Optimization of Emergency Medical Service with Fixed Centers

Marek Kvet

Faculty of Management Science and Informatics, University of Žilina, Slovakia

Univerzitná 8215/1, 010 26 Žilina, Slovakia

Keywords: Location Analysis, Urgent Healthcare System, Service Accessibility Optimization, Radial Approach,

Fixed Centers.

Abstract: The research reported in this scientific paper focuses on practical usage of optimization methods aimed at

improving the service accessibility for clients spread over the whole Slovak Republic. The results of previous

research confirmed by a computer simulation indicated that the weighted p-median problem is a suitable way

of optimization. Here, we pay attention to the inconvenience of current ambulance stations deployment, which

consists in the fact that there are same locations with two or more stations equipped with an ambulance vehicle.

On the other hand, the standard weighted p-median problem formulation allows locating at most one station

to one place. Furthermore, when searching for a better service center locations, the capacity of a center should

be taken into account at least partially. Otherwise, the station with a high number of assigned clients would

not be able to satisfy all the demands. Such result may be considered inacceptable. We believe that mentioned

disadvantages could be overcome by fixing some stations, which will not be allowed to change their current

location. The results of suggested optimization process are compared with the analysis of current ambulance

stations deployment form more points of view.

1 INTRODUCTION

Emergency Medical Service (EMS), fire brigades and

many other rescue systems are established to ensure

rapid information, activation and effective usage and

coordination of the forces and resources of rescue

services in providing the necessary assistance. The

role of such systems is to provide the affected person

with the necessary assistance in the case of a threat to

life, health or property without any delay to prevent

from irreversible losses on health or life. Obviously,

the quality and efficiency of the EMS system depends

mainly on the number of stations operating in the

considered area (in our case in the whole state) and

on the location of the stations. Determining the right

number of facilities is a very sensitive issue that must

take into account two conflicting requirements. The

first of them follows from the main mission of the

EMS system - to save the life and health of the

population. This task can be adequately fulfilled if the

network of EMS stations is dense enough. Then the

system is able to respond to an emergency call

immediately and can provide first aid in a short time.

On the other hand, there is a legitimate requirement

for the efficient use of public resources, which limits

the number of ambulance stations to be located.

Limiting the number of service providing facilities

results in an increase in their workload and a

reduction in the availability of emergency care, as the

nearest ambulance may be occupied at the time of an

emergency call by providing a service to another

patient. A situation in which a patient does not receive

urgent medical care within a predetermined time limit

is evaluated as a system failure (Brotcorne et al.,

2003, Current et al., 2002, Doernet et al., 2005,

Ingolfsson et al., 2008, Matiaško, Kvet, 2017).

Therefore, this paper focuses on the strategic level of

management of emergency health care. The main

attention is paid to determining the optimal locations

of EMS stations so that the accessibility of the service

for patients is the highest possible. It can be assumed

that the accessibility is the better the closer the EMS

station is to the affected patient (Jánošíková, 2007).

The reasons to optimize the EMS system (to find

new optimal service center deployment) may follow

from more ideas, not only from establishing a new

system. The necessity of system optimization usually

follows from the fact that the distribution of demands

changes in time and space. Naturally, the originally

determined stations deployment may not fit now.

214

Kvet, M.

Optimization of Emergency Medical Service with Fixed Centers.

DOI: 10.5220/0010890700003117

In Proceedings of the 11th International Conference on Operations Research and Enterprise Systems (ICORES 2022), pages 214-221

ISBN: 978-989-758-548-7; ISSN: 2184-4372

Another reason for optimization of current EMS

system consists in basic performance characteristics.

Analysis of data given by EMS providers has shown

that the average response time, i.e. time necessary to

achieve the patient from the EMS station after an

emergency call, has risen by almost one minute in the

last years and thus the accessibility of urgent medical

care for patients in critical condition has worsened.

Such situation results not only in a deterioration in the

availability of the service, but possibly in an increase

in the number of unnecessary and avoidable deaths.

Furthermore, new roads have been built and the

traffic has changed, too. Therefore, the deployment of

current EMS stations should be regularly checked and

optimized if necessary. We believe that some changes

in the locations of EMS centers (without any change

of their number) may contribute to improve average

service accessibility for clients.

Let concentrate on the optimization process itself,

now. It must be realized that there are several cities or

smaller city districts, which are inhabited by a high

number of potential patients. Such big demands for

service are covered by more stations located at the

same address. Such a situation needs to be taken into

account also in the process of system optimization.

There are several ways to cope with this problem. If

we want to formulate a model that would allow

locating more stations at the same place, we should

follow the principle of multiple facility location

problem as suggested in (Janáček, 2021). In such a

case, the optimized design quality criterion should be

based on the concept of generalized disutility. It

means that the service does not have to be provided

only by the nearest located EMS station, but by the

nearest station being currently available (Kvet,

Janáček, 2018, Kvet et al., 2019). If the minimized

objective function takes into account only the

distance or travel time from clients’ locations to the

nearest located source of urgent healthcare, than the

mentioned modeling approach does not hold.

The optimization process studied in this paper is

based on two steps. In the first phase, some of EMS

stations get fixed. It means, they are not allowed to

change their current location due to the large number

of emergency calls assigned to them. The second

phase of the optimization approach is based on the

mathematical model, which searches for the best

possible locations of the remaining stations.

The structure of this paper is organized as follows.

The next section contains an analysis of current EMS

stations deployment and it explains the emergency

system in Slovakia. The third section contains the

details about the suggested optimization strategy and

the proposed mathematical model. In the fourth

section, we provide the readers with a computational

study, in which the results of suggested method are

presented. This section contains also a comparison of

the obtained results to the current state. Finally, the

last section brings some brief concluding remarks and

suggests new possible future research directions.

2 EMS SYSTEM IN SLOVAKIA

The Emergency Medical Service system represents a

pre-hospital part of the urgent care provision, which

forms the highest level of differentiated medical care.

It can be also defined as providing the urgent health

care to a person in such a condition in which their life

or health is suddenly endangered and the affected

person is dependent on the rescue service. The EMS

system is a part of the Integrated Rescue System of

the Slovak Republic.

In its current form, the EMS system in Slovakia

operates 274 stations, which can be divided according

to the type of crew into the following two groups:

1. RZP stations – The crew consists of two

members - a paramedic and an ambulance

driver, or two paramedics (one as a driver).

There are currently 188 ambulances of this

type in Slovakia. Some of them are equipped

with an incubator to transport newborns.

2. RLP stations – The ambulance staff consists

of three members: a doctor specialist in

emergency medicine, anesthesiology and

intensive care (or another specialization);

paramedic and an ambulance driver, or a

doctor with two paramedics. There are 86

such ambulances in the Slovak Republic.

In addition, the private company Air - Transport

Europe, operates 7 stations of the Helicopter Rescue

Medical Service. Some of the RLP ambulances are

equipped with a mobile intensive care unit for the

transport of critically ill patients. This special

equipment follows from the decision of the Ministry

of Health of the Slovak Republic based on the

recommendation of the Emergency Medical

Operations Center. In August 2014, the number of

extra equipped RLP stations was set at 5. Other types

of EMS ambulances, such as in the surrounding

countries, are not recognized by Slovak legislation

(Doerner et al., 2005, Marianov, Serra, 2002, Reuter-

Oppermann et al., 2017, Schneeberger et al., 2016).

For completeness, the RZP stations are located in

166 different places (in some of them, there are two

or even more). The RLP stations are placed totally in

80 locations. The total number of network nodes with

Optimization of Emergency Medical Service with Fixed Centers

215

at least one ambulance regardless of its type is 207.

These 274 stations cover the demands of totally 2,934

municipalities spread over the area of Slovakia.

As mentioned in previous parts of the paper, the

accessibility of the EMS is generally the better the

closer is the service provider to the client location.

From the point of the service access analysis, it is

necessary to distinguish two basic approaches:

1. Take into account the average distance of all

clients from the nearest station, regardless of

its type. In the case of selected specific

diagnoses from the first hour quintet, this

view may not be appropriate, because the

RLP needs to be present at the scene.

2. Analyze the distance only to the nearest RLP

station. This value of service accessibility

will be logically higher than in the previous

approach, but in cases of specific diagnoses,

it models the situation better.

The following Table I summarizes selected basic

performance characteristics of the system not only for

the entire system (RZP and RLP stations together),

but also for RLP type stations separately. Let us

remind that patients who need to be satisfied in the

case of an acute life and health threat are concentrated

in totally 2,934 municipalities. The municipality's

weight can be expressed in many different ways:

1. Number of emergency calls of patients in

critical or urgent condition (this number may

not be proportional to the population of the

municipality)

2. Absolute number of inhabitants sharing the

location

3. The value of one (all municipalities have the

same weight, the municipality size does not

play any role)

In this computational study, we report the results

for each possible weight of a client location. The final

selection of the correct municipality weight is up to

the decision-maker or other authority responsible for

the decision-making process. The basic numerical

characteristics to express the service accessibility are:

 Average time in minutes the ambulance

vehicle needs to achieve the affected patient,

 Maximal time in minutes that the ambulance

crew must travel to get to the farthest patient,

 Percentage of demands covered within 8 or

15 minutes from the nearest located station.

The service providers defined the limits 8 and 15

minutes according to their internal rules following

from the standards of urgent healthcare.

Table 1: Analysis of current EMS stations deployment.

Indicator

Municipality weight

Calls Citizens One

Entire

EMS

system

axima

response time 31.5 31.5 31.5

verage response time 5.73 5.72 7.75

15 min percentage 98.29 98.48 93.76

8 min

ercentage 73.28 73.03 48.06

RLP

only

aximal response time 38.1 38.1 38.1

verage response time 7.98 7.99 11.72

15 min percentage 86.75 87.09 69.97

8 min percentage 53.97 53.50 20.79

The analysis of current EMS stations deployment

shows many important things: The positive is that the

current situation is not bad, rather the opposite.

Almost 100 percent of requests can be satisfied within

15 minutes by the nearest located service center

regardless the type of ambulance staff. On the other

hand, the obtained characteristics indicate that the

accessibility of the service provided by RLP stations

only deserves a strong improvement. Therefore, this

research paper introduces an optimization method to

improve the current state. Presented approaches are

suggested in such a way that they perform only little

changes in current service center deployment with

great effect on service accessibility. We expect that

since the performed changes will not be too large,

public authorities responsible for EMS system

performance efficiency could accept them.

3 TWO-PHASE OPTIMIZATION

OF CURRENT EMS SYSTEM

The main goal of this section is to provide the readers

with the details of proposed optimization method

suggested to achieve better EMS stations deployment

mainly from the point of RLP stations performance

efficiency.

As it was mentioned in the introducing section,

the proposed optimization method is based on two

phases. Since we want to make such a mathematical

model, which avoids locating more than one center to

the same place, and we assume the objective function

to consider only the nearest EMS station for each

client, the first phase of the algorithm consists in pre-

processing those center locations, in which there are

currently more than one facility.

The first phase does not contain any optimization.

Its core idea consists in pre-processing the input data.

Let us introduce necessary denotations to formulate

the first phase precisely. We will use the set I to

denote the set of locations, which are the candidates

for ambulance station locating. Similarly, the symbol

J will denote the set of served municipalities.

ICORES 2022 - 11th International Conference on Operations Research and Enterprise Systems

216

Obviously, the sets I and J can be the same as it is in

our case. Each element jJ is connected with its

weight denoted by w

, which is usually an integer or

real number. The coefficient w

can be interpreted in

many different ways. As already mentioned, it can be

the number of expected emergency calls from the

location j, it can express the number of inhabitants

sharing the location j, etc. In our implementation of

the algorithm, the weight w

represents the number of

calls of patients in a critical or urgent condition. The

operators of current EMS stations provided us with

the weights. Since the first phase may decrease the

original values of w

, we will use the symbol c

denote the final weight of a municipality j used in the

next steps of the optimization process. In many cases,

= w

, but there will be also some locations, for

which c

< w

or even c

= 0. If c

= 0 then all demands

of the municipality jJ are covered by the stations

located at j, which are not allowed to change their

location. Furthermore, it can be generally assumed

that an ambulance regardless of its type has limited

capacity and it is able to serve only Q = 19919 calls.

This value is the average number of calls assigned to

one station. If a station must remain in its current

location, it is excluded from further optimization. At

the same time the weight w

of given municipality j is

reduced by Q in such a way that it can not drop below

zero. If we denote the current number of stations in

municipality j by the symbol r

, then three different

situations may occur:

1. If w

> r

Q, the stations cannot be relocated.

The uncovered demand in municipality j

that represents an input parameter of the

model is c

= w

− r

2. If w

> Q and at the same time w

< r

Q, then





stations must remain in the

municipality, the others may be relocated.

The uncovered demand in municipality j

will be c

= w

mod Q.

3. If w

< Q and r

> 1, one station must

remain in the town, the others may be

relocated. Municipality j is completely

served by the fixed station and so the

uncovered demand will be c

= 0.

The last rule is related to managerial decisions

made in the past. There are not apparent reasons why

there are multiple stations in some small towns today

(maybe a good hospital is nearby). Nevertheless, we

try to respect them to some extent since severe

changes in the current system may not be acceptable.

This way, we get the list of stations, which must

stay at their current place and new values of the

weights c

. After the fixation of some centers in their

current location, the type of stations must be decided

about. We prefer fixing the RLP stations. If there are

more stations that need to be fixed, we fix the RLP

stations at the particular location first (if there are

any) and then we add the remaining number of RZP

stations. This first phase results in 48 fixed RLP and

19 fixed RZP stations according to the rules 1 and 2.

The stations, which should be fixed according to the

rule 3 are not added to the list of fixed station due to

the following fact. The capacity of the previously

fixed stations is fully utilized and the stations fixed

according to the rule 3 have some free capacity to

accept additional calls. Therefore, for each station

fulfilling the rule 3 we add a separate constraint in the

next step in order to keep the station located at its

current place, but we allow to assign some additional

calls to it. Let all such stations form the set F.

After obtaining the list of fixed centers and the list

of stations for which we need additional constraint in

the following mathematical model, we can formulate

the second step of suggested optimization method.

All centers, which are not fixed, should undergo an

optimization process in order to find the best location

to achieve the optimal value of used criterion. Since

we have two types of EMS stations, first, we will find

the best locations of the stations regardless their type,

and then we will decide about the type of stations.

To formulate the mathematical model, we need to

introduce

further notation. As above, let the symbol I

denote the set of candidates for EMS station locating.

In our case, the set I contains all 2,934 cities and

villages of Slovakia. The same elements are used to

form the set J of used municipalities. As a weight of

individual location jJ we use the coefficient c

obtained from the first phase. As far as the objective

function is concerned, it considers the average time

the ambulance vehicle from the nearest center needs

to achieve the affected patient. Let the time distance

between the locations iI and jJ be denoted by t

Finally, we need the integer number p of stations to

be located. In our case, p = 274 – 48 – 19 = 207. To

complete the model, the decision about locating a

EMS station at the location iI will be modelled by a

binary variable y

{0, 1}. The location-allocation

formulation of the model does not hold because of the

model size (the sets I and J contain approximately

3,000 elements each) and the necessity to model

assignment of clients to their located centers. The

matrix of allocation variables would contain about 9

million variables (Avella et al., 2007). To overcome

this obstacle, so-called radial formulation can be used

(Avella et al., 2007, García et al., 2011, Janáček,

2008, Kvet, 2014, Kvet, 2015).

Optimization of Emergency Medical Service with Fixed Centers

217

In accordance with the radial formulation, let the

symbol m denote the largest value in the matrix {t

i.e. m = max{t

: iI, jJ}. For simplicity, we assume

that all values in the matrix are integer. Of course, the

radial formulation can be easily adjusted also for real

values. For each location jJ and for each integer

value v = 0, 1 … m-1 we introduce a variable x

{0,

1}. This variable takes the value of one, if the time t

spent by travelling from the client located at jJ to

the nearest EMS station is greater than the value of v

and it takes the value of zero otherwise. Then, the

expression (1) holds for each jJ.

jjv







(1)

Similarly to the set-covering problem, a binary

matrix {a

} must be computed according to the

formula (2), in which iI, jJ and v = 0, 1 … m-1.

1if

0otherwise











(2)

After these preliminaries, the radial model of the

problem can be formulated by the expressions (3)-(8).

jJ v

inimize c x







(3)

,0,1 1

jv ij i

Subject to x a y

for j J v , ,m





 





(4)







(5)

yforfF

(6)

{0, 1}

yforiI

(7)

{0, 1} , 0, 1 1

xforjJv,,m

(8)

The quality criterion of the design formulated by

the objective function (3) expresses the sum of time

distances from all clients to their nearest EMS station.

The link-up constraints (4) ensure that the variables

are allowed to take the value of 0, if there is at least

one center located in radius v from the location j and

the constraint (5) limits the number of located EMS

stations by

p. The constraint (6) follows from the first

phase of suggested approach and its task is to arrange

that the centers fixed according to the rule 3 stay at

their current locations. The last obligatory constraints

(7) and (8) keep the domain of the variables

and x

It must be realized that the optimal solution of the

model (3)-(8) may bring such system design that

differ from the current stations deployment a lot. If

the proposed changes are too large, then they do not

have to be accepted neither by private EMS providers

nor by public authorities responsible for the service.

Therefore, we suggest a simple model extension,

which would limit the number of current stations,

which can change their location. Such an extension is

seemingly simple, but it can be achieved only with

additional constraint. The problem is to define a

change in center locating. Generally, a change is

performed only in such a case, if there is a location,

in which more centers will be located than there are

currently. Therefore, we need to introduce a constant

for each iI. This constant takes the value of one,

either if all EMS stations at the location

i are fixed or

if there is no station located at

i. In case when only

some of the current stations are fixed, but not all of

them, this coefficient takes the value of zero. Then the

model (3)-(8) can be extended by the expression (9),

in which the parameter

q limits the number of stations

that are allowed to change their current location. The

value of

q is the parameter of suggested method.

ny q







(9)

By solving the model (3)-(9) we obtain the list of

the optimal locations of EMS stations regardless of

their types. The final decision about the type of each

located ambulance can be made in a simple way. Let

all EMS stations following from the result of the

model (3)-(9) form a set of candidates for further

processing. The model (3)-(8) can be used again to

select the RLP stations from the set of all located

centers. Obviously, the input data need to be adjusted.

To sum up the whole optimization approach, it is

based on two phases. First, the biggest cities are

solved and if there are more EMS stations located at

the same place, some of them get fixed according to

the defined rules. The stations which do not get fixed

are subject of the optimization, which consists of two

steps. In the first one, we find the optimal locations of

all EMS station and then, we select the RLP stations

from the set of all candidates.

4 COMPUTATIONAL STUDY

The main goal of performed computational study is to

show and compare the obtained results for various

settings of parameter

q to the current EMS stations

deployment. The results are summarized on the

following Tables 2-7. Each table contains the results

of different value of

q. Note that the parameter q

expresses the maximal number of centers, which can

change their current location.

ICORES 2022 - 11th International Conference on Operations Research and Enterprise Systems

218

Table 2: Analysis of EMS system design obtained by

suggested optimization approach, in which at most 10

percent of current EMS stations are allowed to be relocated.

Indicator

Municipality weight

Calls Citizens One

Entire

EMS

system

aximal response time 30.2 30.2 30.2

verage response time 5.28 5.36 7.41

15 min percentage 98.71 98.82 94.51

8 min percentage 77.94 76.69 52.15

RLP

only

aximal response time 38.1 38.1 38.1

verage response time 7.75 7.82 11.43

15 min percentage 88.84 88.81 71.98

8 min percentage 54.52 53.55 21.57

Table 3: Analysis of EMS system design obtained by

suggested optimization approach, in which at most 20

percent of current EMS stations are allowed to be relocated.

Indicator

Municipality weight

Calls Citizens One

Entire

EMS

system

aximal response time 25.4 25.4 25.4

verage response time 5.04 5.12 7.27

15 min percentage 98.83 98.98 94.61

8 min percentage 82.30 80.84 53.99

RLP

only

aximal response time 38.1 38.1 38.1

verage response time 7.73 7.78 11.44

15 min percentage 88.72 88.80 72.02

8 min percentage 55.20 54.26 21.85

Table 4: Analysis of EMS system design obtained by

suggested optimization approach, in which at most 30

percent of current EMS stations are allowed to be relocated.

Indicator

Municipality weight

Calls Citizens One

Entire

EMS

system

aximal response time 25.4 25.4 25.4

verage response time 4.92 5.02 7.13

15 min percentage 99.02 99.12 95.13

8 min percentage 83.07 81.48 55.08

RLP

only

aximal response time 38.1 38.1 38.1

verage response time 7.73 7.78 11.43

15 min percentage 88.59 88.71 71.88

8 min percentage 55.07 54.19 22.02

Table 5: Analysis of EMS system design obtained by

suggested optimization approach, in which at most 40

percent of current EMS stations are allowed to be relocated.

Indicator

Municipality weight

Calls Citizens One

Entire

EMS

system

aximal response time 25.1 25.1 25.1

verage response time 4.83 4.94 7.04

15 min percentage 99.04 99.13 95.33

8 min percentage 83.77 82.09 55.79

RLP

only

aximal response time 38.1 38.1 38.1

verage response time 7.73 7.79 11.43

15 min percentage 88.47 88.56 72.09

8 min percentage 55.16 54.06 22.05

Table 6: Analysis of EMS system design obtained by

suggested optimization approach, in which at most 50

percent of current EMS stations are allowed to be relocated.

Indicator

Municipality weight

Calls Citizens One

Entire

EMS

system

aximal response time 25.1 25.1 25.1

verage response time 4.77 4.88 6.98

15 min percentage 99.15 99.24 95.54

8 min percentage 84.28 82.68 56.75

RLP

only

aximal response time 38.1 38.1 38.1

verage response time 7.73 7.80 11.48

15 min percentage 88.21 88.33 71.47

8 min percentage 54.89 53.90 22.09

The last Table 7 reports the results of suggested

optimization approach, in which the number of

centers allowed to be relocated does not play any role.

It means that the parameter

q was set to the value of

p. All centers could change their current locations,

except of those being fixed. This way, the additional

constraint (9) does not make any sense and it can be

excluded from the model. Table 7 keeps the structure

of previously reported tables.

Table 7: Analysis of EMS system design obtained by

suggested optimization approach, in which all current EMS

stations except for the fixed are allowed to be relocated.

Indicator

Municipality weight

Calls Citizens One

Entire

EMS

system

aximal response time 25.1 25.1 25.1

verage response time 4.76 4.87 6.97

15 min percentage 99.11 99.22 95.57

8 min percentage 84.21 82.64 56.51

RLP

only

aximal response time 38.1 38.1 38.1

verage response time 7.74 7.81 11.50

15 min

ercentage 88.15 88.27 71.44

8 min percentage 54.75 53.79 22.05

The results reported in Tables 2-7 show that the

higher the number of stations allowed to be relocated,

the better service accessibility can be achieved. In

other words, the mathematical model respecting

given limitations tries to locate the center in those

places, in which they are the nearest to the demand

points. On the other hand, if we look at the results for

RLP stations only, the obtained results indicate that

the coverage within the time limit of 15 minutes is

quite good, but the coverage by the time of 8 minutes

is still insufficiently weak. This observation deserves

development of another approach aimed primarily at

optimization of RLP stations.

As far as the computational time requirements of

suggested approach are concerned, the computational

times are not reported here. It must be noted that the

first phase does not contain any optimization process

and the fixation of EMS stations can be computed via

one cycle very fast. The second phase consists in

Optimization of Emergency Medical Service with Fixed Centers

219

solving the above-described model (3)-(9) to obtain

the optimal locations of all EMS stations and then, the

model (3)-(8) is used again to select the RLP stations.

The radial formulation makes the model simpler than

the location-allocation formulation and thus, the

optimal solution of the problem can be reached by

about three minutes using a common notebook with

standard technical parameters and basic equipment.

5 CONCLUSIONS

This paper was focused on practical usage of the

optimization method based on the weighted

p-median

problem formulation. The goal of optimization was to

achieve better access to urgent medical healthcare

provided by private or public emergency agencies.

Suggested method was based on current station

deployment analysis, which showed that there are

some station locations with multiple facilities. This

fact should be considered also in the optimization

process. Such a request may cause several difficulties

when formulating the model. The researchers could

either create a model with multiple facility locations

and apply the concept of generalized disutility or this

obstacle could be handled in a different way.

The optimization approach studied in this paper is

based on two phases. The first phase searches for such

stations, that can not change their current locations for

different reasons. After that, a simple model based on

the weighted

p-median problem is solved to obtain

the optimal location of EMS stations. All located

EMS stations become candidates for RLP, which are

searched for by solving another mathematical model.

Since the radial formulation enables us to solve real-

world sized instances, we hope that suggested method

can significantly contribute to the state-of-the-art in

the field of service system optimization approaches.

Obviously, this method is not the only possible way

to improve current stations deployment.

Based on achieved results reported in previous

section, the future research in this scientific are could

be aimed at RLP stations, which could be primarily

solved by the second phase of suggested algorithm.

Another scientific topic to be studied could be focus

on developing new algorithms, which would be able

to apply different criteria and bring better results.

ACKNOWLEDGEMENT

This work was supported by the research grant VEGA

1/0216/21 “Design of emergency systems with

conflicting criteria using artificial intelligence tools”.

This work was supported also by the Slovak Research

and Development Agency under the Contract no.

APVV-19-0441.

REFERENCES

Avella, P., Sassano, A., Vasil’ev, I., 2007. Computational

study of large scale p-median problems. In

Mathematical Programming, Vol. 109, No 1, pp. 89-

114.

Brotcorne, L., Laporte, G., Semet, F., 2003. Ambulance

location and relocation models. European Journal of

Operational Research 147, pp. 451–463.

Current, J., Daskin, M., Schilling, D., 2002. Discrete

network location models. In Drezner Z. (ed) et al.

Facility location. Applications and theory, Berlin,

Springer, pp. 81-118.

Doerner, K. F. et al., 2005. Heuristic solution of an

extended double-coverage ambulance location problem

for Austria. In Central European Journal of Operations

Research, Vol. 13, No 4, pp. 325-340.

García, S., Labbé, M., Marín, A., 2011. Solving large p-

median problems with a radius formulation. INFORMS

Journal on Computing, Vol. 23, No 4, pp. 546-556.

Ingolfsson, A., Budge, S., Erkut, E., 2008. Optimal

ambulance location with random delays and travel

times, In Health Care Management Science, Vol. 11,

No 3, pp. 262-274.

Janáček, J., 2008. Approximate Covering Models of

Location Problems. In Lecture Notes in Management

Science: Proceedings of the 1st International

Conference ICAOR, Yerevan, Armenia, pp. 53-61.

Janáček, J., 2021. Multiple p-Facility Location Problem

with Randomly Emerging Demands. In: Proceedings of

the 14th International Conference on Strategic

Management and its support by Information Systems

2021, pp. 120-125.

Jánošíková, Ľ., 2007. Emergency Medical Service

Planning. Communications Scientific Letters of the

University of Žilina, 9(2), pp. 64-68.

Kvet, M., 2014. Computational Study of Radial Approach

to Public Service System Design with Generalized

Utility. Digital Technologies 2014: Proceedings of the

10th Interna-tional IEEE Conference, pp. 198-208.

Kvet, M., 2015. Advanced Radial Approach to Resource

Location Problems. Studies in Computational

Intelligence: Developments and Advances in Intelligent

Systems and Applications, Springer, pp. 29-48.

Kvet, M., Janáček, J., 2018. Reengineering of the

Emergency Service System under Generalized

Disutility. In the7th International Conference on

Operations Research and Enterprise Systems ICORES

2018, Madeira, Portugal, pp. 85-93.

Kvet, M., Janáček, J., Kvet, M., 2019. Computational Study

of Emergency Service System Reengineering Under

Generalized Disutility. Operations Research and

Enterprise Systems: 7th International Conference,

ICORES 2022 - 11th International Conference on Operations Research and Enterprise Systems

220

ICORES 2018 Funchal, Madeira, Portugal, January 24–

26, 2018, Springer, pp. 198-219.

Marianov, V., Serra, D. 2002. Location Problems in the

Public Sector. Drezner, Z. (Ed.): Fa-cility location -

Applications and theory, Berlin: Springer, pp. 119-150.

Matiaško, K., Kvet, M. 2017. Medical data management.

Informatics 2017: IEEE International Scientific

Conference on Informatics, Danvers: Institute of

Electrical and Electronics Engineers, pp. 253-257.

Reuter-Oppermann, M., van den Berg, P. L., Vile, J. L.

2017. Logistics for Emergency Medical Service

systems. Health Systems, Vol. 6, No 3, pp 187-208.

Schneeberger, K. et al. 2016. Ambulance location and

relocation models in a crisis. Central European Journal of

Operations Research, Vol. 24, No. 1, Springer, pp. 1-27.

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