Chapter 7

Optimizing Resources Involved in the Reception

of an Emergency Call

P. Guaracao, D. Barrera, N. Velasco, and C.A. Amaya

Abstract One of the most important performance criteria in the management of

medical emergencies is response time, the time between the moment an incident is

reported and the arrival of an ambulance. The physical well-being of the patient

depends on when prehospital care is started. The mission of Bogota’s Center of

Emergency Management (Centro Regulador de Urgencias y Emergencias, CRUE),

over the next few years is to reduce median response times by 5 min. This work

contributes to the achievement of this goal through study of the system to identify

critical aspects and the evaluation of resources available to receive emergency calls

by using discrete events simulation. The model considers the dynamics of the

system from Monday to Thursday, inclusive. The analysis of the remaining days

of the week is left for future work. Through a new configuration in the call center

and use of resources other than ambulances in the process, a 45% reduction in

response time for 90% of cases is achieved.

7.1 Introduction

Emergencies are not predictable events. Consequently, the study of potential risks

and the preparation of an effective response plan are essential elements in the

protection of a social group. The emergency medical care system SAMU (Spanish

initials) consists of cooperation centers that integrate medical and paramedical

attention by processing emergency calls, dispatching the appropriate type of vehi-

cle, treating the patient in-situ and/or transporting him or her to the best medical

center available (Martinez et al. 2003). In Bogota, CRUE is responsible for the

administration of this system.

P. Guaracao • D. Barrera • N. Velasco (*) • C.A. Amaya

Department of Industrial Engineering, Universidad de Los Andes, Bogota, Colombia

e-mail: nvelasco@uniandes.edu.co

G. Mejıa and N. Velasco (eds.), Production Systems and Supply ChainManagement in Emerging Countries: Best Practices,DOI 10.1007/978-3-642-26004-9_7, # Springer-Verlag Berlin Heidelberg 2012

115

According to the last population census, conducted in 2005, Bogota had 6,840,116

inhabitants. The District Health Secretary estimates that the population in 2009 was

7,290,000 inhabitants. If the number of people serviced by each ambulance in the

city (97,200) is compared with the number reported in London (15,938) or Seville

(19,156), it is clear that improving response times with current resources is not an easy

task. Thus, CRUE is interested in knowing the percentage share that each subprocess

makes up as a part of the overall response time, and the implications of resource

assignment changes in the call center in respect to the same performance measure.

Response time is the main performance indicator. It is defined as the time

interval between the time of the call informing CRUE of the emergency and the

time at which the vehicle arrives on the scene. The United States Emergency

Medical Services Act states that 95% of calls must be attended to within 10 min;

in Canada, this standard is 7 min for 90% of the cases (Gendreau et al. 2001). In

contrast, in August 2008, 90% of cases in Bogota were attended to within 271 min

(Huertas et al. 2009). The evident difference in standards is of critical importance to

CRUE’s current administration.

This research contributes to the achievement of this goal in two ways. First, it

aims to minimize response time by generating significant reductions in call

processing time. Second, it aims to optimize resources without affecting the overall

performance of the system. Finally, the study discusses the robustness of

recommendations made by analyzing the effects of changes in ambulance transpor-

tation times. While the process clearly possesses more stages, this work focuses

only on a call center simulation and the statistical analysis of the duration of the

different activities. As shown in the following section, the search for potential

improvements in other phases of the process has been widely reported in past

academic literature and will be explored by this research group in later studies.

Due to the complexity of the operation and the nature of the expected results, this

study evaluates “what-if” models through discrete-event simulation. When the

times between arrivals or the service times do not have exponential distribution,

analytical models may become too complex. In this situation there is no guarantee

that the system performs as a Markov process, so simulation is a more accurate tool.

Experimental results show configurations for (a) reducing the 90th percentile of the

response-time distribution by 45%, and (b) operating economically without

changes in the service level.

This paper is organized as follows. Section 7.2 presents a brief literature review.

The system is described in Sect. 7.3. A preliminary data analysis of mean

and variance of the main processes is included in Sect. 7.4. Section 7.5 discusses

the construction of the simulation model, experimental design and sensibility

analysis. Section 7.9 presents a report implementation. Finally, Sect. 7.10 presents

conclusions.

116 P. Guaracao et al.

7.2 Literature Review

7.2.1 Operations Research in Emergency Management

Planning emergency systems operations has been, from an operations research

perspective, a constantly researched topic since the mid 1950s. Simpson and

Hancock (2009) identified Valinsky (1955) as the pioneer of this line of research,

while Green and Kolestar (2004) believed that the publication surge in respect to

this topic began in the late 1960s. Nonetheless, the authors of both papers are in

agreement that these early years of academic study concentrated mainly on research

relating to fire and police station allocation.

To gain a better understanding of the evolution of emergency management

models proposed so far, Simpson and Hancock (2009) proposed a four-heading

approach to organize previous research effectively and to present an historic

evaluation. Of these four groups, the one with the greatest participation from

the academic community was the category of urban services planning. This

heading represents 33% of the research work outlined by the authors, and for

which mathematical programming and simulation were the first- and third-

most-often-used tools, respectively, according to publication frequency.

Green and Kolestar (2004) undertook a literature review exclusively dedicated

to this branch of investigation, known as emergency operations research (EOR).

They proposed that ambulance systems research began with Savas (1969). This

work identified research relating to firemen and policemen as the most commonly

studied topics. An important finding was that, during the first years of research

(1969–1989), published results referred to successful implementation experiences.

According to the authors, examinations of this area of activity have decreased

considerably, and work published in recent years does not seem to be aligned

with emergency systems management practices.However, for Brotcorne et al. (2003), there is plenty of academic discussion of

urban emergency systems planning. They believe that the prehospital attention

system has a particular set of characteristics that makes it eligible to be studied

independently from the rest of the system. Furthermore, Andersson and Varbrand

(2007) defined ambulance logistics and identified that, in operational research,

efforts have been focused on reducing response times by solving ambulance

allocation and, recently, reallocation problems. Brotcorne et al. (2003) classified

this contribution in deterministic, probabilistic and dynamic models.

A review of published articles on ambulance-system planning starting from 2000

led the authors of this paper to the same conclusion, namely that the main approach

in response-time reduction is still how to allocate ambulances to maximize cover-

age. Between 2000 and 2005 two frequently cited articles were particularly influ-

ential, Harewood (2002) and Gendreau et al. (2001). The former article presented a

multiobjective version of the maximum availability problem in which the first

objective was to maximize population coverage and the second was to minimize

7 Optimizing Resources Involved in the Reception of an Emergency Call 117

coverage costs. The latter article proposed a dynamic model for ambulance reallo-

cation solved via tabu search and validated with a simulation model.

The following recent research was also considered highly relevant. Moeller

(2004) focused on measuring emergency-system performance. Haghani et al.

(2004) presented a simulation model used to evaluate different ambulance assign-

ment strategies. Sathe et al. (2005) addressed fixed-fleet allocation and reallocation

problems for response units through a mixed-integer programming model solved

via a heuristic method. Finally, Brotcorne et al. (2003) reviewed the existing work

in the field.

Between 2006 and 2009, different variations of the allocation problem were

proposed. Beraldi and Bruni (2009) presented a probabilistic model and three

heuristic solution methods; Silva and Serra (2008) formulated a model that includes

call prioritization, incorporating queuing theory results. Ingolfsson et al. (2008)

presented a model that minimized the number of ambulances required to cover a

given demand within a defined service level. Jia et al. (2007) addressed allocation

as a maximum-coverage problem with multiple depots and demand zones

characterized by a defined quantity and quality of required services. Erkut et al.

(2008) proposed a maximum coverage deterministic model that incorporates a

survival function. Finally, Gendreau et al. (2006) dealt with establishing a

policy for emergency vehicle reallocation guaranteeing a good coverage level in

all demand zones.

The authors of this paper could not find any articles from the same time period

that analyzed the percentage composition of each aspect of waiting time to deter-

mine which has the most impact. However, we did find some work relating to other

phases of the process. Singer and Donoso (2008) addressed the assignment problem

and proposed a set of recommendations based on queuing theory. Henders and

Mason (2004) presented a simulation study to support the decision making process.

Finally, Mendonca and Morabito (2001) illustrated an application of the hypercube

model (Larson 1974) to evaluate the emergency systems of two Brazilian cities.

7.2.2 Emergency Calls

After analyzing operational research advances in emergency planning, a set of

articles relating to emergency calls was examined in order to identify commonly

occurring issues. Kuisma et al. (2005) showed the importance of this analysis by

discussing the relationship between call length and the survival probability of a

patient suffering from ventricular fibrillation. In spite of showing that there was a

greater survival probability when the dispatcher had fewer assignments (i.e., was

less busy), the act of determining required staff, and optimal response time was left

unexplored by the authors.

Publications that examined emergency-call length included the following. Santiano

et al. (2009) analyzed the effect of criteria defined by medical staff for incoming calls.

Pell et al. (2001) reached the conclusion that a 5 min reduction in call time can nearly

118 P. Guaracao et al.

double a patient’s survival rate. Kuisma et al. (2004) made an evaluation of survival

rate and call time in contexts in which dispatch operators responded to a previous

classification according to urgency level. Finally, Kuisma et al. (2009) analyzed the

impact of using electronic medical records in conjunction with emergency call times.

Their main conclusion was that, although this technological change affects patients’

initial attention at a health care facility, there was no statistical evidence to support the

hypothesis that this could change the duration of response time.

The work developed byKuisma et al. (2004), besides looking at call time, was also

part of the answer to a question relating to a call center’s activities that has beenwidely

researched, namely, what effect does call prioritization have on ambulance dispatch?

Wilson et al. (2002) systematically reviewed publications relating to the effect that this

triage has on ambulance usage and on patient health. The investigation found 126

articles, of which only 20 have original data for validation purposes. It also suggested

that there is not enough evidence to draw conclusions on this effect.

On the same matter, other researchers have published more recent material.

Hinchey et al. (2007), with a sample of 23,939 ambulance dispatches, concluded

that medical priority dispatch system (MPDS) traditional protocols are effective in

identifying calls that do not require urgent dispatches more than 99% of the time.

Snooks et al. (2008) presented Delphi method results for the purposes of prioritizing

research topics for prehospital attention. After two rounds of the method, experts

concluded that distinct performance measures different from ambulance response

time should be developed. Cone et al. (2008) concluded that the emergency medical

dispatch system (EMDS) can reduce the volume of calls that result in dispatch by

50% while maintaining patient safety, Finally, Mohd et al. (2008) presented the

results of a successful implementation case in which the EMDS significantly

reduced ambulance response time.

Although there are multiple examples of discrete-event system simulation’s

application to the improvement of call centers in hotels, banks and airlines, simula-

tion applications to emergency networks are very few. Riano (2007), Giraldo

(2005), Garcıa (2003) and Rosas (2003) discussed developments in service com-

pany call centers. In Colombia, Rojas et al. (2007) used linear programming to

determine ambulance location and tested the effectiveness of their results through

discrete-event system simulation. However, after a thorough literature review, the

authors found that this was the only paper to use discrete-event system simulation in

the improvement of the reception of medical emergency calls as a mechanism to

improve the global response time.

7.3 System Description

Bogota covers 1,587 km2 and is home to 17% of Colombia’s total population

(approximately 7,290,000 inhabitants). On a daily basis, the city’s emergency

system receives 1,500 calls, with 580 resulting in patient transfer to health care

facilities. These calls mainly originate from 6 of the 19 city zones, in which more

7 Optimizing Resources Involved in the Reception of an Emergency Call 119

than 70% of the population lives in poverty. For this reason, people who live in

these areas do not hire private ambulance services. The public ambulances used in

these zones are managed by CRUE.

CRUE operates through five integrated subsystems:medical urgencies, psychiatric

urgencies, emergencies, urgent transfers and non-urgent transfers of patients between

hospitals. Themain difference between amedical urgency and amedical emergency is

the number of people affected and the amount of resources needed to address them.

Emergencies (i.e., natural disasters) endanger the physical integrity of large groups

and to address them, the system must use a significant percentage of its resources. In

short, CRUE is responsible for different types of medical situations. For example, the

emergencies system exclusively manages cases that require the cooperation of police,

firemen or any other governmental body involved in emergency situations. Members

of the medical and psychiatric urgencies subsystems, in contrast, are responsible for

those cases that do not require the intervention of other entities.

In Bogota, 40,000 emergency telephone calls are made per month. From these,

17,000 result in ambulance call-outs. Nearly 98% of these are considered medical

urgencies. This paper focuses on the analysis of medical urgencies because they

represent an important percentage of total variability. From now on, the terms

“urgency” and “emergency” will make reference to medical urgencies.

CRUE has a fleet of 75 ambulances, 15 of which are subcontracted from private

organizations. The other 60 are equipped and assigned as follows:

• 30 ambulances with basic equipment for urban areas

• 2 ambulances with basic equipment for rural areas

• 14 ambulances with specialized equipment

• 4 ambulances for neonatal care

• 6 motorcycles for immediate response

• 2 psychiatric vehicles

• 1 ambulance for special support for disasters

• About 50% of the fleet vehicles have GPS

The emergency system works 24 h a day, 7 days a week, and uses three shifts per

day. The city is geographically divided into northern and southern areas. Three

receptionists, a doctor and a dispatcher work in each zone. Even during the night

shift, when only two receptionists are working, there is still a doctor and a

dispatcher in each zone.

The doctors manage operations, dispatchers are the contact point for ambulance

crews, and receptionists are the contact point for the person calling. A third

dispatcher manages the private operators’ vehicles; he receives cases for both areas.

Six main stages are used to process an emergency call effectively. First, all calls

requiring immediate response by doctors, policemen or firemen are processed by a

unique center named Bachue, where operators record names, addresses, phone

numbers and basic information relating to the condition of the patient. At this

point, the case is classified as a high-, medium- or low-priority case and sent on

to CRUE, if it has a medical or psychiatric component. (This activity is represented

by operation 1 in Fig. 7.1.)

120 P. Guaracao et al.

Second, when the patient needs additional instructions, the call is dealt with by

one of the receptionists responsible for the appropriate area. The receptionists also

receive the information already recorded on the computer system and occasionally

discuss their decisions with the doctor. In theory, the receptionists are supposed to

answer calls according to their priority. However, the triage system has been shown

to be inadequate, so this order of priority is not always followed. Instead, the

receptionists receive calls according to the patient’s condition recorded on the

system: heart attacks first, then unconscious patients and finally those with breathing

difficulties. According to the situation, the availability of resources, the position of

vehicles and the doctor’s criteria, the dispatcher selects the ambulance that will

respond to the emergency. Observations reveal that GPS devices are not used in

the current operation of the system; rather, the dispatcher selects the ambulance based

on the locations of each ambulance. He then uses the radio to inform the ambulance

crew of the key facts of the incident. (This activity is represented by operation 2 in

Fig. 7.1). In the third stage, the ambulance travels to the patient’s specified location.

(This activity is represented by operation 3 in Fig. 7.1).

Fourth, the patient receives paramedical assistance. The dispatcher records the

ambulance’s time of arrival and adds information relating to the patient’s condition.

If the patient needs to be taken to a medical center, the center is selected according

to the condition of the patient, his insurance, the proximity of the center to the

original location and the services available nearby. (This activity is represented by

operation 4 in Fig. 7.1).

The fifth and sixth stages relate to transportation and the patient’s admission to

the chosen medical center. The dispatcher records the ambulance’s departure, the

arrival time at the hospital and the moment the vehicle is declared “available”

again. (This activity is represented by operation 5 in Fig. 7.1). The last stage may

take many hours, since, if a medical center lacks a bed to deal with the urgency, the

patient must wait in the ambulance until a bed becomes available. (This activity is

represented by operation 6 in Fig. 7.1).

As shown in Fig. 7.1, these six stages can be grouped into three stations

according to the resources used. The first station represents the call center and

includes stages 1 and 2. The second station relates to the travel time from the base to

the scene and the first medical intervention of the patient. Finally, the third station

covers the fifth and sixth stages. This paper is an exploration of the percentage

contribution of each stage to the overall response time and a formulation of

recommendations to reduce the processing time from stations one to three.

1

Station 1 Station 2 Station 3

2 3 4 5 6

Fig. 7.1 Processing stations

7 Optimizing Resources Involved in the Reception of an Emergency Call 121

This study initially presents a statistical analysis of incoming calls to CRUE

from June to August 2008 to identify the contribution of each subprocess to the total

response time. The obtained result is part of the input analysis for a simulation

model built to identify the effects of different call-center configurations over total

response time. From this, recommendations are made concerning resource distribu-

tion in each area and the parts of the process that need to be changed. Both

recommendations were implemented and data analysis is presented in Sect. 7.9.

7.4 Preliminary Data Analysis

A statistical analysis was done for call reports from June to August 2008 to gain an

initial understanding of the system and to determine which of the subprocesses

could cause a bottleneck. From these reports, the time taken by each phase was

calculated and comparable performance measures were obtained. The result of this

analysis and the interviews carried out with the people responsible for each phase

will be used to identify improvements to those subprocesses requiring the most

urgent action.

Gendreau et al. (2001) use United States emergency standards as a benchmark.

Figure 7.2 shows the comparison between those standards and the current CRUE

operation. Although the CRUE process shows deficiencies, according to those

standards, the difference in total time is most easily explained by the amount of

time spent in stage 6. Put simply, the fact that ambulances have to wait for patients

to be admitted to hospitals makes the response time much greater than desired.

Figure 7.3 illustrates the percentage composition of response time in terms of the

same process phases. The figure shows that the only phase that exceeds U.S.

standards, in percentage terms, is phase 6, whereas, interestingly, phases 3–5 are

superior to these standards. On the other hand, the initial part of patient attention

(i.e., phases 1 and 2) is the same.

A box diagram (Fig. 7.4) shows that the final stages have the largest mean

and dispersion. This affects ambulance availability and, thus, response time. After

carefully reviewing the process of selecting the hospital, it is evident that the

dispatcher considers where services are available but not how busy each of

the different medical centers is. Consequently, they do not consistently make

the optimal decision. The closest hospital may not be the best choice if there are

long queues for the service required. As a result of this, CRUE recently included a

vehicle responsible for carrying beds to the hospitals where ambulances were

waiting to offload their patient.

There are also computational tools that aid these types of decisions by analyzing

travel times and opportunities to get beds in eachmedical center (Guerrero et al. 2008).

An adaptation of such a tool is another effective way to improve the general perfor-

mance of the system

122 P. Guaracao et al.

7.5 System Simulation

The system was simulated in accordance with the following assumptions:

• The process starts when CRUE receives a call. Bachue’s processing time is

considered additional time that does not use the resources of the medical

urgencies subsystem.

400

300

200

100

0

1

10 193 11 10

77

1711

11

13 16

15

2

1

67

2 3 4Process Phases

5 6

min

Fig. 7.4 Box diagram of the six stages involved in an emergency call answer

0.8

0.6Percentageparticipation 0.4

0.2

01 and 2 3 and 4 5

Phases

CRUE

USA

6

Fig. 7.3 Percentage participation in each phase

300

250

200

150

100

50

05

Process phases

Res

po

nse

tim

e (m

in)

6

USA

CRUE

Total time1 and 2 3 and 4

Fig. 7.2 Current CRUE attention time vs. U.S. standards

7 Optimizing Resources Involved in the Reception of an Emergency Call 123

• The receptionists use the FIFO (first-in-first-out) queue processing technique.

• Receptionists are identical and independent.

• Two or more ambulances cannot be dispatched simultaneously for the same case.

According to input analysis, this assumption ignores approximately 12% of cases.

• Doctors will not be considered as a factor. In practice, their functions includemaking

relevant decisions regarding the selection of ambulances, answering receptionists’

and dispatchers’ questions, and authorizing ambulance crews to go off-duty. Their

participation is quantified in dispatchers’ and receptionists’ service times.

• There is one arrival at each point in time. The times between arrivals were

calculated and identified as exponential; hence the arrivals follow a Poisson

process (see Table 7.3).

The model’s diagram is divided into four stages. The first stage summarizes the

steps and decisions made before the selection of the vehicle (see Fig. 7.5). The

second stage shows the ambulance selection and the processes that take place

afterwards, not only in the ambulance, but also at CRUE (Fig. 7.6). The question

“Does the emergency require a vehicle?” is answered first by the receptionist and

then by the dispatcher when, for example, he detects that there has been previous

notification of the incident. In some cases, while the ambulance is traveling to the

Call isreceived

InItial Process atBachue

Does it go straightto the dispatching

area?

Yes

YesDoes the emergency require a vehicle

Time taken toselectavehicle

No

No

Dispatchingarea

Exit

Thereceptionisttake the call

Fig. 7.5 First stage of the conceptual model diagram

Does the emergencyreqire a vehicle?

YesAmbulance selection.The dispatcher informsthe crew the key aspectsof the incident

No

Exit

NoTime taken by the

ambulance toarrive to the place

of the incident

Ambulance

Transportationto the place of the incident

Yes Receptionistcall again

is it necessaryto call the

patlent back?

Fig. 7.6 Second stage of the conceptual model diagram

124 P. Guaracao et al.

location of the reported incident, the receptionist may have to call the patient back

to give additional instructions and/or confirm information.

The third stage is initiated when the dispatcher registers the arrival time at the

urgency site (Fig. 7.7). Next, some decisions presented in the structure do not

follow the chronological order but assist in obtaining the desired probabilities.

Finally, “yes” and “no” responses indicate the flow of decisions made regarding

transportation to the hospital (Fig. 7.8).

If the answer is “no,” the case is closed; if it is “yes” and there are two

ambulances where the urgency is, one of them will be released and the other will

continue to the hospital. If there is just one ambulance, it will go to the indicated

medical center. The delivery of the patient to the hospital is shown in Fig. 7.9.

Recordingambulancearrival timeto the placeof theincient

Time taken tofinish

paramedicalattention

Yes

Yes

Yes

Yes

Is it necessaryto use an additional

vehicle?

Yes

Arrivelamb. #2

No

No

No

2

2

One ofthevehiclesisreleased

No*

*

**Will the

patient’s conditionbe registeredimmediately?

No Recording thepatient’scondition

Does itrequire

additional medical

attention?

Ambulance

Paramedical attention

Fig. 7.7 Third stage of the conceptual model diagram

Time takento select a

vehicle

Ambulanceselection

Recordingthe arrivaltime

Time taken to finish

paramedicalattention

Time taken bythe ambulance to

arrive to the place of the

incident

Fig. 7.8 Arrival of the second ambulance

Theambulance isavailable

The case isclosed

No

No

Time taken to finishmedical attention

Medical Attention

Timetaken by

theambulance

to arriveto the

hospital

Yes

2

Yes Recording“waiting fora bed

Recordingthe time ofambulancearrival tothe hospital

Ambulance

Transportationto the hospital

Will thecenter

recordanexcessive

delay?

Had thepatient’s condition

been recordedbefore?

Recordingthepatient’scondition

Fig. 7.9 Fourth stage of the conceptual model diagram

7 Optimizing Resources Involved in the Reception of an Emergency Call 125

Since the demand, delays and service times on the weekends differ significantly

from those during the week, the simulation will consider the dynamics of the system

from Monday to Thursday. Analysis of the remaining days of the week is left for

future work.

7.6 Input Analysis

Confidence in the research relies not only on a coherent formulation, but also on

accurate input analysis. CRUE’s database provides precise information about

service times, discrete probabilities and the time between arrivals. However, it

lacks data about software failures, which have the potential to interrupt operators’

work and leave them inactive. The following paragraphs will not only the show

probable distributions for each of the parameters mentioned above, but will also

provide a detailed description of the processes used to obtain and test data.

Service times: The computer software records detailed information related to

service times. It records the operator’s ID, the time at which he or she takes the case,

the time at which the resource is released and all notes added during the interim

period. In this way, it was easy to define the beginning and the end of service times,

as well as relevant delays, according to the structure of the virtual model.

The next step was the construction of histograms to identify a probability density

function. Goodness-of-fit tests were undertaken using the “fit-all” option of Arena’s

input analyzer (version 10.0). Figure 7.10 shows histograms. Chi-square tests were

used for large sample sizes, while sample sizes under 30 were analyzed using the

Kolmogorov-Smirnov test (Banks et al. 2005). Table 7.1 shows descriptive informa-

tion about service times. The items “Recording of the ambulance arrival to the scene

of the incident,” “Recording of the ambulance arrival at the hospital” and “Recording

of the need to wait for a bed” were considered to have the same distribution. A

Kruskal-Wallis test (Conover 1999) supports the hypothesis with a p-value of 11.9%.

Something similar happens with “Recording of the patient’s condition” at the place of

the reported incident and in the hospital (p-value of 10.6%). The analysis outputs are

shown in Table 7.2. Finally, the data was tested using the Ljung-Box Q test to detect

autocorrelation problems in the first n/4 lags.

Process decisions: These decisions are related to ones on the conceptual model.

The probability of saying “yes” for each process decision was calculated in a

number of different ways, including by using statistics that the entity recorded

periodically and estimating using a sample. Finally, CRUE managers confirmed the

figures. Table 7.3 shows the final results of this analysis.

Demand: The estimation of the time between arrivals required several steps.

First, only the cases that require a vehicle (40%) are recorded in a report of

successive arrivals. If this type of arrival performs as a Poisson process, then the

total arrival rate is easily calculated. The process entails obtaining times between

arrivals of the cases recorded, testing their goodness-of-fit to an exponential

126 P. Guaracao et al.

Initial process

Ambulance selection

Recording Finish paramedical attention Recording of patient condition

Case ClosureMedical attentionTransportation to the hospital

Reception

Recptionist calls again

Select a vehicle

Transportation

Fig. 7.10 Service-time distributions

Table 7.1 Descriptive information regarding service time

Processes Time (minutes)

Min. Max. Deviation Mean

Initial process at Bachue 0.98 3.57 0.83 2.03

Operation 1 – – – 2.03

Reception of the call 0.38 7.32 0.19 2.55

Time taken to select a vehicle 0.08 11.45 0.19 1.60

Ambulance selection 0.23 1.88 0.59 0.75

Receptionist calls again 0.25 7.42 0.17 2.28

Operation 2 – – – 7.19

Transportation to the incident 5.03 49.00 0.43 16.05

Recording 0.03 0.43 0.04 0.18

Operation 3 – – – 16.23

Time taken to finish paramedical attention 5.18 70.66 0.51 22.83

Operation 4 – – – 22.83

Recording of patient condition 0.35 4.05 1.08 1.71

Transportation to the hospital 3.88 134.50 0.69 28.17

Operation 5 – – – 29.88

Medical attention 21.67 72.67 1.56 132.17

Case closure 0.07 1.88 0.07 0.34

Operation 5 – – – 132.51

7 Optimizing Resources Involved in the Reception of an Emergency Call 127

distribution and using the properties of the random split of Poisson process to obtain

an accurate estimation of the overall performance (Kulkarni 1995).

As an example, Fig. 7.11 shows the number of processed calls in 1 month. In

order to evaluate whether there was a significant difference between the days of the

week, several Kruscal-Wallis tests were performed. The p-value of the test was 7%,

which fails to reject the null hypothesis (see Table 7.4).

The last test considered the differences between time intervals in a given day; its

p-valueswere less than 0.01.All the results show that there are no significant differences

between the days of the week, but the arrival rate changes throughout the day.

Table 7.2 Probability distribution of the service times

Processes Distribution p-value

Initial process at Bachue (minutes) 0.72 + WEIB(1.48, 2.05) >0.15

Reception of the call (seconds) 23 + EXPO(130) >0.15

Time taken to select a vehicle (seconds) 5 + EXPO(91.2) >0.15

Ambulance selection (minutes) 0.06 + LOGN(0.69, 0.35) >0.15

Receptionist calls again (seconds) 15 + EXPO(122) >0.15

Transportation to the incident (seconds) 302 + EXPO(661) >0.15

Recording (seconds) 1.5 + LOGN(9.57, 6.54) >0.07

Time taken to finish paramedical attention (minutes) 311 + EXPO(1053) >0.15

Recording of patient condition (minutes) ERLA(0.8532) >0.15

Transportation to the hospital (seconds) 233 + EXPO(1460) >0.15

Medical attention (seconds) 1300 + WEIB(5700, 0.73) >0.15

Case closure (minutes) 4 + WEIB(16.2, 0.99) >0.15

Table 7.3 Probability of

saying “yes” in each decisionDecision Probability (%)

Does the case belong to the south area? 61.29

Does it go straight to the dispatching area? 97.89

Does the emergency require a vehicle? 40.00

Is it necessary to call the patient back? 64.52

Does it require additional medical attention? 75.00

Will the patient’s status be registered

immediately?

71.43

Is it necessary to dispatch an additional

vehicle?

10.00

600

400

200

0Monday Tuesday

Day of the week

Processed Calls

Wednesday Thursday

Fig. 7.11 Processed calls in 1 month

128 P. Guaracao et al.

Based on Fig. 7.12, 11 intervals can be defined. The first interval covers 7:00 a.m.

to 9:00 p.m., and each of the next 10 intervals is 1 h. Chi-square tests reveal satisfac-

tory results for the estimation (see Table 7.5). Having identified the probability density

functions for each time interval (Fig. 7.13), we must ensure the generation of their

according arrivals. One option is to use an Arena schedule (Kelton et al. 2010).

Failures: When there are computer software failures, operators cease their

activities. The length and time between failures were estimated by interviewing

the operators. The time between failures varies widely. However, for this specific

Table 7.4 Kruscal-Wallis

resultsp-value

From Monday to Tuesday 0.729

From Monday to Wednesday 0.762

From Monday to Thursday 0.499

140

120

100

80

60

40

20

07 10 12 14 16 18 20 22 0 2 4 6

Hour

Monday

Tuesday

Wednesday

Thursday

Num

ber

of a

rriv

als

Fig. 7.12 Arrival rate of cases requiring a vehicle

Table 7.5 Results of the Goodness-of-Fit Tests to Exponential Distributions using Chi-Square

Tests

Hour Distribution of the time

between arrivals (Seconds)

p-value Degrees of freedom Squere Error

0 3 + EXPO(291) >0.75 3 0.00054

1 4 + EXPO(405) 0.552 3 0.00254

2 8 + EXPO(437) >0.75 3 0.00273

3 13 + EXPO(579) 0.097 2 0.01169

4 0.999 + EXPO(466) >0.75 2 0.01169

5 2 + EXPO(360) 0.184 3 0.00766

6 0.999 + EXPO(208) 0.264 7 0.00180

7 to 20 0.999 + EXPO(157) 0.597 7 0.00180

21 0.999 + EXPO(190) 0.124 6 0.00674

22 2 + EXPO(203) 0.078 5 0.00410

23 2 + EXPO(281) 0.156 5 0.00620

7 Optimizing Resources Involved in the Reception of an Emergency Call 129

aspect there are no historical data. Accordingly, information provided by experts in

the system is accepted as valid (Kuhl et al. 2010). Distribution for time between

failures was uniform between 4 and 120 h. The length of each failure was modeled

as triangular (1, 2.5, 5 min).

7.7 Construction and Validation of the Model

The virtual model was represented using Simulation Software Arena 10.0. The

main structure was replicated for the two areas defined and covered by CRUE.

Since the system works steadily, it is necessary to determine a warm-up time.

Following the ensemble averages methodology proposed by Banks et al. (2005), the

warm-up time is calculated to be 12 h. Total replication length is 96 h fromMonday

to Thursday, with the 12 warm-up hours mentioned immediately above.

Fig. 7.13 Input results

130 P. Guaracao et al.

The last step is to determine the number of replications based on an established

error criterion. In this case, it is desired to have a confidence interval for the

response time of 1.2 min, or 0.02 h. Using this information, we can conclude than

three replications are needed (Banks et al. 2005).

Before using the model, there must also be statistical proof of its validity. Two

important performance indicators were selected for this purpose: “Response Time”

and “The time an ambulance takes from leaving the hospital until the case is

considered closed.” The former was previously defined in this paper; the latter

includes stages 2 through 6 of Fig. 7.1. Table 7.6 shows the performance indicators’

mean, with units given in minutes.

The objective test of the model as a whole is its ability to predict the future

behavior of a real system. In order to validate our model we used historical data to

“predict the past.” Prediction intervals were generated for selected indicators and in

both cases; the 95% prediction and confidence intervals, generated by the simulated

system, include the real-system mean. According to Banks et al. (2005), the model

is close enough to reality to be considered valid.

7.8 Experimental Design

It is important to define the model’s domain of action before introducing any

changes. Although an increase in the number of receptionists and dispatchers

would reduce the dispatch time, this aspect of the overall response time makes up

only 15.7% of the total. Consequently, a significant change in the dispatch time may

not be important in assessing the performance of the system in its entirety. The

implementation of algorithms to reduce transportation times is left for future work.

A study of the system in practice reveals that the utilization of receptionists is

less than 10%, whereas the utilization of dispatchers is 40%. The nature of the

system does not allow long queues, which explains the low levels of productivity.

According to the objectives of this study, the number of dispatchers was increased

in the hope of improving service. However, in contrast, the number of receptionists

was reduced in the hope that the service could operate at the same levels of

performance, but at a lower cost. The “compare means” option of Arena’s output

analyzer was used to check whether there were statistical differences with this

Table 7.6 Simulation outputs vs. real system performance

Performance criterion (minutes) Real-

system

mean

Simulated

mean

Prediction

interval 95%

Confidence

interval 95%

Response time 20.1 20.22 18.8 21.6 19.62 20.82

Time elapsed between an ambulance

leaving the hospital and the case

being closed

209.1 211.35 173.78 248.9 194.55 228.15

7 Optimizing Resources Involved in the Reception of an Emergency Call 131

option calculating the confidence intervals using a paired-t test. Table 7.7 presents asummary of the results.

The most effective way to reduce the response time and at a low cost is to add

operators to the most frequently used centers. The first scenario adds one dispatcher

to the south area. There is a reduction of 5.09% in the response time generated by a

decrease of 16.84% in the dispatching time. The second instance includes a second

dispatcher to deal with the private network. The reduction in the dispatching time of

10.5% is not enough to cause significant changes in the overall response time.

Finally, the combination of the two scenarios shows the most important reduction:

12.13% in the 90th percentile of the response time distribution – more than the sum

of the results above. This change is not only more effective, but also more

economical than other solutions, such as increasing the ambulance fleet. The

configuration proposed for dispatchers during the day shifts is as follows: one in

the north area, two in the south area and two for the private network. No change is

proposed in the night shift.

To operate at a lower cost, it is logical to remove the least-utilized resource

during times of lowest demand. The first scenario removes a receptionist from the

north area at night. The dispatching time significantly increases, by 2.66%, but there

is no statistical evidence of a difference in the overall response time. Then, a

receptionist from the south area is removed from the same schedule. There are no

significant changes in this case, either. Finally, the third scenario leaves one

receptionist in place per area for the night shift. This configuration was not found

to affect general performance, either. Therefore, this finding forms the main

recommendation of this part of the study. Interestingly, removing receptionists

during the day led to a response time significantly different from the original; as

a result, it was not considered.

The numbers of ambulances available, demand for the service, condition of the

roads, traffic and even weather conditions have a direct influence on (a) the time

taken to select the vehicle, (b) transportation to the location of the reported incident

and (c) transportation to the hospital. A sensitivity analysis shows significant

changes in the response time when the mean and standard deviation for each time

increases by 5%, 10%, 15% and 20%. The three times have exponential

distributions, so the mean and variability are altered simultaneously.

The first recommendation increases the response time by over 4% when “Time

to select the vehicle” or “Transportation to the place of the incident” increases by

5%. This indicates that the scenario is sensitive to minimal changes in the

Table 7.7 General results for each type of scenario

Measure Difference of means

removing two receptionists

Difference of means adding

two people in the

dispatching area

C.I. at 95% Percentage C.I. at 95% Percentage

Dispatch time [�0.0001,0.002] 2.29 [�0.014,0.010] �23.67

Response time [�0.001,0.011] 1.42 [�0.005,0.029] �12.13

Time until the ambulance used

becomes available again

[�0.171,0.065] �1.50 [�0.380,0.043] �4.78

132 P. Guaracao et al.

parameters of the distributions. The second recommendation, in contrast, possesses

such a robust quality that significant changes appear only when delays increase by

20%.

Finally, the study questions the need to divide the city into northern and southern

areas. Since a significant amount of information communicated between recep-

tionists, doctors and dispatchers is verbal, a geographic division establishes clear

channels, reduces the probability of errors and facilitates case tracking. In addition,

the system does not use GPS devices for its current operation. Thus, operators are

completely dependent on the location of the incident through processes like ambu-

lance selection and duplicate elimination. Therefore, due to the organizational,

economic and technological constraints described above, it is felt that it is unfeasi-

ble to work without a partition of the city.

However, in a hypothetical scenario, the division was removed and calls were

answered on a first-in-first-out basis. In the current configuration, calls cannot be

answered by the operators of the other zone, even if the proper system is busy and

the alternative is empty. Therefore, it was expected that integrating the two areas

would have a positive impact on performance measures. The results did not

contradict that prediction: decreasing the mean dispatching time by 18.40% reduces

the response time by 10.69%. The simulation shows that this is a more efficient

design, since it significantly improves performance with the same workforce. These

findings suggest that decision makers should explore a new set of solutions that

would operate outside current budgetary structures and constraints, but which

would be more effective in the long term.

7.9 Implementation Report

After including the two strategies as permanent changes in CRUE operations, call

lengths were collected from June and November 2009 to evaluate their effect on

performance indicators. In total, 35,657 calls were processed, and the performance

measures proposed in Sect. 7.4 were calculated. Figure 7.14 shows a comparison of

the duration of each process before and after implementation.

Response time is shorter than it was before the implementation, and the main

reduction is focused on stage 6 of the process. Previously, 90% of cases were

treated in 271 min or less, and in 90% of cases stage 6 lasted 171 min or less. The

collected data shows a reduction in the overall indicator of nearly 45%. Total time is

now 149 min and stage 6 is completed in 26 min, which means a reduction of 85%.

Assigning resources, other than ambulances, reduces the variability of the release

phase and the total duration of each event. This new configuration of the process

suggests that there is a much closer relationship to the U.S. performance indicators,

related to the percentage share for each phase. Figure 7.15 compares the American

standard with CRUE’s measures, by percentage of each station.

7 Optimizing Resources Involved in the Reception of an Emergency Call 133

As shown, under current CRUE operating conditions, another research question

becomes highly relevant, one which has been widely studied in the literature: How

can the overall response time be reduced by reducing travel time in an ambulance?

The question now becomes increasingly important because, after this study and

its recommendations, travel time becomes the “new” critical phase in the process in

terms of percentage duration. Members of the research groups are studying this

issue through location-relocation models. As a first phase of the new study, a

dispatch process diagnosis was proposed. This diagnosis includes double dispatch

events, mobilization speed, occupancy rates of ambulances and unmet demand.

7.10 Conclusions

This research had two main objectives: reducing the response time and, at the same

time, operating at a lower cost whilst maintaining the appropriate/the same service

levels. Decreases in response time by way of attacking ambulance travel time have

been extensively studied in articles using location and relocation models. However,

0.5

0.4

0.3

0.2

0.1

01 and 2 3 and 4 5 6

USA

CRUE

Fig. 7.15 U.S. and CRUE performance indicators

300

250

200

150

100

50

0

BEFORE

AFTER

1 and 2 3 and 4 5 6 Total time

Fig. 7.14 Process time before and after implementation

134 P. Guaracao et al.

this study proves that important reductions in response time may also be obtained

through the robust selection of suitable levels of the most appropriate type of

resource within call center operations, an area traditionally overlooked when

emergency systems are examined.

The complexity of the system was successfully modeled through discrete-event

system simulation. Two main configurations were proposed, one per objective:

• Adding two new dispatchers reduces the response time by 12.13%.

• The system can operate with one receptionist per area during night shifts without

significant changes in general performance.

The robustness of the recommendations was tested to enhance their credibility.

The first set of tests tolerated increases of 20% in transportation times and was,

therefore, the stronger scenario.

In Bogota, ambulances must wait until the patient is admitted to the hospital’s

emergency department. This set of circumstances creates significant challenges for

the system administrator and must be carefully analyzed in order to identify

bottlenecks in the service flow so that improvement efforts can be prioritized.

The initial statistical analysis showed that, under these operating characteristics,

the wait time for ambulances at the hospitals’ emergency departments has the

highest variability and is the main determinant of the total length of response

time. In this specific respect, carrying beds to the hospitals with long queues at

their emergency rooms has proven to be the most effective strategy to increase

vehicle availability.

This work was used by CRUE administration as an engineering tool to objec-

tively support decisions such as size and availability of resources. This is a clear

example of a productive relationship between two distant disciplines, medicine and

operational research, leading to improvements in a vital system designed to protect

any social group in the event of a medical emergency. Current work derived from

this study is the design of a tool that can be operated by non-expert professionals.

Acknowledgments The authors want to thank Manuel Villamizar M.D., Consuelo Castillo M.D.

and the CRUE administration for their unconditional support for this study.

References

Andersson T, Varbrand P (2007) Decision support tools for ambulance dispatch and relocation.

Journal of the Operational Research Society 58 (2):195–201. doi:10.1057/palgrave.

jors.2602174

Banks J, Carson J, Nelson B, Nicol D (2005) Discrete-event System Simulation. Pearson PrenticeHall, Upper Saddle River, NJ

Beraldi P, Bruni ME (2009) A probabilistic model applied to emergency service vehicle location.

Eur J Oper Res 196 (1):323–331. doi:10.1016/j.ejor.2008.02.027

Brotcorne L, Laporte G, Semet F (2003) Ambulance location and relocation models. Eur J Oper

Res 147 (3):451–463. doi:10.1016/s0377-2217(02)00364-8

7 Optimizing Resources Involved in the Reception of an Emergency Call 135

Cone DC, Galante N, MacMillan DS (2008) Can emergency medica dispatch systems safely

reduce first-responder call volume? Prehospital Emergency Care 12 (4):479–485. doi:10.1080/

10903120802290844

Conover W (1999) Practical nonparametric statistics. John wiley & Sons, New York

Erkut E, Ingolfsson A, Erdogan G (2008) Ambulance location for maximum survival. Naval

Research Logistics 55 (1):42–58. doi:10.1002/nav.20267

Garcıa PA (2003) Analisis de capacidad del Call Center de una entidad financiera.Gendreau M, Laporte G, Semet F (2001) A dynamic model and parallel tabu search heuristic for

real-time ambulance relocation. Parallel Computing 27 (12):1641–1653

Gendreau M, Laporte G, Semet F (2006) The maximal expected coverage relocation problem for

emergency vehicles. Journal of the Operational Research Society 57 (1):22–28. doi:10.1057/

palgrave.jors.2601991

Giraldo M (2005) Simulacion y asignacion de recursos para el Call Center de una entidadfinanciera. Universidad de los Andes, Bogota

Green L, Kolestar P (2004) Improving emergency responsiveness with management science.

Journal of the Institute for operational research and management sciences 50:1001–1014Guerrero W, Amaya CA, Velasco N Modelo de programacion multi-objetivo en el sistema de

remision de pacientes entre hospitales de Bogota. In: XIV Congreso Latino Iberoamericano deInvestigacion de Operaciones, Cartagena, Colombia, 2008.

Haghani A, Tian Q, Hu HJ, Trb (2004) Simulation model for real-time emergency vehicle

dispatching and routing. In: Transportation Network Modeling 2004. Transportation Research

Record, vol 1882. pp 176–183

Harewood SI (2002) Emergency ambulance deployment in Barbados: A multi-objective approach.

Journal of the Operational Research Society 53 (2):185–192

Henders NS, Mason A (2004) Ambulance service planning: Simulation and data visualisation. In:

University C (ed) Operations research and health care.

Hinchey P, Myers B, Zalkin J, Lewis R, Garner D (2007) Low acuity EMS dispatch criteria can

reliably identify patients without high-acuity illness or injury. Prehospital Emergency Care 11

(1):42–48. doi:10.1080/10903120601021366

Huertas J, Barrera D, Amaya CA, Velasco N (2009) Evaluacion del despacho de ambulancias del

Centro Regulador de Urgencias y Emergencias CRUE de Bogota. Universidad de los Andes,

Bogota

Ingolfsson A, Budge S, Erkut E (2008) Optimal ambulance location with random delays and travel

times. Health Care Management Science 11 (3):262–274. doi:10.1007/s10729-007-9048-1

Jia HZ, Ordonez F, Dessouky MM (2007) Solution approaches for facility location of medical

supplies for large-scale emergencies. Computers & Industrial Engineering 52 (2):257–276.

doi:10.1016/j.cie.2006.12.007

Kelton WD, Sadowski RP, Swets B (2010) Simulation with Arena. BostonKuhl ME, Ivy JS, Lada EK, Steiger NM, Wagner MA, Wilson JR (2010) Univariate input models

for stochastic simulation. Journal of Simulation 4:81–97

Kuisma M, Boyd J, Vayrynen T, Repo J, Nousila-Wiik M, Holmstrom P (2005) Emergency call

processing and survival from out-of-hospital ventricular fibrillation. Resuscitation 67

(1):89–93. doi:10.1016/j.resuscitation.2005.04.008

Kuisma M, Holmstrom P, Repo J, Maatta T, Nousila-Wiik M, Boyd J (2004) Prehospital mortality

in an EMS system using medical priority dispatching: a community based cohort study.

Resuscitation 61 (3):297–302. doi:10.1016/j.resuscitation.2004.01.008

Kuisma M, Vayrynen T, Hiltunen T, Porthan K, Aaltonen J (2009) Effect of introduction of

electronic patient reporting on the duration of ambulance calls. American Journal of Emer-

gency Medicine 27 (8):948–955. doi:10.1016/j.ajem.2008.07.033

Kulkarni VG (1995) Modeling and analysis of stochastic systems. New York

An hypercube queuing model for facility location and redistricting in urban emergency services

(1974).

Martinez M, Valcarcel O, Montessi LJ (2003) Manual para los equipos de regulacion medica.

136 P. Guaracao et al.

Mendonca FC, Morabito R (2001) Analysing emergency medical service ambulance deployment

on a Brazilian highway using the hypercube model. Journal of the Operational Research

Society 52 (3):261–270

Moeller B (2004) Obstacles to measuring emergency medical services performance. EMS Mngt 1(2):8–15

Mohd C, Mohd I, Mohsin S (2008) Ambulance response time and emergency medical dispatcher

program: A study in Kelantan Malaysia. Southeast Asian Journal of tropical Medecine &public health 39:1140–1153

Pell J, Sirel J, Marsden A, Ford I, Cobb S (2001) Effect of reducing ambulance response time on

deaths from out of hospital cardiac arrest: Cohort study. British Medical Journal322:1385–1388

Riano G (2007) Analisis de Call Centers. Modelos probabilısticos con aplicaciones.Rojas A, Avarez L, Parra J (2007) Diseno metodologico para la ubicacion de ambulancias en el

sector de atencion prehospitalaria en Bogota D.C. Revista de Ingenierıa Industrial 6 (1):77–94

Rosas JC (2003) Optimizacion del Call Center de Credibanco-Visa Colombia. Universidad de losAndes, Bogota

Santiano N, Young L, Hillman K, Parr M, Jayasinghe S, Baramy LS, Stevenson J, Heath T, Chan C,

ClaireM, Hanger G (2009) Analysis ofMedical Emergency Team calls comparing subjective to

“objective” call criteria. Resuscitation 80 (1):44–49. doi:10.1016/j.resuscitation.2008.08.010

Sathe A, Miller-Hooks E, Trb (2005) Optimizing location and relocation of response units in

guarding critical facilities. In: Network Modeling 2005. Transportation Research Record, vol

1923. pp 127–136

Savas E (1969) Simulation and cost-effectiveness analysis of New York’s emergency ambulance

service. Management Science 15:608–627Silva F, Serra D (2008) Locating emergency services with different priorities: the priority queuing

covering location problem. Journal of the Operational Research Society 59 (9):1229–1238.

doi:10.1057/palgrave.jors.2602473

Simpson NC, Hancock PG (2009) Fifty years of operational research and emergency response.

Journal of the Operational Research Society 60:S126-S139. doi:10.1057/jors.2009.3

Singer M, Donoso P (2008) Assessing an ambulance service with queuing theory. Computers &

Operations Research 35 (8):2549–2560. doi:10.1016/j.cor.2006.12.005

Snooks H, Evans A, Wells B, Peconi J, Thomas M (2008) What are the highest priorities for

research in pre-hospital care? Results of a review and a Delphi consultation exercise. Journalof Emergency Primary Health Care 11:42–48

Valinsky D (1955) A determination of the optimum location of firefighting units in New York City.

Opns Res 4:494–512.Wilson S, Cooke M, Morell R, Bridge P, Allan T (2002) A systematic review of the evidence

supporting the use of priority dispatch of the emergency ambulance. Prehospital EmergencyCare 6:42–49

7 Optimizing Resources Involved in the Reception of an Emergency Call 137