of potential facility locations. We report the results of a series of computational experiments demonstrating that, thanks to this decomposition techniques, optimal solutions can be found very quickly for some benchmark instances with one hundred potential facility locations and involving up to 15 and 40 million customer demand points for the MCLP and the PSCLP, respectively.

Using an optimization algorithm to establish a network of video surveillance for the protection of Golden Camellia

The natural environment is facing increasing human disturbance. Many species of flora are extinct or endangered. To improve the efficiency of ecological management and monitoring, this study proposed to establish a video monitoring network to protect a world-famous rare flora: Golden Camellia, in Fangcheng nature reserve, Guangxi Province, China. Based on the model of LSCP (location set covering problem), we attempted to establish full monitoring coverage of camellias while minimizing the number of video cameras. The model was solved by integer programming. In case of multiple solutions, this study proposed two additional criteria, maximize monitoring area and maximize overlapping count, to eliminate suboptimal solutions. Both of the two optimal solutions included 80 cameras covering a monitoring area of over 55km2. Together, these cameras are able to monitor 97.2% of golden camellia in the reserve. The findings of this study suggest that this location optimization model can be used to improve the conservation effectiveness of rare species.

Application of Set Covering Location Problem for Organizing the Public Postal Network

Most countries of the European Union ensure certain obligations (criteria) which universal service providers must meet to ensure the realization of the universal service. These criteria vary from country to country, giving their own choice of an optimal model for the density of the postal network. Such postal network of the operator providing universal postal service must be organized so that post offices are accessible at the optimal distance from the user. This paper presents two different approaches. The first one is based on the population criteria determined in the previous study. The second one is new, a general method created to determine the minimum number of postal unit applications of Set Covering Location Problem. The authors apply both methods on real data collected from the Serbian municipalities and finally, compare the obtained results.