Ambulance Location Problem Research Articles

Using Genetic Algorithm and Mathematical Programming Model for Ambulance Location Problem in Emergency Medical Service

Using Genetic Algorithm and Mathematical Programming Model for Ambulance Location Problem in Emergency Medical Service

An analysis of ambulance location problem from an equity perspective

In this paper, we study the Emergency Medical Services (EMS) vehicle location problem from an equity perspective. We construct several mathematical programming models using a set of objective functions and constraints commonly used in facility location problem literature. Due to the uncertainty involved in incident handling times, travel times, and the occurrence of emergency service demand, we use simulation models to assess the performance measures of the EMS systems resulting from the location models. We assess the equity of the system from a Rawlsian perspective, and we report the disparities in service quality among demand nodes using the Gini coefficient, the variance of region-wise mean response time, and lost demand. We utilize multivariate analysis of variance (MANOVA) to demonstrate the significance of mathematical models and the main and interaction effects of network features, such as the distribution of demand nodes across the plane, the number of vehicles, and incident handling rates. Our analysis offers a comprehensive investigation into the impact of mathematical models and network features on equity in the EMS vehicle location problem. Our findings indicate that the choice of mathematical model significantly influences equity, with certain models yielding more equitable outcomes than others. Additionally, we identify the distribution of demand nodes across the plane as a significant factor affecting equity. Ultimately, our results provide valuable insights for decision-makers responsible for designing and operating EMS systems.

Adaptive variable neighbourhood search approach for time-dependent joint location and dispatching problem in a multi-tier ambulance system

Location-allocation of ambulances is a critical planning problem in the efficient operation of an emergency medical services system. This work considers a joint ambulance location and dispatch problem for a multi-tier ambulance system. The proposed problem addresses three key decisions: the location of ambulance stations, allocation of ambulances to these stations, and the preference order of stations for dispatching ambulances. We consider various other important factors, such as temporal variation in demand and travel time, station-specific ambulance busy probabilities and possible relocation of ambulances over the day. A mixed-integer non-linear programming model is formulated with a survival probability-based objective function to represent the problem. A queueing-based iterative approximation approach is presented to estimate the station-level dispatch probability of ambulances. We propose an adaptive variable neighbourhood search approach to solve the problem that utilises the approximation approach to obtain the objective function. A relaxed station location problem combined with a particle swarm approach for ambulance allocation is solved to obtain an initial solution. The effectiveness of the proposed approach is validated using a dataset generated based on the city of Kolkata in India.

Capturing delays in response of emergency services in Delhi

Response time of an ambulance plays a significant role in pre-hospital care. The absence of response standards in India has made it challenging for emergency services to provide efficient and timely pre-hospital services. Also, traffic congestion in a city like Delhi may prove detrimental to a patient who needs urgent transport. Since travel times fluctuate throughout the day, solving an ambulance location problem with average travel times would not suffice. Therefore, the Gaussian Mixture Model (GMM) has been used to capture the variability in travel time between each origin-destination pair for Delhi's vast transportation network. This variation in travel times and delays in the dispatch of an ambulance (pre-trip delay) has been incorporated into the traditional double standard model as a chance constraint. The study thus builds three different variations of model, one being deterministic and the other two stochastic with probabilistic response times. These models are referred to as the Chance Constrained Double Standard Model (cc-DSM), Chance Constrained Double Standard Stochastic Model (cc-DSSM) and Double Standard Stochastic Model (DSSM). This study shows the similarity of previously used relocation approaches with the current approach and highlights the difference between vehicle busyness concept from the concept of multiple coverage.

MULTI-OBJECTIVE OPTIMIZATION OF AMBULANCE LOCATION IN ANTOFAGASTA, CHILE

In this paper, we solved an ambulance location problem with a multi-objective framework considering the case of the study of Emergency Medical Service (EMS) of Antofagasta (Chile). Nowadays, in Antofagasta, the ambulances are located in bases that are not necessarily the optimal location achieving an estimated 67% of coverage under the 8 min not meeting the requirements dictated by the Chilean Ministry of Health. We used a multi-objective model considering mean response time, maximum response time, and the demand not covered. The model is solved using an iterative ε-constraint method to generate a Pareto set of efficient solutions. We considered historical data from the years 2015 and 2016 to generate the demand and emergency nodes with a clustering algorithm. The results show improvements on all criteria of the multi-objective model, where we highlight a potential increment on coverage within 8 min from 67 to 99%. In order to test the new policy in a real setting, a pilot plan is proposed, which reaches 89% of coverage within 8 min.

Correction of the travel time estimation for ambulances of the red cross Tijuana using machine learning

This paper addresses the problem of estimating the response time to a medical emergency, specifically from the Red Cross of Tijuana (RCT), which provides most of the emergency medical services (EMS) in the city of Tijuana, Mexico. For institutions with low funding, such as the RCT, relying on free or open source mapping systems to estimate travel times is necessary but also error prone because these systems are not tuned for ambulance movements within a city. Therefore, this work formulates a supervised machine learning problem where the goal is to predict the difference in travel time between the ground truth travel time provided by a GPS and the approximation offered by two mapping systems, Google Maps (GM) and Open Source Routing Machine (OSRM). To this end, this work develops a new dataset based on the EMS logs of the RCT, considering calls from January 2017 to April 2017. The posed learning problem is solved under different scenarios, including using an off-the-shelf default configuration of a Random Forest classifier, applying a hyper-parameter optimization process and using an Auto Machine Learning (AutoML) system. Considering all of the dataset for GM, test accuracy was 69.6% for the first two learning approaches and 71.6% using AutoML. For OSRM, performance was 64.6%, 65.2% and 66.4% for each of the learning approaches, respectively. Results show that it is possible to predict the level by which a mapping system over or under estimates the true travel time of an ambulance. Finally, the impact of the model is demonstrated by using it to solve the ambulance location problem, with notable differences in ambulance deployments and percentage of double coverage achieved relative to using the standard mapping system. Results show that without correcting the travel time the percentage of double coverage is 83.90%; on the other hand, double coverage reaches 100% when applying travel time correction.

An ambulance location problem for covering inherently rare and random road crashes

Ambulance Location Problem (ALP) is studied in the field of covering road crashes, which are often rare and random in nature. On the account of rareness, crashes should be attributed to the network edges rather than nodes. Therefore, a covering problem with edge demand is the most compatible location problem. Accordingly, this paper proposes an edge maximal covering location problem with partial coverage of the facilities on the edges. Randomness is a feature associated with the frequency and severity of crashes. An Empirical Bayes (EB) method is applied to the observed frequency of crashes to reduce errors caused by the random feature of the crashes. The randomness associated with crash severity is investigated by adding the data derived from Property Damage Only (PDO) crashes to the network demand. As a result, an equivalent PDO measure is proposed to satisfy the demand of the network edges. The proposed method is applied to a real case study and some insights are presented.

A multi-period ambulance location and allocation problem in the disaster

To achieve quick response in the disaster, this paper addresses the issue of ambulance location and allocation, as well as the location problem of temporary medical centers. Considering budget and capacity limitations, a multi-period mixed integer programming model is proposed and two hybrid heuristic algorithms are designed to solve this complex problem. The proposed model and algorithm are further verified in a real case study, and the numerical experiments demonstrate the effectiveness of our proposed model. Specifically, we obtain several findings based on the computational results: (1) The best locations of ambulance stations should change in each period because the demand rate changes over time. (2) Involving temporary medical centers is necessary to reduce the average waiting time of injured people. (3) It may not be optimal to allocate ambulances from the nearest ambulance stations because of potentially limited station capacity.

Fairness in the Ambulance Location Problem: Maximizing the Bernoulli-Nash Social Welfare

In this paper we discuss how to position ambulances across an EMS region in a fair way. We argue that an appropriate measure of fairness is the so-called Bernoulli-Nash Social Welfare Function. We introduce a mathematical model that determines the ambulance configuration that maximizes this welfare measure. This fairness is contrasted with the more classical ambulance models that aim for efficiency by maximizing the overall average performance. We juxtapose the Bernoulli-Nash optimal solution with the most efficient solution and show that the most efficient ambulance configuration benefits people living in cities, at the cost of people living in remote areas. The Bernoulli-Nash solution on the other hand, provides a more balanced performance across the region. Furthermore, we demonstrate how our model can be applied using a variety of performance measures, such as a survival function and the probability of an ambulance arriving within a response time threshold. Our numerical work uses a case study based on one of the Netherlands’ largest EMS regions.

Variations of Double Coverage Ambulance Location Model Using Call Volume and Population Data

ABSTRACTIn Emergency Medical Services (EMS) ability to respond to emergency situations rapidly is very crucial. One of the main decisions that need to be made by the EMS provider is to locate available ambulances in an efficient way that all possible demand can be covered at a reasonable amount of time. For the ambulance location problem, we propose three new optimization models, employing Double Standard Model as a base. We make an elaborate analysis to decide on the minimum number of ambulances required in each location. Using real-life data from İzmir, Turkey, proposed optimization models are solved for both the population and the call volume data. Consequently, this study mainly showed that in solving ambulance location problem, the use of call volume data and preparing periodical plans are more efficient than using either population data or preparing plans based on daily call volume data.

A new idea for ambulance location problem in an environment under uncertainty in both path and average speed: Absolutely robust planning

When human life is the point in question, plans of healthcare transportation in an urban area must be immunized against uncertainty as much as possible due to its vital impact on many aspects. At this point, absolutely robust and also cost-efficient plans in healthcare transportation in an urban area are surely desired. Unfortunately, for ambulance location problem (ALP) in an environment under uncertain distance of path that emergency vehicle uses and uncertain average speed of the emergency vehicle, an absolutely robust plan has not yet been achieved. Therefore, in this study, a new model providing absolutely robust and also cost-efficient plans for ALP in an environment under two-dimensional uncertainty is clearly achieved. In addition, according to the best knowledge of the authors, this work is one of the precessor implementations that demonstrate robust counterpart (RC) approach can provide incredibly beneficial and useful results for the ALP. The proposed model is developed via utilizing RC approach, which is a very convenient tool for the main goal of this study. For the sake of demonstrating how the proposed model works in real life and what the results are, a case study is employed, which is tested in a simulation process under several scenarios in order to increase reliability. Results being obtained by the case study demonstrate that the proposed model works well and absolutely robust solutions are able to be obtained in return significantly sufferable costs for all of the scenarios. It is hoped that a crucial gap in the literature is -at least partially- filled by the proposed model.

Improving fairness in ambulance planning by time sharing

Most literature on the ambulance location problem aims to maximize coverage, i.e., the fraction of people that can be reached within a certain response time threshold. Such a problem often has one optimum, but several near-optimal solutions may exist. These may have a similar overall performance but provide different coverage for different regions. This raises the question: are we making ‘arbitrary’ choices in terms of who gets coverage and who does not? In this paper we propose to share time between several good ambulance configurations in the interest of fairness. We argue that the Bernoulli–Nash social welfare measure should be used to evaluate the fairness of the system. Therefore, we formulate a nonlinear optimization model that determines the fraction of time spent in each configuration to maximize the Bernoulli–Nash social welfare. We solve this model in a case study for an ambulance provider in the Netherlands, using a combination of simulation and optimization. Furthermore, we analyze how the Bernoulli–Nash optimal solution compares to the maximum-coverage solution by formulating and solving a multi-objective optimization model.

A Bi-objective Covering Location Problem

PurposeAmbulance response time is an important factor in saving lives and is highly linked with the ambulance location problem. The Maximum Expected Covering Location Problem (MEXCLP), introduced by Daskin (1983), is one of the most used ambulance location models that maximize the probability of stratifying demands for emergency medical service (EMS) centers. Due to huge increase in the operational costs of EMS centers, ambulance location models must consider the cost of coverage and the opportunity to use other companies’ private ambulances to answer emergency calls. The paper aims to discuss these issues.Design/methodology/approachIn this paper, the authors propose to extend the MEXCLP to a bi-objective optimization problem where the cost of satisfying emergency calls is minimized.FindingsThe proposed model is tested using data retrieved from the Lebanese Red Cross (LRC) in Beirut capital of Lebanon. The reported findings show significant enhancements in the results where the LRC can fully satisfy the perceived demands from all areas in Beirut within 9 min with an affordable cost.Originality/valueThe model is a first attempt to reduce operational costs of EMS centers while constraining the response time to satisfy emergency calls at an acceptable rate.

Distribution-Free Model for Ambulance Location Problem with Ambiguous Demand

Ambulance location problem is a key issue in Emergency Medical Service (EMS) system, which is to determine where to locate ambulances such that the emergency calls can be responded efficiently. Most related researches focus on deterministic problems or assume that the probability distribution of demand can be estimated. In practice, however, it is difficult to obtain perfect information on probability distribution. This paper investigates the ambulance location problem with partial demand information; i.e., only the mean and covariance matrix of the demands are known. The problem consists of determining base locations and the employment of ambulances, to minimize the total cost. A new distribution-free chance constrained model is proposed. Then two approximated mixed integer programming (MIP) formulations are developed to solve it. Finally, numerical experiments on benchmarks (Nickel et al., 2016) and 120 randomly generated instances are conducted, and computational results show that our proposed two formulations can ensure a high service level in a short time. Specifically, the second formulation takes less cost while guaranteeing an appropriate service level.

Modeling Uncertainty for the Double Standard Model Using a Fuzzy Inference System.

This paper studies the issue of uncertainty in the ambulance location problem to cover the maximum number of demand points in a city. The work is based on the double standard model (DSM), a popular coverage model where two radii are considered to cover a percentage of the demand points twice. Uncertainty is introduced in the expected travel time between an ambulance and a demand point, before computing the optimal placement of ambulances in potential bases by solving the linear program posed by the DSM. The following three approaches are considered: (1) solving the DSM without uncertainty; (2) uncertainty in the travel time is based on triangular fuzzy set; and (3) a fuzzy inference system (FIS) with a rule base derived from the problem properties, which is the main contribution of this work. Results show that considering uncertainty can have a significant effect on the solutions for the DSM, with the solutions produced with the FIS approach achieving a higher total coverage of the demand. In conclusion, the proposed strategy could provide a reliable and effective tool to support decision making in the ambulance location problem by considering uncertainty in the ambulance travel times.

Analysis of MCLP, Q-MALP, and MQ-MALP with Travel Time Uncertainty Using Monte Carlo Simulation

This paper compares the application of the Monte Carlo simulation in incorporating travel time uncertainties in ambulance location problem using three models: Maximum Covering Location Problem (MCLP), Queuing Maximum Availability Location Problem (Q-MALP), and Multiserver Queuing Maximum Availability Location Problem (MQ-MALP). A heuristic method is developed to site the ambulances. The models are applied to the 33-node problem representing Austin, Texas, and the 55-node problem. For the 33-node problem, the results show that the servers are less spatially distributed in Q-MALP and MQ-MALP when the uncertainty of server availability is considered using either the independent or dependent travel time. On the other hand, for the 55-node problem, the spatial distribution of the servers obtained by locating a server to the highest hit node location is more dispersed in MCLP and Q-MALP. The implications of the new model for the ambulance services system design are discussed as well as the limitations of the modeling approach.

Erratum to: Scenario-based approach for the ambulance location problem with stochastic call arrivals under a dispatching policy

This paper proposes a scenario-based ambulance location model which explicitly computes the availability of ambulances with stochastic call arrivals under a dispatching policy. The model utilizes two-stage stochastic programming to represent the temporal variations in call arrivals as a set of call arrival sequences. Constraints are embedded in the model to ensure that available ambulances are assigned to incoming calls following a dispatching policy. A logic-based Benders decomposition algorithm is presented to solve the model. The advantage of using our algorithm is demonstrated by comparing its performance with those of other location models.

Scenario-based approach for the ambulance location problem with stochastic call arrivals under a dispatching policy

Scenario-based approach for the ambulance location problem with stochastic call arrivals under a dispatching policy

Optimizing the location of ambulances in Tijuana, Mexico

In this work we report on modeling the demand for Emergency Medical Services (EMS) in Tijuana, Baja California, Mexico, followed by the optimization of the location of the ambulances for the Red Cross of Tijuana (RCT), which is by far the largest provider of EMS services in the region. We used data from more than 10,000 emergency calls surveyed during the year 2013 to model and classify the demand for EMS in different scenarios that provide different perspectives on the demand throughout the city, considering such factors as the time of day, work and off-days. A modification of the Double Standard Model (DSM) is proposed and solved to determine a common robust solution to the ambulance location problem that simultaneously satisfies all specified constraints in all demand scenarios selecting from a set of almost 1000 possible base locations. The resulting optimization problems are solved using integer linear programming and the solutions are compared with the locations currently used by the Red Cross. Results show that demand coverage and response times can be substantially improved by relocating the current bases without the need for additional resources.

A multi-period dynamic location planning model for emergency response

We investigate a multi-period ambulance location problem for an emergency medical service (EMS) provider that routinely aims for high quality medical response in a short period of time. However, both quality and timing of service are very costly goals to achieve. In this research, our goal is to minimize the total operational cost of an EMS organization while maintaining acceptable response times for a newly defined EMS network that consists of supply centers, hospitals, responder locations, and incidents. We propose a new dispatch model, a deferred service model, to analyze the daily operations of ambulances that involve dispatch as needed and redeploy periodically. The main premise of this model is, given incident priority levels, incident demand patterns, and EMS provider resources, to decide which incidents to serve immediately and which incidents to defer to following periods while incurring deferral penalty costs. Additionally, high-priority incidents that are not addressed within the required response window incur delay penalty costs. Considering network size, fleet size, incident patterns, and time-dependent parameters as different factors that may influence the solution, we compare the results in terms of service quality, response time, and total cost through extensive experimentation. Experimental results indicate that sending the closest ambulance to an incident site is not always the best choice.