Joint ground and air emergency medical services coverage models: A greedy heuristic solution approach

doi:10.1016/j.ejor.2010.05.047

European Journal of Operational Research

Volume 207, Issue 2, 1 December 2010, Pages 736-749

https://doi.org/10.1016/j.ejor.2010.05.047 Get rights and content

Abstract

Aeromedical and ground ambulance services often team up in responding to trauma crashes, especially when the emergency helicopter is unable to land at the crash scene. We propose location-coverage models and a greedy heuristic for their solution to simultaneously locate ground and air ambulances, and landing zones (transfer points). We provide a coverage definition based on both response time and total service time, and consider three coverage options; only ground emergency medical services (EMS) coverage, only air EMS coverage, or joint coverage of ground and air EMS in which the patient is transferred from an ambulance into an emergency helicopter at a transfer point. To analyze this complex coverage situation we develop two sets of models, which are variations of the Location Set Covering Problem (LSCP) and the Maximal Covering Location Problem (MCLP). These models address uncertainty in spatial distribution of motor vehicle crash locations by providing coverage to a given set of both crash nodes and paths. The models also consider unavailability of ground ambulances by drawing upon concepts from backup coverage models. We illustrate our results on a case study that uses crash data from the state of New Mexico. The case study shows that crash node and path coverage percentage values decrease when ground ambulances are utilized only within their own jurisdiction.

Section snippets

Introduction and motivation

Both ground and air ambulances are used in transportation of trauma patients. There are many factors that affect which type of transportation is more advantageous to the seriously injured trauma victim in terms of providing less out-of-hospital time (i.e. the time from the accident’s occurrence until reaching the hospital). For example, if the incident scene is close to a trauma center (TC), then ground ambulances are preferred; if the scene is in a rural area far away from a TC, then air

Literature review

We now review some of the literature on EMS location-coverage models. The literature on coverage models for emergency services is divided into two major parts: the Location Set Covering Problem (LSCP) and the Maximal Covering Location Problem (MCLP). LSCP was introduced by Toregas et al. (1971) and determines the minimum number of servers (and server locations) required to cover all demand points. However, the number of resources to cover all demand points could be excessive in many cases, and

Preliminaries for model development

The models that we developed address the problem of locating ground and air ambulances, and transfer points (landing zones). We consider three options of sending ground and air EMS to trauma cases:

GROUND: Send only a ground ambulance.
AIR: Send only an air ambulance.
JOINT GROUND–AIR: Send an ambulance and a helicopter (simultaneous dispatch).

These three options lead to three different coverage definitions respectively. A trauma incident location is covered if and only if:

GROUND COVERED: At least

Set cover with backup model

We call our first model the Set Cover with Backup Model (SCBM). The thrust of this model is to determine the cost associated with covering all crash locations using a combination of ground and air ambulances. This provides an upper bound or maximal budget needed to create an optimal EMS system. The next model (Section 5) assumes there is a limited budget.

The major difference between SCBM and the variants of LSCP in the location-coverage literature is that SCBM permits coverage through joint use

Maximal cover for a given budget model

We now introduce the second model called the Maximal Cover for a Given Budget Model (MCGBM). In this model, we want to find the optimum mix of ground and air ambulances, and transfer points that maximize a weighted combination of first coverage for all crash nodes and paths, and backup coverage for the crash nodes and paths that are covered exactly once by ground or joint ground–air. The numbers of each EMS server to be located are not given separately. Instead, there is a limited budget and we

Computational studies

To test the performance of the greedy heuristics, we generated both small and large problem instances for SCBM and MCGBM using an instance generator coded in C++. Inputs of the instance generator are x and y coordinates of crash nodes and the two end points of the crash paths. The user may also assign weights to crash nodes and paths. Other inputs are the size of the study region, on-scene and off-scene times of ground and air ambulances, transferring time of the patient from a ground ambulance

Case study

To illustrate the applications of SCBM and MCGBM in designing ground and air EMS systems, we worked on a case study that uses motor vehicle crash data and emergency hospital data from the state of NM. Even if most of the parameter settings in the models are based on real data, some of the parameter requirements are based on the realistic estimations used previously in the computational studies (Section 6). Therefore, the case study results do not necessarily provide guidance for a real

Conclusions

In this paper, we presented three coverage types; sending only a ground ambulance, sending only an air ambulance, or providing joint coverage using a combination of a ground and an air ambulance in which the two rendezvous and the patient is transferred from the ground ambulance to the air ambulance at a transfer point. A crash node or path is said to be covered if it is within a pre-determined response time limit from one of the located EMS servers and also within a pre-determined service time

Discussion

We close the paper by providing a discussion on (a) coverage types, (b) unavailability of EMS servers, and (c) area coverage.

Acknowledgements

The authors thank the two anonymous referees and the editor for their helpful comments that significantly improved this paper. This material is based upon work supported by the Federal Highway Administration under Cooperative Agreement No. DTFH61-07-H-00023, awarded to the Center for Transportation Injury Research, CUBRC, Inc., Buffalo, NY. Any opinions, findings, and conclusions are those of the Author(s) and do not necessarily reflect the view of the Federal Highway Administration.

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Production, Manufacturing and LogisticsJoint ground and air emergency medical services coverage models: A greedy heuristic solution approach

Abstract

Section snippets

Introduction and motivation

Literature review

Preliminaries for model development

Set cover with backup model

Maximal cover for a given budget model

Computational studies

Case study

Conclusions

Discussion

Acknowledgements

Heuristic methods for the analysis of a queuing system describing emergency medical service deployed along a highway

Cybernetics and Systems Analysis

A hypercube queuing loss model with customer-dependent service rates

European Journal of Operational Research

A hybrid fleet model for emergency medical design

Social Science and Medicine

A trauma resource allocation model for ambulances and hospitals

Health Services Research

An iterative switching heuristic to locate hospitals and helicopters

Socio-Economic Planning Sciences

Ambulance location and relocation models

European Journal of Operational Research

Multiple unit dispatches in emergency services” models to estimate system performance

Management Science

The multi-level location set covering model

Geographical Analysis

The maximal covering location problem

Papers of the Regional Science Association

Network and Discrete Location: Model Algorithms and Applications

A hierarchical objective set covering model for emergency medical service vehicle deployment

Transportation Science

Determining emergency medical deployment in Austin, Texas

Interfaces

Production, Manufacturing and Logistics
Joint ground and air emergency medical services coverage models: A greedy heuristic solution approach