Automatic Nurse Allocation based on a Population Algorithm for Home

Health Care

Filipe Alves

1,2 a

, Ana Maria A. C. Rocha

2 b

, Ana I. Pereira

1,2 c

and Paulo Leit

1 d

Research Centre in Digitalization and Intelligent Robotics (CeDRI), Instituto Polit

ecnico de Braganc¸a, Braganc¸a, Portugal

ALGORITMI Center, University of Minho, Braga, Portugal

Keywords:

Home Health Care, Nurse Allocation, Optimization, Particle Swarm Optimization.

Abstract:

The provision of home health care services is becoming an important research area, mainly because in Portugal

the population is ageing and it is necessary to perform home care services. Home care visits are organized

taking into account the medical treatments and general support that elder/sick people need at home. This health

service can be provided by nurses teams from Health Units, requiring some logistics for this purpose. Usually,

the visits are manually planned and without computational support. The main goal of this work is to carry out

the automatic nurse’s allocation of home care visits, of one Braganc¸a Health Unit, in order to minimize the

nurse’s workload balancing, spent time in all home care visits and, consequently, reduce the costs involved.

The developed methodology was coded in MatLab Software and the problems were efﬁciently solved by the

particle swarm optimization method. The nurse’s allocation solution of home care visits for the presented case

study shows a signiﬁcant improvement and reduction in the maximum time, in the nurse workload balancing,

as well as the patients waiting time.

1 INTRODUCTION

According to the World Health Organization the age-

ing people and dependency rate care of older people

in Europe, namely in Portugal, is increasing. The

number of people who need home care services, con-

sequently, is growing over the years. The National

Health System has to deal with more and more de-

manding scenarios in what concerns home care.

This scenario — to provide home care services —

is not only advantageous to elder/sick people but also

to the National Health System since it is economically

advantageous to keep people at home instead of pro-

viding them with a hospital bed (Nickel et al., 2012;

Rest and Hirsch, 2015).

The home-based care provided by public or pri-

vate entities has been the subject of recent research

mainly in the operations research area with particu-

lar attention on route’s optimization and on the staff

teams composition that provide this kind of services

(Nickel et al., 2012; Benzarti et al., 2013; Bertels

https://orcid.org/0000-0002-8387-391X

https://orcid.org/0000-0001-8679-2886

https://orcid.org/0000-0003-3803-2043

https://orcid.org/0000-0002-2151-7944

and Fahle, 2006; Rasmussen et al., 2012). According

to previous studies, the use of optimization strategies

contributes to improve the Home Health Care services

(Liu et al., 2013a; Sahin and Matta, 2015).

The Portuguese public health system consists in

two types of units: Hospitals and Health Units. Health

units are closer to the population, as they continuously

monitor their patients and home care services are pro-

vided by the teams of health professionals (usually

nurses) of these units. In this context, Health Units

have to perform the schedule and the best allocation

of the nursing teams inside and outside of the Health

Units.

The schedule of the home care visits provided by

the Health Unit teams depends on the patients, nurse

proﬁles and resources to perform the home care. This

represents a complex problem whose main goal is to

minimize the time required to perform all the home

care visits (considering the travel and treatment pa-

tient time) and to return to the Health Unit. In addi-

tion, the best allocation of the nurse teams should be

provided, taking into account the workload balancing

between them.

The rest of the paper is organized as follows: Sec-

tion 2 gives a brief description of the literature re-

view involved in Home Health Care and its applica-

Alves, F., Rocha, A., Pereira, A. and Leitão, P.

Automatic Nurse Allocation based on a Population Algorithm for Home Health Care.

DOI: 10.5220/0009386103950402

In Proceedings of the 9th International Conference on Operations Research and Enterprise Systems (ICORES 2020), pages 395-402

ISBN: 978-989-758-396-4; ISSN: 2184-4372

395

tions. Section 3 overviews the problem deﬁnition and

formulation for nurses allocation, and Section 3 de-

scribes the general real data collection implemented

in the case study. Section 4 presents the population-

based algorithm applied and coded to solve the opti-

mization problem. Section 5 will present and discuss

the obtained results and compared with is currently

being performed. Finally, Section 5 rounds up the pa-

per with the conclusions and future work.

2 LITERATURE REVIEW

Many countries, such as Portugal, face a growing

elderly population, which increases the pressure on

institutions and professionals to provide social and

medical care in the most cost-effective way.

In this sense, a small literature review was car-

ried out to determine the state of the art involved

in keywords such as ”Home Health Care”, ”Alloca-

tion”, ”Optimization” and ”Scheduling”. The same

search was performed on the Scopus database which

enabled the results of 94 documents from different

sources such as journals, books and conference pro-

ceedings. With the bibliographic database collected,

it was organized to enable the use of the Bibliometrix

R-package (Aria and Cuccurullo, 2017). It is impor-

tant to refer that today Bibliometrix is more than just

a statistical tool, which includes all the main biblio-

metric methods of analysis, but we use it especially

for science mapping and networks and not for mea-

suring science, scientists, or scientiﬁc productivity. In

this purpose, it was used the shiny interface for Bib-

liometrix, called Biblioshiny. It supports in a easy

way of use the main features of Bibliometrix, like for

example, data importing and conversion to data frame

collection, data ﬁltering, analytics and plots for three

different level metrics (sources, authors, documents)

and analysis of three structures of knowledge (con-

ceptual structure, intellectual structure, social struc-

ture). In this sense, after analyzing the obtaining in-

formation, it is possible to observe that the annual

scientiﬁc production in the ﬁeld of applications and

Home Health Care study has grown exponentially in

the last 5 years. Figure 1 illustrates the extreme im-

portance of studies and works that enhance the opti-

mization of health logistics, such as primary care ser-

vices and their decision support in this scientiﬁc envi-

ronment.

Another analysis, more related to the scientiﬁc

mapping and its conceptual structure, it was pos-

sible to collect the networks of conceptual words,

which makes it possible to discover links and con-

cepts through co-occurrences of terms. The concep-

Figure 1: Annual Scientiﬁc Production related to Home

Health Care and its applications.

tual framework is often used to understand the top-

ics covered by scholars (called the research front) and

identify which are the most important and most recent

questions. Thus, the co-word analysis through cor-

respondence analysis was collected, according to the

dendrogram topic, which enables the iconic represen-

tation that organizes the particular links. This analysis

employs a quantitative method that leads to groupings

and their ascending hierarchical order (similar to the

branches of a tree).

The analysis and representation obtained can be

visualized in Figure 2. In this ﬁgure, it is possible

to highlight, from the top, the two large clusters that

group the co-word analysis of the literature review

performed. The weights vary depending on a spe-

ciﬁc co-word or its grouping, however it was possi-

ble to create connections already existing in the lit-

erature, with the work developed here. With a blue

rectangle, you can focus on the terms nursing, home

care services, workload balancing and decision mak-

ing. In a smaller rectangle, scheduling algorithms and

swarm optimization using particle swarm optimiza-

tion (PSO) are referred to. Thus, it is easy to identify

the importance of the literature involved, its health

context and how the solution will be obtained in terms

of an automatic nurse allocation system in a Health

Unit. Moreover, it is expected to enhance the growth

of this co-words in the future.

With this literature review, we sought to under-

stand the domains that inﬂuence Home health care,

such as its continuity of care and consistency, the staff

involved, their competence and of course, the quality

of this increasingly common practice, especially in re-

gions of the interior of Portugal. The use of a biblio-

metric analysis made possible the optimized identiﬁ-

cation of relevant documents, according to, for exam-

ple, the citation analysis as a quantitative evaluation

of the main works in the area. From the obtained re-

sults and after its analysis, there is a steady growth of

applications and studies on the home health care prob-

lem, and it is possible to highlight some works such

ND2A 2020 - Special Session on Nonlinear Data Analysis and Applications

396

Figure 2: Dendrogram on the Conceptual Structure about the literature involved.

as routing reviews and scheduling of home health

care (Fikar and Hirsch, 2017), multi-objective opti-

mization in Home care (Braekers et al., 2016), assign-

ment and allocation (Cappanera and Scutell

a, 2014),

heuristics and meta-heuristics (Liu et al., 2013b; Hi-

ermann et al., 2015), among others applied to this do-

main, revealing its extensive applicability.

3 PROBLEM DEFINITION

Health Centers have nurses devoted partially to the

task of providing health care at patient’s home, who

live at any location in the area under supervision of

the Health Center. For a given day, a Health Care

Center needs to deal with two problems: the nurse

schedule needs to perform all tasks inside and out-

side of the Health Care Center; and the cars’ sched-

ules availability.

In this work, it is studied the problem to schedule

the tasks outside the Health Care Center, particularly,

to ﬁnd the home care visits schedule for a given day,

in order to minimize the travel time to perform all vi-

sits.Then, the main objective of this study is to per-

form an automatic planning of home care visits by

the nurses team schedule of the Health Care Center,

in order to minimize all the time spent by the nurses

to perform all home care visits. This optimization

problem, is formulated and solved on some general

assumptions. In this sense, it was considered the fol-

lowing assumptions:

• Patients who live in the area of Health Care Center

can have different proﬁles.

• A patient proﬁle is assumed to be known a priori

and does not change during the home care visit.

• The number and average duration of the treat-

ments that characterize a patient proﬁle are known

and are the same among the patients who have the

same proﬁle (deﬁned and given by Health Care

Center).

• The number of patients who need home care ser-

vices and assigned to a working day is known in

advance and does not change during that day.

• Human resources that perform home care visits

are known in advance.

• All the patients assigned to a working day are cov-

ered, which means that all the patients admitted

to the home care visits should be assigned to the

nurses set.

• The locations of all patients are known in advance.

• The time matrix of travel between all the localities

is also known in advance.

• All the travels begin and end up in the Health Care

Center.

• It was considered 15 minutes for the trip, in the

same city, to visit different patients.

Automatic Nurse Allocation based on a Population Algorithm for Home Health Care

397

Taking into account all the above assumptions for

a working day, consider the following general param-

eters for the formulation of nurses’ schedule:

• N is the total number of nurses assigned for home

care visits.

• P is the total number of patients that need some

treatments at their homes.

• L is the total number of different patients’ loca-

tions.

• The list of the treatments that each nurse can per-

form.

Consider the variable X = (p

, ..., p

, ..., n

where the patient p

will be visited by the nurse n

for i = 1, ..., P, and X ∈

{

1, · ·· , P

}

{

1, · ·· , N

}

Then, for a given X it is possible to deﬁne the

nurse schedule and also the total time needed by each

nurse to ﬁnish her work. So, consider the objective

function T

(X) deﬁned as

f (X) = max

n=1,...,N

(X) (1)

which represents the time spent by the nurses to per-

form all treatments, including the returning journey to

the Health Care Center.

Then the constrained integer optimization prob-

lem will be deﬁned as

min f (X)

s.t. 1 ≤ p

≤ P, i ∈

{

1, ..., P

}

, p

integer

1 ≤ n

≤ N, j ∈

{

1, ..., P

}

, n

integer

∪

i=1

{

1, ..., P

}

(2)

4 GENERAL REAL DATA

It is intended to apply the developed problem formu-

lations to a real problem of the Health Care Center.

The data provided by the Health Care Center concern

the day April 18, 2016. The data used were available

by the Healthcare Center of Braganc¸a (chosen by the

institution and simulated a normal working day in the

center), that is, simulated for nurses allocation.

The home care services provided by the assigned

nurses to this job can be classiﬁed into ﬁve different

treatments (or home care visits). The treatments are

thus divided according to their diversity. Thus, Treat-

ment 1 (T.1) refers to curative care with an average

time of 30 minutes, while Treatment 2 (T.2) refers to

Surveillance and Rehabilitation, with an average du-

ration of 60 minutes. Treatment 3 (T.3) is Curative

and Surveillance care averaging 75 minutes, while

Treatment 4 (T.4) is only Surveillance care and has

an average care of around 60 minutes. Finally, Treat-

ment 5 (T.5) concerns more general health care such

as support and monitoring and has an average of 60

minutes as well.

On April 18, there were thirty one patients who

needed home care visits by Health Care Center. The

thirty one patients are from twelve different locations

of the Braganc¸a region, that belong to the action area

of the Health Care Center. In Table 1, the locations are

represented by the corresponding abbreviation. From

hereafter it will be used only these abbreviations. In

third column it is shown the related number of pa-

tients who need health care. The major part of the

patients (18) are from Braganc¸a city while 13 patients

are from rural localities around Braganc¸a.

Table 1: Locations and total number of patients in each one.

Localities Abbreviations Number of Patients

Braganc¸a Bg 18

Parada Pa 2

Rebordainhos Re 1

Carrazedo Car 1

Espinhosela Esp 1

Rebord

aos R 1

Salsas Sal 1

Serapicos Se 1

Outeiro Ou 1

Meixedo M 1

Bragada Bda 1

Milh

ao Mil 2

Each patient, required speciﬁc medical assistance,

one or more different treatments from the 5 treatments

that the nurses can performed.

On the other hand, the time required to travel be-

tween two locations is shown in Table 2. It was as-

signed 15 min to travel between two different places,

in the same location.

Based on all the general data presented, the ob-

jective is to minimize the total time required for each

nurse to provide all the treatments to all patients and

return to the Health Unit in order to obtain the nurses

allocation in a speciﬁc schedule. In addition to all

the data previously presented, more speciﬁc informa-

tion is needed to produce nurses’ schedule. Thus, it is

necessary to know, how many nurses are available for

the study day and what treatments each one performs

(nurses are allocated in different types of treatments,

information obtained by the Health Care Unit).

The Health Care Center has twelve nurses desig-

nated to perform home care visits during the day in

study. Table 3 shows the type of treatment that each

nurse can perform, as well as the average time of each

treatment.

ND2A 2020 - Special Session on Nonlinear Data Analysis and Applications

398

Table 2: Data about travel times between different locations (in minutes).

Bg Pa Re Car Esp R Sal Se Ou M Bda Mil

Bg 15 28 25 26 20 14 23 31 23 20 22 24

Pa 28 15 27 39 37 25 25 23 27 40 26 36

Re 25 27 15 33 34 22 12 20 32 37 14 33

Car 26 39 33 15 24 23 34 42 38 39 33 39

Esp 20 37 34 24 15 24 32 40 33 18 31 34

R 14 25 22 23 24 15 20 28 26 27 19 27

Sal 23 25 12 34 32 20 15 8 30 34 9 31

Se 31 23 20 42 40 28 8 15 38 42 17 39

Ou 23 27 32 38 33 26 30 38 15 29 30 14

M 20 40 37 39 18 27 34 42 29 15 34 31

Bda 22 26 14 33 31 19 9 17 30 34 15 31

Mil 24 36 33 39 34 27 31 39 14 31 31 15

Table 3: Treatments performed by the nurses.

T.1 T.2 T.3 T.4 T.5

(30 min) (60 min) (75 min) (60 min) (60 min)

Nurse 1 X X

Nurse 2 X X X

Nurse 3 X X

Nurse 4 X X X

Nurse 5 X X

Nurse 6 X X X

Nurse 7 X X X

Nurse 8 X X

Nurse 9 X X

Nurse 10 X X

Nurse 11 X X

Nurse 12 X X

5 PARTICLE SWARM

OPTIMIZATION

The global optimization method used to solve the

constrained integer optimization problem deﬁned in

(2) was the Particle Swarm Optimization (PSO). This

method is a population-based stochastic optimization

technique that is brieﬂy described in the following.

The Particle Swarm Optimization was developed by

Kennedy and Eberhart (Kennedy, 2010) and it is in-

spired on natural social intelligent behaviors of bird

ﬂocking.

PSO is a computational method that optimizes a

given problem by iteratively measuring the quality of

the various solutions. This method consists in the

optimization of an objective function through the ex-

change of information between individuals (particles)

of a population (swarm).

The PSO idea is to perform a set of operations and

move each particle to promising regions in the search

space (Poli et al., 2007; Imran et al., 2013).

The steps of the PSO are presented in Algorithm 1.

Algorithm 1: Particle Swarm Optimization.

1: Generates a randomly population of individuals, P

, with dimension

pop

2: Set the values of w, c

, r

. Deﬁne c

, r

random numbers in [0, 1].

Set v

= 1, for i = 1, ..., N

pop

, and k = 0.

3: while stopping criterion is not met do

4: Set k = k + 1.

5: Update the value of xbest

for the individual with index i,

for i = 1, ..., N

pop

6: Update the value of gbest for all population P

, for j = 1, ..., k.

7: Update the individual velocity according to:

k+1

= wv

+ c

(xbest

− x

) +

(gbest − x

8: Update the individual position according to: x

k+1

= x

+ v

k+1

9: If necessary, adapt x

k+1

to a feasible schedule.

10: end

11: The solution is given by gbest

At each iteration the velocity of each individual i,

, is adjusted. The velocity calculation is based on

the best position found by the neighborhood of the in-

dividual, the best position found by the particle itself

- xbest and the best position found by the whole pop-

ulation, taking into account all individual - gbest or

the best position overall (Bratton and Kennedy, 2007).

During the iterative process if any coordinate of x

k+1

falls outside the search space it is projected to the fea-

sible region.

The iterative procedure ends after a maximum

number of iterations and/or after a maximum number

of function evaluations.

6 RESULTS AND DISCUSSION

The main objective is to produce the best allocation

for the existing problem in Health Units: nurses’

schedule for home care visits.

Automatic Nurse Allocation based on a Population Algorithm for Home Health Care

399

The present study was carried out at the Health

Care Center of Braganc¸a, on a date provided by the

Health Center, April 18, 2016. The planning daily

route carried out on April 18 was made manually,

that is, without any mathematical model or subject

to computational mechanisms. The nurses’ schedule

was built and made available by the Health Care Cen-

ter on April 18 for the twelve nurses that performed

the home care visits in that day.

Analyzing the scheduling carried out manually by

the Health Care Center, it is possible to conclude that

all nurses have different work schedules ranging from

86 to 369 minutes. The number of patients that each

nurse visits change from 1 (Nurse 8) to 7 (Nurse 3)

and the Nurse 3 has the highest time to provide the

home care visits. The time needed for each nurse to

perform the health treatment is shown in the Table 4.

Table 4: Time needed to perform home care visits by each

nurse.

Time (minutes)

Nurses

1 221

2 260

3 369

4 212

5 86

6 90

7 241

8 70

9 194

10 90

11 240

12 183

On this working day, the highest time needed for

home visits ended after 369 minutes. Therefore, and

as mentioned above, the HUB presents an inconsistent

schedule, with nurses performing many home care

visits and others performing only one, ending with

quite different travel times. Once again, and as men-

tioned above, the Health Unit of Braganc¸a presents an

inconsistent schedule, with an unbalanced workload.

The idea is to optimize this process of home care

visit, and produce for the day in question (April 18,

2018), the nurses’ best allocation.

In an attempt to plan the schedules automatically,

one computational algorithm was used — the Particle

Swarm Optimization method.The numerical results

were obtained using an Intel(R) Core(TM) i7 CPU

2.2GHz with 6.0 GB of RAM and using the MatLab

software. The ﬁxed variable values for both methods

were N

pop

= 30, w = 1 and c

= r

= 2.

Since the PSO is a stochastic method, each imple-

mentation was tested with 100 runs in order to evalu-

ate the results obtained and compare them with those

originally elaborated by the Health Care Center. The

stopping criteria were based on the maximum number

of function evaluation and maximum number of itera-

tions that were limited to 5000 and 1000, respectively.

PSO had 100% of successful rate since they found

a feasible solution in all runs. The Figure 3 depicts

the obtained solution using PSO.

Regarding the identiﬁcation of patients and treat-

ments, P(1) - T.1 represents Patient 1 who needs

Treatment 1. For example, the schedule of the Nurse

1, which has an effort per day of 4 hours, will be:

moving from the HUB to the village of Parada (Bg -

Pa) to carry out the home care visit of Patient 2, who

requires the Treatment 1 (P(2) - T.1). After this, the

nurse returns to the point of origin, the Health Care

Center (Pa - Bg). For this nurse, the time spent in this

home care visit was 86 minutes.

From Figure 3 it is possible to see that the maxi-

mum time needed for the last nurse to perform all the

visits and return to the Health Care Center was 260

minutes. The solution obtained has a signiﬁcant time

reduction (109 minutes) when compared to the HUB

manual allocation/planning, which was 369 minutes.

Table 5 presents the summary of PSO results, such

as: the best optimal solution found among all runs

( f

∗

min

), the average optimal solution ( f

∗

avg

), and, ﬁ-

nally, the average time needed to solve the optimiza-

tion problem (Time

avg

) in seconds.

Table 5: Results obtained by PSO method.

∗

min

∗

avg

Time

avg

(s)

PSO 260 307 98

Analyzing the numerical results presented in the

previous table, it is possible to verify the minimum

total time found by PSO is 260 minutes and the av-

erage optimal solution among all runs was 307 min-

utes. Finally, it appears that the average time to solve

the problem was 98 seconds, which means that PSO

found the optimal solution very quickly.

In PSO, it was obtained an optimal solution, ﬁnd-

ing the best nurse allocation, searching for the best

workload balancing as well as minimizing the maxi-

mum time in home care visit. This allows conclude

that the Health Care Center can now opt for an opti-

mized allocation that proposes the end of visits after

260 minutes.

In order to compare (in an easy and fast way) the

time spent by each nurse, using the PSO allocation

and the time obtained manually by the HUB, Table 6

lists for each nurse (ﬁrst row), the time needed to ﬁn-

ND2A 2020 - Special Session on Nonlinear Data Analysis and Applications

400

# Nurse Start Effort

1 Nurse 1 18//04//2018 9:00 AM 4h

2 Nurse 2 18//04//2018 9:00 AM 4h

3 Nurse 3 18//04//2018 9:00 AM 4h

4 Nurse 4 18//04//2018 9:00 AM 4h

Bg - Pa

Bg - Re

Nurse 5

Nurse 6

Nurse 7

Nurse 8

Nurse 9

Nurse 10

Nurse 11

Nurse 12

Allocation using PSO

P(3) - T.1

Bg - Sal

Bg - Pa

Bg - Mil

Bg - M

Bg - Esp

P(2) - T.1 Pa - Bg

P(6) - T.2 P(5) - T.2 P(7) - T.2

P(14) - T.1 Sal - Bg

Re - Bg

P(29) - T.4 Bg - Car P(8) - T.1 Car - Bg

Bg - Bg

P(1) - T.1 Bg - Bg

P(26) - T.4 P(10) - T.1 P(15) - T.3 Bg - Bg

18//04//2018 9:00 AM

P(21) - T.4 P(18) - T.5 P(28) - T.4

Bg - Bg

P(20) - T.3 Bg - Se P(16) - T.4 Se - R P(11) - T.1 R - Bg

P(17) - T.1 Pa - Bg

P(30) - T.4 Mil - Bg P(23) - T.1 Bg - Bda P(25) - T.4 Bda - Bg

P(22) - T.1 M - Mil P(31) - T.4

Mil - Bg

P(12) - T.1 P(4) - T.1 Bg - Bg

P(9) - T.1 Esp - Bg

P(24) - T.1 P(27) - T.4 Bg - Ou P(19) - T.1

Ou - Bg P(13) - T.1 Bg - Bg

Time Travelling

Treatment time

Return to Health Unit

Figure 3: Automatic Nurse Allocation for HUB Scheduling.

ish the home care visits done manually (second row)

and the obtained time spent with PSO (third row).

Table 6: Total time spent by each nurse in home care visits.

Time required in each nurse allocation

Nurses Manual PSO

1 221 86

2 260 260

3 369 105

4 212 225

5 86 218

6 90 240

7 241 253

8 70 86

9 194 242

10 90 255

11 240 70

12 183 241

From the above table it is possible to state that

with PSO algorithm, the maximum time spent by the

nurses is 260 minutes. In turn, the maximum time

spent by the nurses in HUB scheduling is 369 min-

utes (greater than the PSO computational solution).

On the other hand, an automatic allocation is achieved

that allows a faster solution and its quick replacement,

if necessary, a better workload balance, favoring not

only the work of nurses but also limiting the patients’

waiting time.

7 CONCLUSIONS AND FUTURE

WORK

Since, at the HUB, home care visits are planned man-

ually and without computational support, this implies

that the nurse’s allocation of home care visits may not

be the most appropriate in terms of the logistics of

nurses and patients.

In this way, and in an attempt to optimize the lo-

gistic process, specially in the nurses allocation, it

is necessary to use strategies to minimize the maxi-

mum time spent by each nurse on home care sched-

ule, without, however, worsening the quality of the

provided services and, always, looking for the best

schedules organization. Optimization can be used

very advantageously in the context of Health Care

Centers allocation for home care aged people visits.

The allocation problem of nurses in the HUB was

efﬁciently solved using the PSO method. When com-

pared to the manual solution and in use by the health

unit, the maximum value of home visits was opti-

mized, from 369 to 260 minutes, improving the work

effort required by nurses. Moreover, the optimal solu-

tion was found quite fast and provides a better nurses

workload balancing. This approach represents a gain

for all the involved people, health professionals and

patients.

For future work, it is possible to reformulate the

Automatic Nurse Allocation based on a Population Algorithm for Home Health Care

401

problem taking into account a multi-objective ap-

proach providing strategic, tactical and operational

decision-making support. This approach may con-

sider minimizing not only the maximum time for each

nurse, but also minimizing the total kilometers per-

formed and necessary for each car, and also minimiz-

ing the total cost involved. In addition, as a future

approach, more real health problems (with different

parameter sizes) will be considered and compared not

only to the manual case, but also with other stochastic

algorithms in the literature, such as the Genetic Algo-

rithm.

ACKNOWLEDGEMENTS

This work has been supported by COMPETE:

POCI-01-0145-FEDER-007043 and FCT - Fundac¸

para a Ci

encia e Tecnologia within the projects

UID/CEC/00319/2019 and UIDB/5757/2020.

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