Maximal Covering Location Problem Research Articles

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.

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.

Locating helicopter ambulance bases in Iceland: efficient and fair solutions.

Fixed-wing air ambulances play an important role in healthcare in rural Iceland. More frequent use of helicopter ambulances has been suggested to shorten response times and increase equity in access to advanced emergency care. In finding optimal base locations, the objective is often efficiency-maximizing the number of individuals who can be reached within a given time. This approach benefits people in densely populated areas more than people living in remote areas and the solution is not necessarily fair. This study aimed to find efficient and fair helicopter ambulance base locations in Iceland. We used high-resolution population and incident location data to estimate the service demand for helicopter ambulances, with possible base locations limited to twenty-one airports and landing strips around the country. Base locations were estimated using both the maximal covering location problem (MCLP) optimization model, which aimed for maximal coverage of demand, and the fringe sensitive location problem (FSLP) model, which also considered uncovered demand (i.e., beyond the response time threshold). We explored the percentage of the population and incidents covered by one to three helicopter bases within 45-, 60-, and 75-min response time thresholds, conditioned or not, on the single existing base located at Reykjavík Airport. This resulted in a total of eighteen combinations of conditions for each model. The models were implemented in R and solved using Gurobi. Model solutions for base locations differed between the demand datasets for two out of eighteen combinations, both with the lowest service standard. Base locations differed between the MCLP and FSLP models for one combination involving a single base, and for two combinations involving two bases. Three bases covered all or almost all demand with longer response time thresholds, and the models differed in four of six combinations. The two helicopter ambulance bases can possibly obtain 97% coverage within 60 min, with bases in Húsafell and Grímsstaðir. Bases at Reykjavík Airport and Akureyri would cover 94.2%, whereas bases at Reykjavík Airport and Egilsstaðir would cover 88.5% of demand. An efficient and fair solution would be to locate bases at Reykjavík Airport and in Akureyri or Egilsstaðir.

Designing soil contamination monitoring network in petroleum refineries by XGBoost weighting and geostatistical facility allocation methods.

Petroleum refineries are deemed strategic industrial sectors that can release toxic materials to the environment and cause potential hazards. In this regard, designing and installation of soil contamination monitoring networks at petroleum refineries is a necessity. In this research, we designed an optimal monitoring network with maximum coverage and minimum number of monitoring boreholes. The main regarded parameters are the groundwater contamination history, the location of effective structures, the location of flare stacks and the soil texture. In addition, the soil contamination was calculated based on previous contamination of the soil at the sampling points by the Entropy Weighting Model. It was employed with other parameters to estimate the soil contamination across the site. The Machine Learning method of XGBoost was implemented for estimating and assigning priority for every point of the site. To achieve the optimal network in the optimization program, four parameters were regarded including (a) the optimal value of the optimization program's objective function, (b) the number of Advance Zero-half cuts of the Cut Generation algorithm, (c) the consumed time, and (d) the optimal boreholes number of the network corresponding with different effective contamination detection radius. The network was designed by generalized Maximal Covering Location Problem and for optimizing it, the advantages of Mixed-Integer Linear Programming method were used. To evaluate the applicability of the method, it has been developed and implemented in a refinery in the south of Iran. 92.84% of XGBoost estimation accuracy, the optimal number of 113 and the effective contamination detection radius of 160 m were obtained for boreholes of the network. To investigate the efficiency of the model, a new Regret function has been defined. Furthermore, sensitivity analysis of the parameters and feature importance analysis of XGBoost both showed that the main parameter of the model was the location of effective structures.

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.

Study on the optimal allocation of public service facilities from the perspective of living circle—A case study of Xiangyang High-tech Zone, China

The equitable allocation of public service facilities is directly related to the healthy development and socially just functioning of cities. Traditional location-allocation models mostly take travel distance and facility construction cost as the decision-making objectives, with relatively single optimization objectives, and are not sufficiently adaptable to reality. The introduction of the accessibility analysis and the concept of equalization of public services diversify the objectives of urban public service facility optimization decisions. The construction of the circle of life is based on residents' behavior and helps to improve its adaptability in the configuration of public services. This study evaluates the accessibility of eight types of public service facilities in Xiangyang High-tech Zone, China, from a Living Circle perspective, based on the Gaussian Two-step Floating Catchment Area (G2SFCA) method. We integrate the advantages of the Minimum Facility Point (MFP) model, Maximum Covering Location Problem (MCLP) model, and P-Median model to address the equity and efficiency issues in facility configuration, and seek the optimal layout scheme under the fairness objective. Results showed that after using the improved location-allocation models, the maximum travel time for residents was reduced from 76 ​min to 13 ​min, and the average travel time was reduced from 19 ​min to 8 ​min. Additionally, the coverage rate of the facilities increased from an average of 57% to 97%, and the spatial layout of facilities was more rational. The research results contributed to the study of spatial problems and spatial equity in facility allocation.

Points-of-Dispensing (PODs) 위치를 고려한 긴급물류창고 위치 선정

The significance of choosing optimal locations for emergency facilities is emphasized both in natural disasters and public health emergencies like pandemics. To ensure effective management of emergency logistics, procurement, and distribution, it is crucial to consider the establishment of facilities such as Points-of-Dispensing (PODs) that facilitate fast and efficient distribution. Consequently, when deciding on the location of logistics warehouses as part of emergency logistics management, it is essential to take into account the positioning of temporary facilities like PODs. We propose an integer programming model that integrates the Maximal Covering Location Problem (MCLP) and includes capacity constraints. Additionally, we conducted a case study in Incheon Metropolitan City to compare the outcomes. Through this case analysis, we present the optimal subset of temporary logistics warehouses, enabling the development of an optimal location-distribution plan. The study holds three main implications: (1) it provides an optimized selection of locations that aids in the decision-making process for policies; (2) the empirical analysis using real data allows for its application in similar disaster management situations; (3) the proposed model can be utilized to determine the positioning of various public facilities

An improved harmony search algorithm using opposition-based learning and local search for solving the maximal covering location problem

In this article, an improved harmony search algorithm (IHSA) that utilizes opposition-based learning is presented for solving the maximal covering location problem (MCLP). The MCLP is a well-known facility location problem where a fixed number of facilities are opened at a given potential set of facility locations such that the sum of the demands of customers covered by the open facilities is maximized. Here, the performance of the harmony search algorithm (HSA) is improved by incorporating opposition-based learning that utilizes opposite, quasi-opposite and quasi-reflected numbers. Moreover, a local search heuristic is used to improve the performance of the HSA further. The proposed IHSA is employed to solve 83 real-world MCLP instances. The performance of the IHSA is compared with a Lagrangean/surrogate relaxation-based heuristic, a customized genetic algorithm with local refinement, and an improved chemical reaction optimization-based algorithm. The proposed IHSA is found to perform well in solving the MCLP instances.

A logic-based Benders decomposition solution approach for two covering problems that consider the underlying transportation

We investigate two maximal covering location problems with capacity restrictions, minimum workload, and transportation. The problems are inspired by a waste collection problem in which large waste containers are scattered throughout the municipality, and the residents bring their waste to these containers. We take the residents’ preferences into account when allocating them to locations. When a container is full, a vehicle transports an empty container from the disposal facility (depot) to that location and replaces it. We propose a mixed-integer linear programming formulation for the problems in which vehicles can carry one or two containers, and apply a logic-based Benders decomposition approach for the latter. Here, the sub problem is a multi-period minimum weight perfect matching problem. We show that our logic-based Benders decomposition approach outperforms the direct formulation in terms of solution quality and speed. We further show that transportation of two containers at a time reduces the distance to be driven by 29.5% on average, without compromising the covering level. Furthermore, we analyze the effect of imposing a minimum workload as well as the effect of changing the focus between transportation and covering.

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.

An Optimization Method for Equalizing the Spatial Accessibility of Medical Services in Guangzhou

Spatial equality of medical services refers to equal access to medical services in all regions. Currently, research on medical facility planning focuses mainly on efficiency, and less on methods for achieving medical facility access equality. In this study, we propose a medical service equality optimization method considering facility grade and Gaode actual travel time data. First, we use the maximum coverage location problem (MCLP) model to locate new medical facilities. Then, we incorporate a service capacity weight matrix reflecting medical facility grade into the quadratic programming (QP) model, with the objective of optimizing the bed configuration of each facility to maximize the spatial equality of medical accessibility. By measuring and optimizing medical accessibility in Guangzhou under different travel time thresholds, we analyzed the optimization results of central, peripheral, and edge areas. The results show that (1) the model significantly improves the spatial equality of medical accessibility. After optimization, fewer locations have very low (or low) and very high (or high) accessibility, while more locations have moderate accessibility. When the travel time threshold is 22 min, the number of locations with medium accessibility level increases by about 18.86%. (2) The higher the travel time threshold, the greater is the overall optimization effect. (3) Different regions have different optimization effects and a larger travel time threshold can improve the optimization effect of the peripheral areas more significantly. It is recommended that new medical facilities be built in the peripheral and edge areas, along with improvements to the transport system.

Efficient presolving methods for the influence maximization problem

AbstractWe consider the influence maximization problem (IMP) which asks for identifying a limited number of key individuals to spread influence in a network such that the expected number of influenced individuals is maximized. The stochastic maximal covering location problem (SMCLP) formulation is a mixed integer programming formulation that effectively approximates the IMP by the Monte‐Carlo sampling. For IMPs with a large‐scale network or a large number of samplings, however, the SMCLP formulation cannot be efficiently solved by existing exact algorithms due to its large problem size. In this paper, we attempt to develop presolving methods to reduce the problem size and hence enhance the capability of employing exact algorithms in solving large‐scale IMPs. In particular, we propose two effective presolving methods, called strongly connected nodes aggregation (SCNA) and isomorphic nodes aggregation (INA), respectively. The SCNA enables to build a new SMCLP formulation that is potentially much more compact than the existing one, and the INA further eliminates variables and constraints in the SMCLP formulation. A theoretical analysis on two special cases of the IMP is provided to demonstrate the strength of the SCNA and INA in reducing the problem size of the SMCLP formulation. We integrate the proposed presolving methods, SCNA and INA, into the Benders decomposition algorithm, which is recognized as one of the state‐of‐the‐art exact algorithms for solving the IMP. We show that the proposed SCNA and INA provide the possibility to develop a much faster separation algorithm for the Benders cuts. Numerical results demonstrate that with the SCNA and INA, the Benders decomposition algorithm is much more effective in solving the IMP in terms of solution time.