Maximal Covering Location Problem Research Articles

DETERMINING THE OPTIMAL TEMPORARY WASTE DISPOSAL SITES IN THE ALANG-ALANG LEBAR SUB-DISTRICT PALEMBANG USING THE P-CENTRE LOCATION PROBLEM AND P-MEDIAN PROBLEM MODELS

The rapid development of Palembang City comes with an increase in population and a proportionate increase in waste. Providing Temporary Waste Disposal Sites (TWDS) with ideal locations is one way to address the waste problem in Palembang City. The location of the existing TWDS could be more regular and optimal. The problem of determining the optimal TWDS location can be solved by optimization science, as classified in the Set Covering Problem (SCP) model. The SCP model is divided into the -Center Location Problem and -Median Problem models. This study aims to determine the optimal locations for TWDS in the Alang-Alang Lebar Sub-District, Palembang City, by comparing the results of the p-Center Location Problem and p-Median Problem models. Initially, the Alang-Alang Lebar Sub-District had 33 TWDS. After formulating the Set Covering Location Problem and Maximal Covering Location Problem models, we obtain the optimal solution, which we then solve using the -Center Location Problem and -Median Problem models. Based on the results and discussion, the optimal TWDS can meet the demand of each village in the Alang-Alang Lebar Sub-District. The -Center Location Problem and -Median Problem models produce the same optimal TWDS, namely TWDS Pramuka 2 Street and around, TWDS Colonel Sulaiman Amin Street, TWDS Talang Kelapa Ujung, and TWDS Beside Soekarno Hatta Street. This study recommends using both models to determine the optimal TWDS.

Strategic placement of volunteer responder system defibrillators.

Volunteer responder systems (VRS) alert and guide nearby lay rescuers towards the location of an emergency. An application of such a system is to out-of-hospital cardiac arrests, where early cardiopulmonary resuscitation (CPR) and defibrillation with an automated external defibrillator (AED) are crucial for improving survival rates. However, many AEDs remain underutilized due to poor location choices, while other areas lack adequate AED coverage. In this paper, we present a comprehensive data-driven algorithmic approach to optimize deployment of (additional) public-access AEDs to be used in a VRS. Alongside a binary integer programming (BIP) formulation, we consider two heuristic methods, namely Greedy and Greedy Randomized Adaptive Search Procedure (GRASP), to solve the gradual Maximal Covering Location (MCLP) problem with partial coverage for AED deployment. We develop realistic gradually decreasing coverage functions for volunteers going on foot, by bike, or by car. A spatial probability distribution of cardiac arrest is estimated using kernel density estimation to be used as input for the models and to evaluate the solutions. We apply our approach to 29 real-world instances (municipalities) in the Netherlands. We show that GRASP can obtain near-optimal solutions for large problem instances in significantly less time than the exact method. The results indicate that relocating existing AEDs improves the weighted average coverage from 36% to 49% across all municipalities, with relative improvements ranging from 1% to 175%. For most municipalities, strategically placing 5 to 10 additional AEDs can already provide substantial improvements.

Automated external defibrillator location selection considering myocardial infarction risk and medical resources

AbstractThe effective deployment of medical emergency equipment, such as automated external defibrillator (AED), is essential to myocardial infarction (MI) patients. However, there are shortcomings in current studies that simultaneously consider the risk of MI and the availability of medical resources when siting the AEDs. In this study, an AED site recommendation framework was proposed to address the lack of consideration for both the MI risk and medical resources when siting the AEDs. It conducts the AED sitting under different scenarios considering the spatial distribution of MI risk and healthcare accessibility in Chinese cities. First, an automated machine learning framework data is proposed to estimate the MI risk at the community scale based on multi‐source spatio‐temporal. Second, the accessibility of medical resources was calculated by an improved Gaussian two‐step moving search algorithm. Finally, the AED siting in multiple scenarios is conducted based on the coverage model. The performance of the AED siting model was evaluated at Wuhan city. The results show that MI risk is impacted by both socioeconomic and cultural characteristics (municipal utilities, streetscape environment, educational and commercial facilities). There is a strong spatial heterogeneity in the distribution of both MI risk and medical resources in Wuhan, and an unreasonable match between the two was detected in some regions. Medical resources need to be strengthened in some high‐risk areas, such as rural areas and tourist attractions. In addition, 1015 AED candidate sites were identified by the location set covering problem model, with a 15‐min accessibility rate of 96.5%. Given the limited resources, mobile AEDs which have about 15‐min service range can be deployed based on the maximum covering location problem model to meet the demand in central urban areas efficiently. This study can contribute to more rational selection of AED sites and the prevention of myocardial infarction among residents, particularly when supported by policies that promote balanced regional development of pre‐hospital medical emergency networks.

Improving service accessibility and equity for sustainable development goals without newly facilities by rural settlement reconstruction

Ensuring the provision of accessible, affordable, and high-quality public services to all individuals aligns with one of the paramount aims of the United Nations’ Sustainable Development Goals (SDGs). In the face of escalating urbanization and a dwindling rural populace in China, reconstructing rural settlements to enhance public service accessibility has become a fundamental strategy for achieving the SDGs in rural areas. However, few studies have examined the optimal methods for rural settlement reconstruction that ensure accessible and equitable public services while considering multiple existing facilities and service provisions. This paper focuses on rural settlement reconstruction in the context of the SDGs, employing an inverted MCLP-CC (maximal coverage location problem for complementary coverage) model to identify optimal rural settlements and a rank-based method for their relocation. Conducted in Changyuan, a county-level city in Henan Province, China, this study observed significant enhancements in both accessibility and equity following rural settlement reconstruction by utilizing the MH3SFCA (modified Huff 3-step floating catchment area) and the spatial Lorenz curve method. Remarkably, these improvements were achieved without the addition of new facilities, with the accessibility increasing by 44.21%, 4.97%, and 3.11%; Gini coefficients decreasing by 19.53%, 1.64%, and 3.18%; Ricci-Schutz coefficients decreasing by 21.09%, 2.09%, and 4.33% for educational, medical, and cultural and sports facilities, respectively. It indicated that rural settlement reconstruction can bolster the accessibility and equity of public services by leveraging existing facilities. This paper provides a new framework for stakeholders to better reconstruct rural settlements and promote sustainable development in rural areas in China.

The Cooperative Maximal Covering Location Problem with ordered partial attractions

The Maximal Covering Location Problem (MCLP) is a classical location problem where a company maximizes the demand covered by placing a given number of facilities, and each demand node is covered if the closest facility is within a predetermined radius. In the cooperative version of the problem (CMCLP), it is assumed that the facilities of the decision maker act cooperatively to increase the customers’ attraction towards the company. In this sense, a demand node is covered if the aggregated partial attractions (or partial coverings) of open facilities exceed a threshold. In this work, we generalize the CMCLP introducing an Ordered Median function (OMf), a function that assigns importance weights to the sorted partial attractions of each customer and then aggregates the weighted attractions to provide the total level of attraction. We name this problem the Ordered Cooperative Maximum Covering Location Problem (OCMCLP). The OMf serves as a means to compute the total attraction of each customer to the company as an aggregation of ordered partial attractions and constitutes a unifying framework for CMCLP models.We introduce a multiperiod stochastic non-linear formulation for the CMCLP with an embedded assignment problem characterizing the ordered cooperative covering. For this model, two exact solution approaches are presented: a MILP reformulation with valid inequalities and an effective approach based on Generalized Benders’ cuts. Extensive computational experiments are provided to test our results with randomly generated data and the problem is illustrated with a case study of locating charging stations for electric vehicles in the city of Trois-Rivières, Québec (Canada).

A Model-Free Approach for Solving Choice-Based Competitive Facility Location Problems Using Simulation and Submodularity

This paper considers facility location problems in which a firm entering a market seeks to open facilities on a subset of candidate locations so as to maximize its expected market share, assuming that customers choose the available alternative that maximizes a random utility function. We introduce a deterministic equivalent reformulation of this stochastic problem as a maximum covering location problem with an exponential number of demand points, each of which is covered by a different set of candidate locations. Estimating the prevalence of these preference profiles through simulation generalizes a sample average approximation method from the literature and results in a maximum covering location problem of manageable size. To solve it, we develop a partial Benders reformulation in which the contribution to the objective of the least influential preference profiles is aggregated and bounded by submodular cuts. This set of profiles is selected by a knee detection method that seeks to identify the best tradeoff between the fraction of the demand that is retained in the master problem and the size of the model. We develop a theoretical analysis of our approach and show that the solution quality it provides for the original stochastic problem, its computational performance, and the automatic profile-retention strategy it exploits are directly connected to the entropy of the preference profiles in the population. Computational experiments on existing and new benchmark sets indicate that our approach dominates the classical sample average approximation method on large instances of the competitive facility location problem, can outperform the best heuristic method from the literature under the multinomial logit model, and achieves state-of-the-art results under the mixed multinomial logit model. We characterize a broader class of problems, which includes assortment optimization, to which the solving methodology and the analyses developed in this paper can be extended. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms—Discrete. Funding: This research was supported by Fonds de Recherche du Québec-Nature et Technologies and Institut de Valorisation des Données through scholarships to R. Legault. E. Frejinger was partially supported by the Canada Research Chair program [Grant 950-232244]. Supplemental Material: The online appendices are available at https://doi.org/10.1287/ijoc.2023.0280 .

The maximal covering location disruption problem

This research sets forth and examines a new sequential, competitive location problem. The maximal covering location disruption problem is a zero-sum Stackelberg game comprised of two stages. A leader denies access to at most q out of n possible facility locations in the first stage and, in the second stage, a follower solves a maximal covering location problem while emplacing at most p facilities. Identifying this problem as both relevant and unaddressed in the current literature, this research examines properties of the bilevel programming formulation to inform heuristic development, subsequently evaluating the efficacy and efficiency of two variants each of an iterative, bounding heuristic (IBH) and a reformulation-based construction heuristic (RCH) over a two sets collectively consisting of 2160 test instances representing a breadth of relative parametric values. Although we illustrate that each heuristic may not identify an optimal solution, computational testing demonstrates the superlative and generally excellent performance of the RCH variants. For the 12.4% of instances for which the RCH does not readily verify the optimality of its solution, lower-bounding procedures characterize solution quality. Both of the RCH variants attain solutions with an average 4.08% relative optimality gap, and they scaled well over different parametric value combinations, solving instances in an average of 98.0 and 123.6 seconds, respectively.

Location optimization of emergency medical services: Considering joint service coverage of ambulances and emergency centers

Emergency Medical Services (EMS) play an essential role in saving lives and improving health outcomes by offering immediate medical care to individuals who experience sudden illnesses or injuries. A complete EMS journey consists of two related trips: one from an EMS station to a scene (Trip 1), and the other from a scene to a definitive care location (Trip 2), where the service is coordinately provided by two types of facilities: EMS stations/ambulances and emergency centers (e.g., trauma centers or stroke centers) that are often affiliated with general hospitals. Current work on EMS location optimization considers only one trip (Trip 1 or Trip 2) which ignores the coordination between EMS stations and emergency centers, or the overall trip alone that overlooks the response time requirement. This paper proposed a spatial optimization model, the maximal coverage location problem based on joint coverage (MCLP-JC), for siting EMS stations and emergency centers simultaneously with a consideration of the two related trips. An empirical study of stroke center planning in Wuhan, China, is implemented to compare the proposed approach with the maximal coverage location problem based on overall coverage (MCLP-OC). The results demonstrate that the MCLP-JC can ensure more people being able to receive the first care from an ambulance within the response time requirement, which is critical to subsequent treatment at emergency centers and the odds of survival. The findings from the two scenarios regarding service relocation and expansion offer insights for future health facility planning.

Data‐efficient and risk‐based pressure sensor placement optimization for water systems

AbstractDeployment of remote metering infrastructure can help utilities improve pressure management and limit pipe break impacts. Since it is cost‐infeasible to install sensors to fully cover an entire system, a risk‐based approach where devices are deployed in areas of systemic vulnerabilities will maximize the benefit of these limited resources. Previous work on sensor allocations requires well‐calibrated hydraulic models that contain a full asset inventory. This high barrier of data requirement makes it difficult to apply existing methods. In this research, we present a more efficient methodology with lower data requirements. Proxies for system vulnerabilities are generated using historic break records, and GIS inventories are used to derive candidate installation points. The problem is presented as a generalized version of the well‐studied maximal coverage location problem, where locations are selected for optimal coverage of risky areas. The workflow is demonstrated on a small suburban utility in Pennsylvania, USA.

Accelerated Benders decomposition and local branching for dynamic maximum covering location problems

The maximum covering location problem (MCLP) is a key problem in facility location, with many applications and variants. One such variant is the dynamic (or multi-period) MCLP, which considers the installation of facilities across multiple time periods. To the best of our knowledge, no exact solution method has been proposed to tackle large-scale instances of this problem. To that end, in this work, we expand upon the current state-of-the-art branch-and-Benders-cut solution method in the static case, by exploring several acceleration techniques. Additionally, we propose a specialised local branching scheme which exploits the separability of the problem by time period. This scheme uses a novel distance metric in its definition of subproblems and features a new method for efficient and exact solving of the subproblems. These methods are then compared through extensive computational experiments, highlighting the strengths of the proposed methodologies.

Optimization of Shared Electric Scooter Deployment Stations Based on Distance Tolerance

The proliferation of shared electric scooters (E-scooters) has brought convenience to urban transportation but has also introduced challenges such as disorderly parking and an imbalance between supply and demand. Given the current inconsistent quantity and spatial distribution of shared E-scooters, coupled with inadequate research on deployment stations selection, we propose a novel maximal covering location problem (MCLP) based on distance tolerance. The model aims to maximize the coverage of user demand while minimizing the sum of distances from users to deployment stations. A deep reinforcement learning (DRL) was devised to address this optimization model. An experiment was conducted focusing on areas with high concentrations of shared E-scooter trips in Chicago. The solutions of location selection were obtained by DRL, the Gurobi solver, and the genetic algorithm (GA). The experimental results demonstrated the effectiveness of the proposed model in optimizing the layout of shared E-scooter deployment stations. This study provides valuable insights into facility location selection for urban shared transportation tools, and showcases the efficiency of DRL in addressing facility location problems (FLPs).

Robust Optimization of Vaccine Distribution Problem with Demand Uncertainty

This study proposes a multi objective optimization model for vaccine distribution problems using the Maximum Covering Location Problem (MCLP) model. The objective function of the MCLP model in this study is to maximize the fulfillment of vaccine demand for each priority group at each demand point. In practice, the MCLP model requires data on the amount of demand at each demand point, which in reality can be influenced by many factors so that the value is uncertain. This problem makes the optimization model to be uncertain linear problem (ULP). The robust optimization approach converts ULP into a single deterministic problem called Robust Counterpart (RC) by assuming the demand quantity parameter in the constraint function is in the set of uncertainty boxes, so that a robust counterpart to the model is obtained. Numerical simulations are carried out using available data. It is found that the optimal value in the robust counterpart model is not better than the deterministic model but is more resistant to changes in parameter values. This causes the robust counterpart model to be more reliable in overcoming uncertain vaccine distribution problems in real life. This research is limited to solving the problem of vaccine distribution at a certain time and only assumes that the uncertainty of the number of requests is within a specified range so that it can be developed by assuming that the number of demand is dynamic.

Dealing with congestion in the optimization of locating single-server battery swapping stations

This paper presents a study on the location problem of single-server battery swap stations, identifying instances of excessively long waiting times at certain stations during their operation in a real-world company scenario. This study innovatively transforms the problem into an extended version of the classic maximal covering location problem, incorporating technology selection and three sets of additional constraints: budget, closest-assignment, and average waiting time constraints. In particular, the closest-assignment constraint is specifically designed to mimic human behavioral patterns. A non-convex integer programming model is proposed and then reformulated thus enabling it to be tackled by some general-purpose solvers. The model is validated considering a test bed of randomly generated instances. The model comprehensiveness added-value is assessed. Finally, real-world data is used which allows discussing the extraction of information in the studied context. That information is used to build an instance that is solved and analyzed to provide valuable managerial insights, emphasizing the importance of technological improvement to the management.

On the complexity of the upgrading version of the maximal covering location problem

AbstractIn this article, we study the complexity of the upgrading version of the maximal covering location problem with edge length modifications on networks. This problem is NP‐hard on general networks. However, in some particular cases, we prove that this problem is solvable in polynomial time. The cases of star and path networks combined with different assumptions for the model parameters are analysed. In particular, we obtain that the problem on star networks is solvable in time for uniform weights and NP‐hard for non‐uniform weights. On paths, the single facility problem is solvable in time, while the ‐facility problem is NP‐hard even with uniform costs and upper bounds (maximal upgrading per edge), as well as, integer parameter values. Furthermore, a pseudo‐polynomial algorithm is developed for the single facility problem on trees with integer parameters.

A Lattice Boltzmann Method-like Algorithm for the Maximal Covering Location Problem on the Complex Network: Application to Location of Railway Emergency-Rescue Spot

Inspired by the core idea of the lattice Boltzmann method (LBM), which is successfully used in complex and nonlinear processes, we developed a lattice Boltzmann method-like (LBM-like) algorithm to effectively solve the maximal covering location problem with continuous- and inhomogeneous-edge demand on the complex network. The LBM-like algorithm developed has three key components, including the basic map, transfer function and effect function. The basic map is responsible for reasonably mapping complex networks with multiple branches and circles. Transfer functions are used to describe the complex covering process of the facility on the network, by splitting the entire covering process into several single-step covering processes, while the effect function is responsible for recording and processing the coverage effect of each covering process, based upon the requirement of an objective function. This LBM-like algorithm has good applicability to a complex network, intuitiveness, relatively low computational complexity, and open developability. Furthermore, the idea of the greedy algorithm was coupled with the LBM-like algorithm, to form two types of hybrid algorithms for improving the computational efficiency for the location problem, with multiple facilities, on a large-scale network. Finally, we successfully applied the LBM-like algorithm to the location problem of an emergency rescue spot on a real railway network, to underline the practicality of the proposed algorithm.

The Capacitated Maximal Covering Location Problem Improves Access to Stroke Treatment: A Cross-Sectional Simulation Study.

Disparities in accessing advanced stroke treatment have been recognized as a policy challenge in multiple countries, including Japan, necessitating priority solutions. Nevertheless, more practical healthcare policies must be implemented due to the limited availability of healthcare staff and financial resources in most nations. This study aimed to evaluate the supply and demand balance of mechanical thrombectomy (MT) and identify areas with high priority for enhancing stroke centers. The target area of this study was Hokkaido, Japan. We adopted the capacitated maximal covering location problem (CMCLP) to propose an optimal allocation without increasing the number of medical facilities. Four realistic scenarios with varying levels of total MT supply capacity for Primary stroke centers and assuming a range of 90 minutes by car from the center were created and simulated. From scenarios 1 to 4, the coverage increased by approximately 53% to 85%, scenarios 2 and 3 had 5% oversupply, and scenario 4 had an oversupply of approximately 20%. When the supply capacity cap was eliminated and 8 PSCs received 31 or more patients, they became priority enhancement targets. The CMCLP estimates demand coverage considering the supply and demand balance and indicates areas and facilities where MT supply capacity enhancement is a priority.

Sponet: solve spatial optimization problem using deep reinforcement learning for urban spatial decision analysis

ABSTRACT Urban spatial decision analysis is a critical component of spatial optimization and has profound implications in various fields, such as urban planning, logistics distribution, and emergency management. Existing studies on urban facility location problems are based on heuristic methods. However, few studies have used deep learning to solve this problem. In this study, we introduce a unified framework, SpoNet. It combines the characteristics of location problems with a deep learning model SpoNet can solve spatial optimization problems: p-Median, p-Center, and maximum covering location problem (MCLP). It involves modeling each problem as a Markov Decision Process and using deep reinforcement learning to train the model. To improve the training efficiency and performance, we integrated knowledge SpoNet. The results demonstrated that the proposed method has several advantages. First, it can provide a feasible solution without the need for complex calculations. Second, integrating the knowledge model improved the overall performance of the model. Finally, SpoNet is more accurate than heuristic methods and significantly faster than modern solvers, with a solution time improvement of more than 20 times. Our method has a promising application in urban spatial decision analysis, and further has a positive impact on sustainable cities and communities.

Spatial justice in healthcare: Advancing equitable geographic access to primary healthcare in Migori County, Kenya

This study aims to demonstrate the utility of location-allocation models in promoting spatial justice and enhancing access to primary healthcare services. Given the limitations of healthcare resources, it is essential to develop sustainable and equitable frameworks for primary healthcare. To accomplish this, the study utilizes the Maximum Covering Location Problem (MCLP) to assess the existing level of access in Migori County and to propose a viable approach for improving access. The proposed approach achieved a spatial coverage rate of 96%, a notable improvement compared to the existing rate of 84%. Therefore, the planning intervention serves as a viable spatial framework to complement the implementation of the Kenya Primary Health Care Strategic Framework (2019–2024) within the county. The study concludes by emphasizing the importance of policymakers and healthcare providers prioritizing the elimination of geographical disparities in primary healthcare access to foster spatial justice and an efficient referral system.

Spatial analysis of primary healthcare accessibility patterns in Migori County, Kenya

The inequitable and insufficient evidence-based allocation of health resources has exacerbated the health disparities in developing nations. Indicators of inadequate accessibility and misuse of health resources include urban-centered health facility site selection and overlapping health service areas. This research employed Service area analysis and the Maximum Covering Location Problem (MCLP) to assess spatial accessibility while considering the operational schedules of basic healthcare providers. Utilizing the motorbike model, the spatial accessibility to basic healthcare facilities amounted to 84%. However, certain facilities did not operate during weekends or around the clock. During the weekends, accessibility decreased to 60%, and for 24-hour accessibility, it dropped to 49%. Consequently, it is evident that the operating hours of healthcare facilities have a significant effect on spatial accessibility. This study proposed the upgrade of strategically positioned healthcare facilities to enhance spatial access and bolster the referral network for the local population.

Optimal locating and sizing of charging stations for large‐scale areas based on GIS data and grid partitioning

AbstractThis research proposes an optimisation model for identifying the optimal locations and sizes of public charging stations for large‐scale areas based on geographic information system (GIS) data and grid partitioning. A grid partitioning technique is utilised to generate subareas and investigate the demand for electric vehicle (EV) chargers calculated based on the number of EVs in each subarea. The optimal locations are formulated as a maximum covering location problem and solved by integer programming to ensure that all vehicle access subareas, according to the GIS data, are covered by charging stations. The sizes of charging stations are formulated as a knapsack problem and solved by the EV‐charge point ratio to guarantee each subarea has the appropriate number of chargers. The Voronoi diagram is integrated to estimate vehicle density and improve visualisation. The model is extended to include potential power loss reduction by adjusting the distribution of chargers in relation to the proximity to electrical substations. The developed methodology has been implemented by the whole country area of Thailand, which covers an area of approximately 510,000 km2. The study results are represented in a map blueprint that is very useful in strategic planning to support the so‐called EV30@30 government policy's ambitious national target of 2,050,000 units of EVs in 2030.