|
Article Excerpt
1. Introduction
Responding to emergency cardiac arrest 911 calls is a major focus of Emergency Medical Service (EMS) systems. EMS systems are evaluated by how effectively they respond to and perform care for out-of-hospital cardiac arrest 911 calls. Cardiac arrest 911 calls are used to evaluate EMS systems, as opposed to other emergency medical calls, such as traffic accident and cancer 911 calls, since a cardiac arrest patient's survival depends on whether treatment was provided within the first few minutes following the cardiac arrest as well as the quality of the care provided. In other emergency medical 911 calls, patient survivability is not as strongly correlated with EMS response and patient care provided at the scene (Davis, 2005, 2007).
The survival rate after out-of-hospital cardiac arrests is low, with approximately 5-7% of cardiac arrest patients surviving to hospital discharge (Nichol et al, 1996; Mosesso et al., 2002). Traditional EMS systems depend on providing Advanced Life Support (ALS) to most calls within a given time target (e.g., within 9 minutes of dispatch). However, medical research indicates that for cardiac arrest calls, it is more important to have early access by the first responder (using CPR or automated external defibrillators) than wait until ALS personnel respond several minutes later (Stiell et al., 1999; Ornato et al, 2003; Hallstrom et al., 2004).
Given that cardiac arrest is the leading cause of death for both men and women despite improved medical care for treating such patients (Minino et al., 2006), next-generation EMS systems need to simultaneously plan and coordinate multiple resources, namely vehicles and personnel, to save lives while observing dispatching standards. This paper considers the scenario when two types of medical units are available for responding to emergency medical 911 calls, namely Basic Life Support (BLS) ambulances and ALS non-transport Quick Response Vehicles (QRVs). Both types of medical units may be dispatched to a single 911 call. Note that if a QRV is dispatched first, then an ambulance must also be dispatched to the call to transport the patient to a hospital, if the patient requires hospital transport.
Emergency medical 911 calls are typically classified as Priority 1, 2, 3, where Priority 1 calls are life-threatening. Priority 2 calls may be life-threatening and Priority 3 calls are not life-threatening. When both ALS and BLS units are available, the protocol is to deploy ALS units to Priority 1 calls, either type of ambulance for Priority 2 calls (ALS is preferred), and BLS units to Priority 3 calls. In order to improve patient survivability, it may be desirable to dispatch BLS medical units to Priority 1 calls if a nearby ALS medical unit is not available in order to stabilize the patient and initialize patient care. Not all calls result in a trip to the hospital, and hence an ambulance does not need to be dispatched to every call. Therefore, there are multiple customer types, and there are dependencies in the EMS response for each medical unit type.
This paper introduces a model for determining how to optimally coordinate and locate emergency medical units in order to improve patient survivability. The model is formulated as an extension to the Maximum Expected Coverage Location Problem (MEXCLP), which has been extensively used to optimally locate servers for public service applications, such as EMS systems (Daskin, 1983). MEXCLP is an integer programming model that determines how to optimally locate a given number of servers (ambulances) in a geographic region (e.g., city or county) given potential server availability.
This paper introduces MEXCLP with Two Types of Servers (MEXCLP2) as an extension to MEXCLP where there are two types of servers, namely BLS ambulances and ALS QRVs, as well as multiple customer types corresponding to Priority 1. 2, 3 calls. MEXCLP2 also lifts two of the assumptions made by MEXCLP, the assumption that servers operate independently and the assumption that servers have the same busy probability. Hence, MEXCLP2 considers the dependencies between the types of servers and between servers of the same type. The Hypercube queuing model can be used to quantify these dependencies (Larson, 1974, 1975). The objective of MEXCLP2 is to maximize the expected number of Priority 1 calls serviced in a given amount of time (e.g., 9 minutes). Only Priority 1 calls are considered since these calls arc life-threatening and a fast EMS response is critical for patient survival (whereas the EMS response is less critical for Priority 2 and 3 calls), and since cardiac arrest calls are a subset of Priority 1 calls. To improve patient survivability, it is assumed that there is no preference as to whether an ALS or BLS medical unit is dispatched to a call first, which is consistent with what has been reported in the medical literature. Note that the advantage of MEXCLP2 as compared to MEXCLP is that MEXCLP2 considers multiple customer types, including the interdependencies of EMS response to each customer type, as well as two different types of vehicles, including non-transport vehicles. By distinguishing call priorities, MEXCLP2 and the Hypercube queuing model can be used to predict and understand the EMS response to multiple classes of patients, including patients that are (and are not) transported to a hospital. This is crucial in an EMS system with multiple types of medical units, since hospital transport time composes the majority of ambulance service time, and hence, largely determines how medical units are used.
This paper is organized as follows. A literature review on models used for EMS systems is performed in Section 2. In Section 3. notation is introduced and the Hypercube model is applied to the scenario where there are two types of servers (vehicle types) with multiple types of customers to estimate the probability that vehicles of each type are busy and to estimate the dependencies between vehicle response. MEXCLP2 is introduced in Section 3, where it is formulated as an integer programming model using the results of the Hypercube model as input parameters. The results arc applied to a scenario using real-world data collected from Hanover County, Virginia in Section 5. Concluding remarks and directions for future research are presented in Section 6.
2. Literature review
Swersey (1994), Brotcorne et at (2003), Goldberg (2004), Green and Kolesar (2004) and Henderson and Mason (2004) summarize research efforts applying operations research models to EMS systems. Many facility location models for EMS systems have involved variations or extensions to a basic facility location model, the Maximal Covering Location Problem (MCLP), where the objective is to maximize the population that can be served in a pre-specified amount time or distance (Church and ReVelle, 1974). In MCLP, there is a set of demand nodes (i.e., a geographic area where calls for service arise) and a set of location nodes (i.e., potential locations for ambulances). MCLP considers a single time period with deterministic travel and service times, and it makes no adjustments for busy vehicles.
Daskin (1983) developed MEXCLP, an extension to MCLP that considers each vehicle being busy with probability p and maximizes the expected number of calls covered in a given amount of time. MEXCLP assumes that servers operate independently, that each server has the same busy probability and that busy probabilities do not depend on server location. Therefore, MEXCLP reflects the benefits obtained when some demand nodes are covered by more than one server.
Batta et al. (1989) introduced the Adjusted MEXCLP (AMEXCLP) to lift three assumptions made by MEXCLP. AMEXCLP embeds the Hypercube model (Larson, 1974, 1975) in an optimization heuristic that adjusts the MEXCLP to account for dependency between servers, dependency on server location and different probabilities that each server is busy. AMEXCLP focuses on location dependencies for a single type of server to a single type of customer, whereas MEXCLP2 focuses on the coordination and interaction between two types of servers as they respond to multiple types of customers. MEXCLP2 is not a particular case of AMEXCLP but rather a distinct problem that predicts system performance in an EMS system with interacting, multiple servers responding to multiple customers.
These basic facility location models have been extended to consider multiple vehicle types and backup coverage (Schilling et al., 1979; Hogan and ReVelle. 1986: Jayaraman and Srivastava, 1995). ReVelle and Hogan (1988, 1989a, 1989b) maximize the proportion of demand that can be covered in a prespecified amount of time with a given level of reliability. This approach was extended by Marianov and ReVelle (1996) to consider dependence between servers. Galvao et al. (2005) explore the relationship between the models given by Daskin (1983) and ReVelle and Hogan (1989b).
Several other facility location models for EMS systems have been developed to consider two types of servers...
|
