Facility Location Model Research Articles

Equity-driven facility location: A two-stage robust optimization approach

This paper explores the computational challenge of incorporating equity in p-median facility location models under uncertain demand and discusses how two-stage robust programming can be employed to address the challenge. Our research evaluates various equity measures appropriate for facility location modeling and proposes a novel approach to reformulating the problem into a two-stage robust optimization framework, enhancing computational efficiency caused by incorporating equity and uncertainty into these models. We provide two solution algorithms: an exact and an inexact column-and-constraint generation (C&CG) method. Our findings suggest that although the exact C&CG method generally outperforms the inexact approach, both methods perform well when the number of variables is small, with the inexact C&CG demonstrating a slight advantage in computational time. We further conduct a detailed evaluation of the tractability of our reformulated model and the effectiveness of various equity measures through a real-world case study of Metro Vancouver.

Optimal resilience-based restoration plan for disrupted interdependent infrastructure networks under uncertainty

The functioning of vital services in a society depends heavily on the proper and continuous operation of critical infrastructure networks, including water, transportation, power, natural gas, and telecommunication. Such networks are essential for maintaining the economy, security, and overall quality of life. However, since these critical networks are interdependent; hence, they are susceptible to various types of disruptions caused by natural disasters, failures, or malicious activities, leading to varying degrees of performance impacts that could directly affect people's daily lives. Thus, a disruption to one network can quickly spread to others, resulting in significant impacts on daily life. Therefore, restoring such disrupted networks in a timely manner is crucial to ensure a prompt recovery and minimize the impact on daily life. In this work, we consider the problem of restoring a set of interdependent infrastructure networks following a disruptive event. We study two essential factors that can accelerate the recovery process: (i) the restoration facilities location, which are considered as dispatching points for restoration crews, and (ii) the routes of the restoration crews within the interdependent networks. Accordingly, we formulate two optimization models using mixed integer programming. The first model, restoration facility location model, finds the optimal location for restoration facilities within interdependent infrastructure networks considering uncertainty in disruptions. The second model, restoration crew routing model, determine the optimal routes for restoration crews within the interdependent infrastructure networks considering: (i) travelled distance, (ii) restoration time required for disrupted network components, and (iii) different importance of network components. The two optimization models are solved through generated interdependent power and water networks to demonstrate their effectiveness.

Use of the Discrete Facility Location Model in Optimizing the Number and Location of Fire Stations: A Case Study

Use of the Discrete Facility Location Model in Optimizing the Number and Location of Fire Stations: A Case Study

Impact of mistriages in on-scene injury assessment on trauma network and patient safety

An accurate on-scene assessment of a trauma patient’s injury by emergency medical service providers is critical to determining the right hospital for prompt care delivery. However, literature and anecdotal evidence from trauma professionals in the Midwestern U.S. suggest that mistriages (i.e., an error in assessing a severely injured patient as having non-severe injuries, and vice versa) often occur in practice. Due to a lack of approaches that consider such mistriages while designing the trauma network, we propose a stochastic nested multi-level, multi-transportation capacitated facility location model, which explicitly considers mistriages in injury assessment, to maximize patient safety by determining the number and locations of major trauma centers (MTCs). Assessment-related mistriages are modeled using a Bernoulli random variable for each of the two injury groups, moderate (ISS 9–15) and severe (ISS>15). We propose a Simheuristic approach that integrates Monte Carlo Simulation with a genetic algorithm. We convert infeasible solutions into feasible ones during offspring generation and maintain a superior population pool to balance quality against computational time. Our findings based on a realistic data set suggest that assessment-related mistriages in the ISS>15 group can substantially decrease patient safety and may lead to a clustering of MTCs, while mistriages in the ISS 9–15 group tend to have a dispersed distribution of MTCs in the resulting network. Our case study using actual 2019 data from a midwestern state of the U.S. resulted in an over 20% reduction in the mistriages, further providing evidence for incorporating injury assessment-related mistriages in trauma network design.

Developing approximation algorithm for elastic competitive facility location model

Developing approximation algorithm for elastic competitive facility location model

A Lagrangian relaxation approach for resource allocation problem with capacity constraints

AbstractThis study evaluates a capacitated facility location model enhanced with distance constraints for an emergency response problem, ensuring certain neighborhoods remain within an accessible range from facilities following a hurricane. The proposed model takes into account the capacity constraints for drones and vehicles. The model determines optimal locations for facilities and the distribution of supplies across the city. It also specifies which facilities should support the needs of each neighborhood and decides on the appropriate mode of transportation—ground vehicles if possible, or drones if roadways are obstructed. To solve the problem, a Lagrangian relaxation technique is employed, relaxing the constraints related to facility capacity and distance. The numerical results confirm the quality and efficiency of the solutions. The findings indicate that ground transportation is more frequently utilized than drones at each operational facility. A comprehensive set of sensitivity analyses is conducted to examine the impact of various variables and parameters on the solution.

Optimizing service networks to support freight rail decarbonization: Flow selection, facility location, and energy sourcing

We present a framework to support decarbonization of energy intensive transportation systems offering periodic service on expansive networks (e.g., freight rail, trucking, and intercity bus services). The framework consists of two optimization problems that respectivelyaddress (i) flow selection and facility location, and (ii) energy sourcing/procurement at the service facilities to enable the selected flows. The framework generalizes mixed integer linear programming formulations for flow refueling facility location and flow-based set cover models appearing in the literature to situations where it is of interest to account for repositioning of assets along cyclical trajectories to allow for periodic service, and to account for intermediate flow capture (i.e., trip chaining). The framework also consists of a minimum cost network flow model to determine optimal energy sourcing and distribution strategies, which dictate capacity requirements at the service facilities. The energy demands are obtained from the solution to the flow selection and facility location model. To illustrate the framework, we analyze the deployment of charging stations to support battery-electric locomotive service on a subset of the US freight rail network (i.e., an aggregate network of 3 Class I Railroads). The results show that the deployment of 30 charging stations can support battery-electric locomotives (with 1600-km ranges) to serve 86% of distance-weighted flows (ton-km) and reduce emissions by approximately 50%.

Electric vehicle charging stations: Model, algorithm, simulation, location, and capacity planning

The transition to sustainable transportation is imperative in mitigating environmental impacts, with electric vehicles (EVs) at the forefront of this shift. Despite their environmental benefits, the global adoption of EVs is curtailed by challenges such as nascent battery technology, high costs, and insufficient charging infrastructure. This study addresses the optimizing electric vehicle charging station (EVCS) locations as a critical step toward enhancing EV adoption rates. Thus, establishing efficient charging stations is critical to meet the increasing demand. By integrating location modeling with demand forecasts and market penetration, we propose a comprehensive approach to determine optimal locations and capacities for EVCS. Firstly, review existing literature, highlighting the significance of facility location models in optimizing EV charging infrastructure and identifying gaps in addressing demand and market penetration. Our methodology uses a genetic algorithm to solve the p-median problem for location selection and Arena 14 simulation software to model station traffic and optimize charging unit types and quantities. The model prioritizes public areas, considering potential demand points and station locations to propose optimal charging areas. Results indicate that our model minimizes travel distances and waiting times, offering a scalable solution adaptable to future EV market growth. This study contributes to the field by presenting a sustainable and economical model for EVCS placement and capacity planning, underlining the importance of a robust charging network in the broader adoption of electric transportation. The findings suggest that proactive infrastructure development, guided by accurate demand predictions and optimized location strategies, can significantly enhance the feasibility and attractiveness of EVs, supporting global efforts towards a cleaner, more sustainable transportation system.

Data-Guided Gravity Model for Competitive Facility Location

Data-Guided Gravity Model for Competitive Facility Location

Urban facility location models focusing on the health benefits of walking

Urban facility location models focusing on the health benefits of walking

Optimizing Electric Vehicle Charging Station Location on Highways: A Decision Model for Meeting Intercity Travel Demand

Electric vehicles have emerged as one of the top environmentally friendly alternatives to traditional internal combustion engine vehicles. The development of a comprehensive charging infrastructure, particularly determining the optimal locations for charging stations, is essential for the widespread adoption of electric vehicles. Most research on this subject focuses on popular areas such as city centers, shopping centers, and airports. With numerous charging stations available, these locations typically satisfy daily charging needs in routine life. However, the availability of charging stations for intercity travel, particularly on highways, remains insufficient. In this study, a decision model has been proposed to determine the optimal placement of electric vehicle charging stations along highways. To ensure a practical approach to the location of charging stations, the projected number of electric vehicles in Türkiye over the next few years is estimated by using a novel approach and the outcomes are used as crucial input in the facility location model. An optimization technique is employed to identify the ideal locations for charging stations on national highways to meet customer demand. The proposed model selects the most appropriate locations for charging stations and the required number of chargers to be installed, ensuring that electric vehicle drivers on highways do not encounter charging problems.

A large-scale heuristic approach to integrate on-demand warehousing into dynamic distribution network designs

A recent business model, on-demand warehousing, enables warehouse owners with extra distribution capacity to rent it out for short periods, providing firms needing flexible network designs a new type of distribution capacity. In this paper, a heuristic is created to solve large scale instances of dynamic facility location models that optimize distribution networks over a multi-period planning horizon, simultaneously considering the selection of different warehouse types with varying capacity granularity, commitment granularity, access to scale, and cost structures. The heuristic iteratively solves selected single-period problems, creating a set of smaller subproblems that are then solved for multiple periods. Their decisions are combined to achieve feasible low-cost solutions, ensuring each customer’s demand point is covered for each period. A set of computational experiments recommends how heuristic settings should be set by industrial decision makers and illustrates the heuristic can generate high-quality solutions for large scale networks during long planning horizons and many decision periods. The heuristic can solve national-level instances with many customer demand points, candidate locations, different warehouse types and capacity levels and many periods.

Industry 4.0 in waste management: An integrated IoT-based approach for facility location and green vehicle routing

The increasing production of solid waste rate in urban areas plays a critical role in sustainable development. To mitigate the adverse effects of waste and enhance waste management efficiency, this paper introduces a holistic approach that notably reduces the overall cost while mitigating social and environmental impacts. Central to the system's efficacy is the critical process of waste sorting, which enhances the output value of the waste management system. While previous studies have not extensively addressed simultaneous waste collection and sorting, this paper provides an innovative integrated framework. This approach Integrates waste collection with various bins, followed by their transfer to separation centers. At these centers, waste is categorized into organic and non-organic varieties, which are then dispatched to a recovery center at the second level. In the context of optimizing the routes at both levels, this paper presents a green, multi-objective location-allocation model. This model is designed to optimize the number and location of separation center facilities. Since the routing problem is influenced by the facility location model, it is addressed as a multi-depot green vehicle routing problem, integrating real-time information from IoT-equipped bins. This paper also proposes the vehicle routing problem with a split pickup, aiming to minimize cost, CO2 emissions, and visual pollution. The developed mathematical models formulate the proposed problem and it is solved by the GAMS optimization software, to apply an exact method, while Social Engineering Optimization and Keshtel algorithms are deployed to solve the routing problem for larger sizes. The proposed approach offers a comprehensive and sustainable solution to waste management, filling crucial gaps in current research and practice.

A novel mathematical model for emergency transfer point and facility location

The significance of emergency transfer point and facility location lies in its potential to save lives, optimize resource allocation, and enhance the efficiency of healthcare services during emergencies. It ensures timely patient access and cost-effective care. So, this study introduces a novel Mixed Integer Programming Model (MIP) for addressing the Multi-Facility and Multi-Transfer Point Location Problem (MFMTPLP). The problem involves determining the optimal locations for q facilities and p transfer points to facilitate direct customer access to facilities or through transfer points. The objective is to minimize the maximum expected weight distance for all the required points via transfer points. The study focuses on identifying the required points that carry weight and proposes a viable solution for solving the associated mathematical problems. An important contribution of this study, which has been overlooked in previous research, is the exploration of relevant costs associated with not transferring patients from demand points and hospitalizing them at transfer points. Additionally, the study emphasizes the significance of prioritizing different points and considering the costs associated with not transferring injured individuals from demand points and admitting them to transfer points. Previous models for locating facility and transfer points did not account for these factors. The study concludes by presenting the computed results, which validate the feasibility and effectiveness of the proposed model.

A refinement of the gravity model for competitive facility location

A refinement of the gravity model for competitive facility location

Sequential customers’ decisions in facility location with comparison-shopping

In the competitive facility location problem, a newcomer firm optimally locates its facilities and offers a product that is a substitute for those of the already located competitors, aiming at maximizing its market. Usual facility location models assume single-stop or single-facility trips. However, when products are non-homogeneous substitutes, customers may want to compare the products before making a decision (comparison-shopping). Moreover, decisions are often made sequentially as facilities are visited. We model for the first time, sequential customers’ decisions in multi-stop trips, represented using a nested logit rule. Customers make decisions at the place of origin (which facility to visit first), at the first visited facility (whether to buy, or not, or to continue comparing), and at the second facility visited (whether to purchase or not and in which facility). To adequately represent the drive to compare, we include in the customers’ utility the value of the gathered information, and the disutility of visiting facilities without purchasing. We propose a linear formulation with an efficient branch-and-cut approach. We analyze the location patterns in randomly generated instances, as well as in a case study on municipalities in Spain. The three-level nested, two-level nested, and multinomial logit rules are compared.

The Obnoxious Competitive Facility Location Model

The Obnoxious Competitive Facility Location Model

Improving access to emergency medical services using advanced air mobility vehicles

AbstractThe latest advancements in electric vertical take-off and landing (eVTOL) vehicles indicate that soon this technology will be available in multiple fields. One potential application of this new technology is in emergency medical services. These vehicles will be able to reach emergency sites faster than ground ambulances at lower costs than traditional helicopters. So in the following years, eVTOL vehicles could be used for aeromedical transportation. One crucial decision in implementing such a technology in emergency medical services is the location of their take-off and landing areas (vertiports). In this work, we propose a methodology for locating the vertiports in a healthcare network to improve emergency medical services coverage in hard-to-reach zones. We studied the system performance locating the vertiports for emergency services in existing healthcare facilities or outside them as auxiliary bases. In addition, we evaluated the performance of different operational scenarios regarding the use of emergency eVTOL. To do so, we used data analytics techniques (i.e., clustering algorithms) in conjunction with facility location models. The approach is tested using data from the Auvergne-Rhône-Alpes region in France. Results showed that locating the vertiports in existing healthcare facilities is the best choice in terms of coverage of hard-to-reach zones. However, on average, the response times increased compared to locating the vertiports as auxiliary bases outside the healthcare facilities. Besides, the results indicated that implementing eVTOL vehicles for aeromedical transportation can provide better access to emergency medical services in hard-to-reach zones. Still, the autonomy of such vehicles plays an essential role in their applicability.

Optimizing vaccine distribution in developing countries under natural disaster risk

AbstractFor many developing countries, COVID‐19 vaccination roll‐out programs are not only slow but vaccination centers are also exposed to the risk of natural disaster, like flooding, which may slow down vaccination progress even further. Policy‐makers in developing countries therefore seek to implement strategies that hedge against distribution risk in order for vaccination campaigns to run smoothly and without delays. We propose a stochastic‐dynamic facility location model that allows policy‐makers to choose vaccination facilities while accounting for possible facility failure. The model is a multi‐stage stochastic variant of the classic facility location problem where disruption risk is modelled as a binary multivariate random process–a problem class that has not yet been studied in the extant literature. To solve the problem, we propose a novel approximate dynamic programming algorithm which trains the shadow price of opening a flood‐prone facility on historical data, thereby alleviating the need to fit a stochastic model. We trained the model using rainfall data provided by the local government of several major cities in the Philippines which are exposed to multiple flooding events per year. Numerical results demonstrate that the solution approach yields approximately 30%–40% lower cost than a baseline approach that does not consider the risk of flooding. Recommendations based on this model were implemented following a collaboration with two large cities in the Philippines which are exposed to multiple flooding events per year.

Optimization models for cloud seeding network design and operations

Water shortage has become a significant challenge in many regions, affecting sectors such as agriculture, energy, industry, and the economy. Based on this subject matter and considering cloud seeding as an emerged water achieving promising technique, this paper provides an effective and innovative optimization approach for cloud seeding. This approach involves location analysis and operational planning, which offers significant potential for addressing water shortage challenges. The proposed approach considers atmospheric conditions, functional properties of facilities, seeding method variants, and cloud seeding system vulnerabilities as strategic programming for integrated facility network design. Additionally, operational planning, including flight routing and ground-based facility scheduling during rainfall storms, is considered to manipulate storms according to atmospheric conditions and systemic/facility operational constraints. To this end, the paper proposes a multi-objective mixed-integer linear programming model for facility location, which uses an innovative and application depended point-to-polygon covering algorithm, with the principal objective of maximization of spatial coverage. Moreover, a bi-objective mixed-integer linear programming model for seeding operations is developed based on the optimally located facilities in the strategic model, which uses an innovative line-to-polygon covering algorithm. The first objective of this model is to maximize precipitation augmentation, while the second objective of the both models is to minimize total system-wide costs. Finally, the applications of the proposed models and the managerial insights are also illustrated in a real case study domain.