Model For Location Problem Research Articles

An optimisation model of hierarchical facility location problem for urban last-mile delivery with drones

Drones have, in recent years, been considered as a promising way for the last-mile delivery of urban logistics. In view of limited or short battery life of drones in every operation, the drone recharging stations and their locations are crucial to ensure delivery accessibility and to accomplish the required mission. Therefore, in addition to considering the selection of service centres and demand nodes, the location of recharging stations should also be incorporated into the proposed model of hierarchical facility location problem (HFLP). Many existing researches on drone recharging station locations assume that the delivery demand is known and only a single path is designed to meet the demand by using queuing theory models to describe node-based service waiting time. However, the reality is that we are still in the infrastructure planning stage for drone delivery, in which the demand is unknown in most cases. Our research proposes a novel mix-integer programming model to solve the HFLP for the last-mile drone delivery in urban areas, aiming to minimise the deployment, operation, and maintenance (DOM) costs of recharging stations, service centres, and paths. We have also incorporated a demand satisfaction constraint into the selection of effective alternative paths that meet the delivery accessibility. On the other hand, a sensitivity analysis in our study reveals varying degrees of impact on DOM costs and effective alternative path quantities, whose results would be useful to practical drone logistics delivery in urban areas.

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.

Robust cooperative hub location optimization considering demand uncertainty and hub disruptions

Amidst the rise of economic globalization and increased commodity trading, the logistics industry is experiencing rapid growth, encountering intricate transportation demands and fierce market competition. Simultaneously, it faces challenges related to infrastructure development and resource allocation efficiency. To enhance the adaptability and robustness of transportation networks when facing uncertain demands and potential hub disruptions, this paper proposes a two-stage robust optimization model for cooperative hub location problem. The model utilizes a hybrid algorithm that effectively combines the global search capability of genetic algorithms with the step-by-step optimization efficiency of Benders decomposition. Case study analyses demonstrate that, irrespective of the uncertainty environment, the cooperative model maintains lower total costs. Particularly in the case of large demand fluctuations, its cost advantages over non-cooperative models become notably prominent, showcasing remarkable performance in meeting service demands and enhancing resource utilization. Additionally, in cooperative networks, hub disruptions have a more significant impact on hub location decisions, with penalty and supplementary costs further exacerbating this influence. These research findings offer crucial insights for management practices: in uncertain market environments, adopting cooperative and robust planning strategies is pivotal for mitigating operational risks. When making decisions on cooperative hub location selection, carriers should comprehensively consider the interaction between uncertainty and economic benefits to achieve an optimal balance between risk and cost, ensuring the sustained economic feasibility of cooperative ventures.

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.

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.

AN ALGORITHM FOR SOLVING A TWO-STAGE CONTINUOUS-DISCRETE LOCATION PROBLEM FOR MEDICAL LOGISTICS OPTIMIZATION

The research paper focuses on logistics optimization, a critical component in supply chain management across various sectors, including healthcare. Efficient coordination of medical logistics is essential for maintaining public health and welfare, particularly during global emergencies where quick and effective distribution of medicine is crucial. This study aims to create and analyze a model and algorithm for a two-stage continuous-discrete location problem within medical logistics applications. We present a mathematical model tailored for a two-stage continuous-discrete location problem in medical logistics, considering the unique aspects of this field. The solution algorithm combines genetic methods with the optimal partition of sets theory. Additionally, we demonstrate the algorithm's effectiveness through a software application, using it to solve a representative model problem.

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.

Optimizing health service location in a highly urbanized city: Multi criteria decision making and P-Median problem models for public hospitals in Jeddah City, KSA.

Rapid urbanization and population growth have increased the need for optimizing the location of health services in highly urbanized countries like Kingdom of Saudi Arabia (KSA). This study employs a multiple-criteria decision making (MCDM) approach, e.g., fuzzy overlay technique by combining the P-Median location-allocation model, for optimizing health services. First, a geodatabase, containing public hospitals, road networks and population districts, was prepared. Next, we investigated the location and services of five public hospitals in Jeddah city of KSA, by using a MCDM model that included a fuzzy overlay technique with a location-allocation model. The results showed that the allocated five hospitals served 94 out of 110 districts in the study area. Our results suggested additional hospitals must be added to ensure that the entire city is covered with timely hospital services. To improve the existing situation, we prioritized demand locations using the maximize coverage (MC) location problem model. We then used the P-Median function to find the optimal locations of hospitals, and then combined these two methods to create the MC-P-Median optimizer. This optimizer eliminated any unallocated or redundant information. Health planners can use this model to determine the best locations for public hospitals in Jeddah city and similar settings.

A Multi-Objective Facility Coverage Location Problem for Emergency Medical Service Decisions in Hajj

This paper proposes a multi-objective facility model of coverage location problem to determine the number, locations, and redeployments of Emergency Medical Services (EMS) system. The EMS runs with two types of ambulances, Basic Life Support (BLS) and Advance Life Support (ALS). The suggested Multi-objective Coverage Location model (MO-CL) considers a bi-objective function, which is minimizing the EMS costs and the fatigue of EMS crew members. This can be managed by reducing the number of redeployments for both types of ambulances while still providing the required coverage levels. The MO-CL model is based on the approximation hypercube model that eliminates the assumptions of autonomous ambulance operation and system-wide busy probability. It can be solved by applying a modified MO-CL search algorithm. The model and solution method have been applied for a case study based on real data collected from the Al Noor Specialist Hospital in Makkah, Saudi Arabia during the period of fifteen days of Hajj pilgrimage. The results showed that, to achieve the 95% coverage threshold of critical and non-critical demand, the MO-CL model needs at least 64 ambulances (29 ALS, 12 for BLS backups, and 23 for BLS) and 19 redeployments for every day (9 for ALS, 2 for BLS backup, and 8 for BLS).

Learning-based demand-supply-coupled charging station location problem for electric vehicle demand management

We present a learning-based, demand-supply-coupled optimization model for the charging station location problem (CSLP), aiming to integrate the concept of electric vehicle (EV) charging demand management into the planning of charging infrastructures. In stage one, a gradient boosting-based learning model is developed to predict the charging demand of a charging station based on 15 defined features. Next, in stage two, a demand–supply-coupled CSLP model is developed to optimize the total charging usage rates of both existing and newly selected charging stations. We design a gradient-based stochastic spatial search algorithm to solve the proposed model. A case study with 6-year charging event data from Kansas City Missouri is performed. Results show that the proposed method can generate satisfactory charging demand predictions, and can increase charging usage rates by 14%, outperforming two benchmark approaches. The results of this research are poised to guide agencies in identifying optimal locations for new charging stations.

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.

Discrete-continuous model for facility location problem with capacity-cost relation constraints

The facility location problem (FLP) involves optimally locating a set of facilities that must satisfy the demands of a group of customers distributed in a planar area. Traditionally, various FLP models have been applied to find new facilities by considering already-existing facilities, and choosing new locations among a given set of discrete candidates. These are unreasonable because a limited set of candidates may not include the optimal locations. In this study, we developed a mathematical model based on mixed-integer linear programming (MILP) for FLP. In this model, the locations of existing facilities are known and categorized as discrete. On the other hand, the locations of new facilities to be found are categorized as continuous and discrete. In addition, the optimal number of new facilities is determined by a judgment formula. The cost of facilities is also considered, including fixed opening costs and variable capacity-related costs. To make the model closer to reality, the entire area is divided into several zones with varying costs. We developed a greedy multiphase location method for the proposed MILP (MPL-MILP) that efficiently determines the exact locations of new facilities in a stepwise manner. For large-scale problems, we developed a two-variable-based dynamic iterative partial optimization (TVB-DIPO) to obtain near-optimal solutions within a given time limit. Computational experiments were conducted to test the performance of the proposed MPL-MILP and TVB-DIPO. The results indicate that MPL-MILP is suitable for small- and medium-sized problems with exact solutions, while TVB-DIPO is more suitable for large-scale problems with higher solution efficiencies.

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.

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.

A robust optimization model for dynamic virtual hub location problem under uncertainty using an M/M/C/K queuing model: two metaheuristic algorithms

A robust optimization model for dynamic virtual hub location problem under uncertainty using an M/M/C/K queuing model: two metaheuristic algorithms

The capacitated location problem of precast concrete component factory

The location and capacity of precast concrete component factories (PC component factories) are not only the key factors for manufacturers to gain competitive advantage, but also the important factors affecting the operational efficiency of the prefabricated construction supply chain. This paper takes the capacitated location problem of PC component factories as the research object. Drawing on the model of traditional capacitated plant location problem, the model of capacitated location problem of PC component factories is constructed by setting the optional production scale by stages. According to the characteristics of this model, the optimal strategy of location is determined by using the Tabu search algorithm. Taking the location problem of PC component factory in the Beijing-Tianjin-Hebei region as the object, the calculation example is designed, in which the influence of the distance parameters on the results of location problem is analyzed. The results can make the configuration of regional PC component factories more reasonable and balanced.

Spatial Accessibility Evaluation and Location Optimization of Primary Healthcare in China: A Case Study of Shenzhen.

The unbalanced allocation of healthcare resources is a major challenge that hinders access to healthcare. Taking Shenzhen as an example, this study aimed to enhance equity in obtaining healthcare services, through measuring and visualizing the spatial accessibility of community healthcare centers (CHC), and optimizing CHC geospatial allocation. We used the number of health technicians per 10,000 to represent the CHC's service capacity, combined with resident points and census data to calculate the population the CHC needs to carry, and then analyzed the accessibility based on the Gaussian two-step floating catchment area method. In 2020, five regions in Shenzhen had better spatial accessibility scores: Nanshan (0.250), Luohu (0.246), Futian (0.244), Dapeng (0.226), and Yantian (0.196). The spatial accessibility of CHCs shows a gradual decrease from the city center to the edge, which is affected by economic and topographic factors. With the support of the maximal covering location problem model, we selected up to 567 candidate locations for the new CHC, which could improve Shenzhen's accessibility score from 0.189 to 0.361 and increase the coverage population by 63.46% within a 15-min impedance. By introducing spatial techniques and maps, this study provides (a) new evidence for promoting equitable access to primary healthcare services in Shenzhen and (b) a foundation for improving the accessibility of public service facilities in other areas.

Service coverage optimization for facility location: considering line-of-sight coverage in continuous demand space

The reliable service coverage of many facilities or sensors used in smart city infrastructure is highly susceptible to obstructions in urban environments. Optimizing the line-of-sight (LOS) service coverage is essential to locating these facilities for smarter city services. Despite progression in the maximal coverage location problem (MCLP) model for locating facilities, maximizing the LOS service coverage in continuous demand space for facility location problems remains challenging. This study defined the LOS-constrained MCLPs (LOS-MCLPs) and proposed a service coverage optimization model to solve these LOS-MCLPs. We employed a computational geometry algorithm named the visibility polygon (VP) algorithm to simulate the LOS coverage in two-dimensional (2D) continuous demand space. We then coupled this algorithm with a robust heuristic algorithm to search for the optimal solutions to maximize effective LOS service coverage. An experiment applied the developed model to a Wi-Fi hotspot planning problem. The experimental results demonstrated that the proposed model can obtain optimal solutions for LOS-MCLPs according to the distribution of obstacles. Comparative results show that ignoring the LOS effect in the optimization of LOS-MCLPs might lead to large areas of service dead zones.

An agent-based modeling approach for public charging demand estimation and charging station location optimization at urban scale

As the market penetration of electric vehicles (EVs) increases, the surge of charging demand could potentially overload the power grid and disrupt infrastructure planning. Hence, an efficient deployment strategy of electrical vehicle supply equipment (EVSE) is much needed. This study attempts to address the EVSE problem from a microscopic perspective by formulating the problem in two steps: public charging demand simulation and charging station location optimization. Specifically, we apply agent-based modeling approach to produce high-resolution daily driving profiles within an urban-scale context using MATSim. Subsequently, we perform EV assignment based on socioeconomic attributes to determine EV adopters. Energy consumption model and public charging rule are specified for generating synthetic public charging demand and such demand is validated against real-world public charging records to guarantee the robustness of simulation results. In the second step, we apply a location approach – capacitated maximal coverage location problem (CMCLP) model – to reallocate existing charging stations with the objective of maximizing the coverage of total charging demands generated from the previous step under the budget and load capacity constraints. The entire framework is capable of modeling the spatiotemporal distribution of public charging demand in a bottom-up fashion, and provide practical support for future public EVSE installation.