Fábio Lima
Centro
Universitário FEI, Brazil
E-mail: flima@fei.edu.br
Matheus Felipe
Cortez
Centro
Universitário FEI, Brazil
E-mail: mfrcortez@hotmail.com
Patricia Pessoa
Schmidt
Centro
Universitário FEI, Brazil
E-mail: patri_schmidt@hotmail.com
Ana Karoline
Silvério
Centro
Universitário FEI, Brazil
E-mail: anakaroline.silverio@gmail.com
Alfredo Manoel
da Silva Fernandes
Incor-Universidade
de São Paulor-HC, Brazil
E-mail: alfredo.fernandes@incor.usp.br
João Chang
Júnior
Centro
Universitário FEI, Brazil
E-mail: chang.joao@gmail.com
Submission: 2/21/2020
Revision: 2/24/2020
Accept: 3/9/2020
ABSTRACT
This paper presents a simulation of an ambulatory processes using timed Petri net (TPN). The simulation considers the flow of patients in the biggest Brazilian cardiology hospital. The TPN is used as a decision support system (DSS) to improve the processes, to reduce the waiting time of the patients in the ambulatory and in this way to assure a high-quality service to the patients. Simulations were carried out using the software Visual Object Net++. This is a free software and therefore the presented solution is a low-cost solution. Providing a low-cost solution has a huge importance in this work since the hospital is kept from the government efforts and operates with limited financial resources. The patients’ flow in the hospital can be faced as a service and the modelling and optimization of these services bring more efficiency to the system as well as improve the human factors involved. The results proved that some changes could be made in the processes to improve the performance of the system.
1.
INTRODUCTION
Hospital
care and organization in ambulatory sectors of hospitals are the main critical
points of the Brazilian public health system. According to the City Hall, the
number of people who go to ambulatories in São Paulo, one of the largest
conurbations of the world, is huge when compared to other hospital sectors.
Thus, it is extremely important to improve the flow and optimize individuals’ length
of stay in the system.
Even
though in Brazil the total per capita spending on healthcare grew 102.8 %
between 1999 and 2009 (Araujo,
Barros & Wanke, 2014) the public health system in
Brazil still suffers from limited resources. For this reason, finding
cost-effective solutions that improve the performance of public health systems
is crucial.
A
recent survey performed by one of the most important survey institute in Brazil
showed that the public health care system is considered the most important problem
in the year of 2019 (Datafolha,
2019). Figure 1 presents the graphical results of the that survey.
The
main objective of this study is to analyze quantitatively the performance of
the ambulatory sector of a public hospital specialized in cardiology, using the
Petri Net tool as a Decision Support System (DSS). The patient’s flow (Ling & Schmidt, 2000; Wang &
Zeng, 2008; Wang, Li & Howard, 2013; Rohleder
et al., 2011) of the ambulatory is modelled. The
diagnosis obtained through this tool were interpreted to reach a qualitative
solution.
Petri
Nets (PN) (Murata, 1989) is used in this study, which is a tool to model and
project systems, using a mathematical representation of the system. In the
Petri Net model, two events that are enabled and do not interact may occur
independently (parallelism or competition). It is not necessary to synchronize
events, unless it is required by the system being modelled. This way, these
events become ideal to model systems of distributed control, with multiple
processes executing concurrently in time. From a logical perspective, the only
important property of time is to define a partial order of events occurrence.
Considering
the theoretical context of Petri Nets, this study initially explores the
techniques of modeling and analysis of health systems (HS) (Xiong, Zhou & Manikopoulos, 1994) based on techniques of discrete events simulation. It is
sought to highlight the potential that the Petri Net has as a technique to
characterize logical structure and systems’ dynamic behavior, in an accessible
language to different professionals, being efficient in its analysis.
The
health system is classified as a system of discrete events defined by
activities from doctors, nurses, technicians, and patients, among others. They
are mapped through states of the health systems, whose evolution (change of
states) may be defined by the occurrence of discrete events (Rau et al., 2013).
Thus,
a simulation tool may raise its dynamic behavior through some explicit rules
and an adequate model, allowing a safe and economic analysis of the decisions
that affect it.
The
Petri Net, among other tools, is one that presents several appropriate tools to
model the health service. As previously mentioned, it has a relatively “simple”
graphic representation, which allows a precise interpretation and makes
dialogue among teams that participate in the system analysis easier. Another
advantage is the ability to build the model in different hierarchical levels of
abstraction (with higher or lower level of details). Finally, it specifies
cases in which items (patients, doctors, medical charts, equipment, etc.)
interact in situations of conflict (occurrence of competition among items for
the same resource), parallelism (occurrence of events in parallel), and sequentialization
(occurrence of events in sequence).
Figure 1: Brazil’s problems according to
citizens
Source: adapted from: Datafolha (2019)
The
paper section structure is: related work; the basics of PN; the ambulatory flow
description; the Petri net models; chosen simulation results and finally, the
conclusion.
2.
RELATED WORK
As
mentioned before, the HS can be modelled and analyzed as a discrete event
system. Several articles use this approach to propose improvements in such
systems using different methods. Some of them uses the Petri net as the main
tool of modelling. Following some related works are presented in chronological
order considering several aspects in HS. The comments highlight the main
features and findings in each article.
An
analysis of the literature in health care is provided by (Brailsford et al.,
2009). The authors separated the articles in several groups to discuss the
consistence of the literature in that area. It is noticed that one of the most
used methods to face health care problems is the discrete event simulation.
Another
review of using Discrete Event Simulation (DES) in HS is presented in (Günal
& Pidd, 2010). The authors discussed the increase number of papers in this
subject from 2004 e also highlight that most of the papers addressed specific
models. General models are still missing.
A
TPN solution is proposed by (Dotoli et al., 2010) applied to a pulmonology
department in a hospital, focusing on the department workflow and the drug
distribution system.
A
stochastic PN is proposed in (Leite et al., 2010) to model the medical care
provided to patients in the intensive care unit.
In
(Astilean et al., 2010) a flexible support system to offer warnings, therapies
and recommendations for remote patient surveillance is presented. An inference
mechanism based on Petri nets and Fuzzy theory was designed and experimentally
implemented for diseases evolution supervising purposes.
Another work that used
DES applied to hospital problems is found in (Rys, 2011). He used the Arena
software (which is not a free software) to analyze the arrival pattern of
patients in an ED.
An
analysis of complex processes in nursing and caregiven services is presented in
(Hiraishi et al., 2012).
After that, the authors propose an implementation based on object-oriented
Petri net.
In
(Mahulea, Garcia-Soriano
& Colom, 2012) HS is modelled using modular Petri
nets. The first module modelled the medical protocols as state-machine Petri
nets and the second add the (shared) medical resources.
In
(Fanti et al., 2013), a three-level strategy of solving HS problems is
proposed. PN is used in the three levels, which are modeling, optimization and,
simulation and decision.
Several
works consider the use of Petri nets for solving problems related to the health
systems (HS). In (Fanti
& Ukovich, 2014) a review of techniques and
models applied to HS are made. The use and importance of TPN is demonstrated.
An
application of PN applied to health care at home is presented in (Fanti et al., 2014). The proposed model detects troubles as accidents and
inform the doctor, the family or the emergency system.
Evolutionary
PN was used by (Suzuki
& Hamagami, 2014) applied to a team medical care
support.
A
PN model for primary HS systems is proposed by (Mahulea et al., 2014).
In that work, the authors modelled the diseases and medical protocol using a
state-machine Petri net.
A
modeling methodology of the primary healthcare system based on Petri nets is
presented in (Mahulea et
al., 2014). A disease of a patient is diagnosed and
cured by following a sequence of treatments and cares belonging to a medical
protocol.
The
researches (Emami & Doolen, 2015) conducted a work in a hospital concerning
the development of a set of
forward-looking metrics at the operational level that should drive all aspects
of performance. They used Analytic Hierarchy Process (AHP) to determine the
most important learning and growth categories and metrics within each category.
Differently of this
proposed work, (Cho, Song & Yoo, 2015) proposed and outpatient process analysis based on process mining.
The idea was to identify the patterns from the hospital data for future use in
the hospital strategies.
A forecast model for
Emergency Departments (ED) using regression and Neural Networks was carried out
by (Gul & Guneri, 2016). The work used the data from a public hospital in
Istambul and the results achieved aimed at providing the managers of the
hospital an accurate forecast to take decisions on ED.
The
objectives of the paper from (Hsieh, 2017) are to propose a viable and
systematic approach to develop a scalable and sustainable scheduling system
based on multi-agent system (MAS) to shorten patient stay in a hospital and
plan schedules based on the medical workflows and available resources. To
achieve interoperability and sustainability, Petri Net Markup Language (PNML)
and XML are used to specify precedence constraints of operations in medical
workflows and capabilities of resource agents, respectively.
The
work of (Khayal & Farid, 2017) is focused on patients with chronic diseases
rather than the traditional models based on patient throughput. paper develops a healthcare dynamic model for
personalized healthcare delivery and managed individual health outcomes. It
utilizes a heterofunctional graph theory rooted in Axiomatic Design for Large
Flexible Engineering Systems and Petri nets.
The
paper from (Mahulea et al., 2018) presents a modular approach for modeling
healthcare systems using Petri nets. It is shown that a healthcare system can
be constructed by different modules whose inputs and outputs are connected
according to their geographical location. A
public healthcare area in Zaragoza is considered as a use case.
The
work of (Li et al., 2018) focuses on a cloud healthcare
system, which is a novel integrated healthcare system by the technique of
Internet in very recent years. A Petri net is presented to describe the
relationship among medical process and resources in that integrated healthcare
system.
The
paper of (Bernardi, Mahulea & Albareda, 2019) presents a decision support
system to be used in hospital management tasks which is based on the clinical
pathways. They propose a very simple graphical modeling language based on a
small number of primitive elements through which the medical doctors could
introduce a clinical pathway for a specific disease.
The
paper from (Zhou, Wang & Wang, 2019) presents a generic and resource
oriented stochastic timed Petri Nets (STPN) simulation engine that provides all
critical features necessary for the analysis of service delivery system quality
vs. resource provisioning. The power of the simulation system is illustrated by
an application to emergency health care systems.
3.
METHODOLOGY
This
methodological work is quantitative and exploratory. The methodological
approach adopted is modeling and simulation, comparing quantitatively the
results obtained from the computer simulation of two laboratories in the
largest cardiology hospital in Brazil. The use of Petri nets and free software
promoted low-cost analysis for the hospital as a support in its
decision-making. The results show the impact of the proposed solutions on the
performance of the outpatient clinics.
4.
BASICS ON PETRI NETS
Petri
nets are a graphical and mathematical modeling tool applicable to many systems
(Murata, 1989). The conceptual paradigm of Petri nets deals inter alia
with modeling, logical analysis, performance evaluation, parametric
optimization, dynamic control, diagnosis and implementation issues (Silva,
2013). This work uses TPN for modeling the workflow
in a Brazilian cardiology hospital. Following are presented the basis of TPN
extracted exactly as appears in (Fanti et al., 2013; Peterson,1981).
Definition
1: A TPN (Peterson,
1981) is a bipartite digraph described by the
five-tuple TPN = (P, T, Pre, Post, F), where P,
T, Pre, Post, and F are defined as follows:
a) P is a set of places with |P| = m.
b) T is a set of exponential transitions with |T| = n.
c) Matrices Pre : P × T → ℕmxn and Post
: P × T →
ℕmxn
are the pre- and post-incidence matrices, respectively, that
specify the arcs connecting places and transitions. More precisely, for each p ∈ P and t ∈ T element, Pre(p,t) [Post(p,t)] is
equal to a natural number indicating the arc multiplicity if an arc going from p
to t (from t to p) exists, and it equals zero if
otherwise.
d) Function F: T → ℝ+ specifies for each
exponentially distributed timed transition tj ∈ T the average firing delay, i.e., F(tj) = 1/lj, where lj is the parameter of the corresponding
exponential distribution.
Note
that ℕ is the set of nonnegative integer numbers, and ℝ+
is the set of nonnegative real numbers.
The
m × n incidence
matrix of the net is defined as C = Post
- Pre. Moreover, for the pre- and
postsets, it is used the dot notation, e.g., •p = {t ∈ T : Post(p, t) > 0} is the transition preset of p.
The
state of a TPN is given by its current marking, which is a mapping M → ℕm, assigning to
each place of the net a non-negative number of tokens. M is described by a |P|vector, and the ith component of M, indicated with Mi,
represents the number of tokens in the ith place pi ∈ P. A TPN system <TPN,M0> is a TPN with initial marking M0.
A transition tj ∈T is enabled at a marking M if and only if (iff), for each pi ∈ •tj , Mi ≥
Pre(pi, tj) holds, and
the symbol M[tj> denotes that tj ∈T is enabled at marking M. When fired, tj produces a new marking M’, denoted by M[tj>M’ that is computed by the PN state
equation M’=M+ C, where is the n-dimensional firing vector
corresponding to the jth canonical basis vector.
To
solve the confliction transition problems, probability values are assigned to
edges connecting places and the multiple transitions in their postset. Hence,
function RS: P×T → ℝ+ associates a
probability value called random switch to conflicting transition edges.
A
TPN system is denoted by the couple <TPN,M0>.
5.
AMBULATORY FLOW DESCRIPTION
The
ambulatory is divided into two parts: the General, which is the gateway of
patients at the ambulatory, and whose focus is to provide an initial treatment;
and the Specialties, which aims at continuing the treatment of those patients
who did not receive discharge from the General ambulatory.
5.1.
General Ambulatory
Patients
may be received by the SUS (National Health System) of São Paulo and all
queries have an appointment.
Initially,
a new patient will enter the General ambulatory. On the appointed day, he must
go to the entrance counter and fill your registration form to then wait for the
query in the waiting room. After the consultation, the patient should return to
counter and remove a chip on which the information will be the next steps of
treatment. Generally, the doctor asks some exams, which can be done in the
clinic and the patient bring them back in the query. There is a counter to input,
two for requesting the return, registration or discharge and five offices that
will serve patients waiting at the waiting room.
5.2.
Specialties Ambulatory
Once
registered, the patient will go to treatment in Specialties ambulatory that
aims at serving patients in different offices depending on their specific
problem. This ambulatory has 19 Specialties and follows the same dynamics of
the General: the patient, with an appointment, arrives on the counter and waits
at the waiting room; after being served, he goes to a counter in the ambulatory
entrance and removes the sheet that contains the information of the next steps.
There
is also the possibility of returning to the Specialties ambulatory. Depending
on the severity of the patient’s problem, the doctor may request that it
conduct exams, or even forwards it to the surgery room. In this case, after
surgery, the patient should mark a return for a follow-up. If the patient does
not show more symptoms, he gets a medical discharge. Figure 2 presents a flowchart of the real condition of both General
and Specialties ambulatory.
5.3.
Data Set
The
data from the General Ambulatory are presented in tables 1 and 2. Table 1
presents the ambulatory patients entrance data and 2 presents the awaiting time
of the patients (in hour:minute:second format). The data from the Specialties
Ambulatory are presented in tables 3 and 4. Table 3 presents the ambulatory
patients entrance data and 4 presents the awaiting time of the patients (in
hour:minute:second format).
6.
PETRI NET MODEL
The
Petri net model was developed to the ambulatories using the Visual ObjectNet ++
software. The transition times mean the time of each step, in minutes, from
table 2 and 4. The values presented in the positions mean the flow of people
during the month of April. This month was chosen because it represents the most
critical situation in terms of number of patients.
Figure 2: Ambulatories flowchart
6.1.
General Ambulatory
The
beginning of the General ambulatory process is presented in Figure 3.
New
patients represented by New Arrivals position (NA) and patients with scheduled
return, represented by Return Arrivals (RA), coming into the system and are
leaded to the Entrance Counter (EC), when it is free (ECF). To define the
service order in EC, synchronizers (S1 and S2) were used, allowing patients to
return to EC along with others. If there is no return patient, Arrivals Free
Return position (AFR) remains with the token and the simulation usually
continues with new patients. The position Awaiting Consultation (AC) indicates
that the patient is awaiting from the moment it takes the return guide to
re-enter the system.
After
entering the EC, the patient goes to the Waiting Room (WR). To facilitate the
construction of the model, the position Distribution (DIST) was created and the
Waiting Room (WR) was divided into five units. However, this adjustment does
not change the result of the simulation. Again, it was used synchronizers (S3,
S4, S5, S6 and S7) to direct patients to doctor’s offices.
After
waiting the average waiting time, the patient enters in one of the Doctors’
Offices (O1, O2, O3, O4 or O5), and after the end of the consultation, is aimed
at Counter Queue (CQ) to wait for service. Patients are only released to enter
the office when the Free Office position (FO1, FO2, FO3, FO4 or FO5) is with
one token. This model is shown in Figure 4.
|
|
Figure
3: General ambulatory
entrance |
Figure
4: Doctor’s offices –
General ambulatory |
According
to Figure 5, when leaving the queue, the patient will be treated in one of the
return counters, registration or discharge (REG and DISC). At this stage, the
patient may receive the guide for exams at the
ambulatory itself, which will be presented at follow-up visit, discharge
from the doctor, or lead to the Specialties ambulatory, which will hold its
registration.
Synchronizers
of capacity (SC1, SC2, SC3, SC4, SC5 and SC6) are used to direct the correct
number of patients that receive a demand for exams, discharge or are leaded to
registration.
Figure
6 presents the entire Petri net model for the General ambulatory.
Figure 5: Patient flow - General ambulatory
Figure 6: General ambulatory: complete model
6.2.
Specialties Ambulatory
The
first step at Specialties ambulatory is the admission of the patients from
registration, represented in the Petri net of the Figure 7 by the position New Arrivals (NA). The patients from
return, represented by the position Return Arrival (RA), go to the Entrance
Counter (EC). Again, as in the General ambulatory, synchronizers (S1 and S2)
were used allowing that patients from return could be admitted in the EC
position as well as the patients from registration. In case there is no return
patient the position Entrance Counter Free (ECF) remains with the token
allowing the continuity of the simulation with the patients from New Arrivals.
Position FAR (Free Arrival Return) allows the admittance of a patient
from return.
Leaving
the Entrance Counter, the patients are redirected to the waiting room for after
being attended in one of the nineteen doctors’ offices of the Specialties
ambulatory. A position called DIST was inserted in the model (Figure 8) to
allow the entrance of the patients into the doctors’ offices. Again,
synchronizers were inserted to lead the patients from the waiting room to the
doctors’ offices. After consultation, the patients go to the counter queue
(CQ).
After
being attended in the Specialties Ambulatories Counter (SAC), the patients are
leading to exams (EXAM), to the surgery room (SR) or directly to return. Some
patients after consultation go to discharge and leave the system. Figure 9
presents the flow of patients in the described system.
Figure 7: Specialties ambulatory entrance
Table 1: General
Ambulatory Entrance Data
|
Jan |
Feb |
Mar |
Apr |
May |
Jun |
Jul |
Aug |
Sep |
working days |
22 |
19 |
20 |
22 |
21 |
20 |
22 |
22 |
21 |
Patients - Total |
2102 |
1772 |
2005 |
2356 |
2296 |
2075 |
2177 |
2254 |
2245 |
New Patients |
1872 |
1578 |
1785 |
2098 |
2045 |
1848 |
1939 |
2007 |
1999 |
New Patients/day |
85 |
83 |
89 |
95 |
97 |
92 |
88 |
91 |
95 |
Return |
230 |
194 |
220 |
258 |
251 |
227 |
238 |
247 |
246 |
Return/day |
10 |
10 |
11 |
12 |
12 |
11 |
11 |
11 |
12 |
Table 2: Waiting Time
General Ambulatory |
|
Queue |
Counter |
Waiting Room |
Consultation |
Average |
00:07:05 |
00:02:23 |
01:07:28 |
00:22:08 |
|
Deviation |
0.00187 |
0.00073 |
0.02034 |
0.00746 |
|
Minimum |
00:00:00 |
00:01:13 |
00:29:42 |
00:09:12 |
|
Maximum |
00:11:28 |
00:05:50 |
01:59:25 |
00:45:13 |
Table 3: Specialties Ambulatory Entrance Data
|
Jan |
Feb |
Mar |
Apr |
May |
Jun |
Jul |
Aug |
Sep |
working days |
22 |
19 |
20 |
22 |
21 |
20 |
22 |
22 |
21 |
Patients - Total |
11460 |
9708 |
10528 |
11960 |
10977 |
10781 |
10504 |
12079 |
10515 |
New Patients |
1627 |
1378 |
1495 |
1698 |
1558 |
1531 |
1491 |
1715 |
1493 |
New Patients/day |
74 |
73 |
75 |
77 |
74 |
77 |
68 |
78 |
71 |
Return |
9242 |
7829 |
8491 |
9646 |
8853 |
8695 |
8471 |
9742 |
8480 |
Return/day |
420 |
412 |
425 |
438 |
422 |
435 |
385 |
443 |
404 |
Discharge |
591 |
500 |
543 |
616 |
566 |
556 |
541 |
623 |
542 |
Discharge/day |
27 |
26 |
27 |
28 |
27 |
28 |
25 |
28 |
26 |
Figure 8: Doctor’s
offices: Specialties ambulatory
Table 4: Waiting
Time
Specialties
Ambulatory |
|
Queue |
Counter |
Waiting Room |
Consultation |
Average |
00:03:56 |
00:01:12 |
01:21:42 |
00:29:51 |
|
Deviation |
0.00310 |
0.00039 |
0.02745 |
0.01220 |
|
Minimum |
00:00:00 |
00:00:35 |
00:24:03 |
00:06:30 |
|
Maximum |
00:11:25 |
00:02:02 |
02:40:01 |
01:09:40 |
Figure
9: Patients’ flow: Specialties ambulatory
7.
CHOSEN RESULTS
After
constructing the models, several scenarios were simulated with the intention of
optimize the system. This means to reduce the length of stay of the patient in
the hospital increasing the quality of the service provided.
7.1.
General Ambulatory
The
simulations focused on the most important positions (WR, CQ, Registration). The
current situation of the system was considered.
Figure
10 presents the number of patients in the waiting room before entering the
doctor’s office. From the Figure 10 it is possible to notice that the maximum
number of patients waiting is 12.
Position
CQ allows to understand the attendance distribution of the doctors’ offices in
the General ambulatory. The Figure 11 presents the uniform characteristic of
the distribution due to the fact of using an average time for all offices. It
is possible to notice some idle time since preceding positions (doctors’
offices, C1 to C5) be the bottleneck of the system. The idle time of the
Counter Queue is 38.8 minutes.
Figure
12 presents the result from the registration position. It is important to
notice here that in the simulation the synchronizers direct the first patients
to make exams, the following to exit and the last ones to the registration.
This guarantee that each position receives the correct number of patients per
day. The last patient for registration reaches this position in 2010.8 minutes.
After
the initial simulations, the model was modified with the intention of reducing
the idle time of the CQ position. The number of doctor’s offices was increased
from six to nine. It was observed that the best results were obtained with
eight offices, reducing the idle time of CQ from the original 38.8 minutes to
18.5 minutes. It means a reduction of 52.3% of the idle time. Increasing the
number of offices beyond nine did not affect the system. Figures 13 and 14
present the new graphics for the waiting room and the registration. The maximum
number of patients in the waiting room was decreased as well as the time for
registration of the last patient. The maximum number of patients at Waiting
Room is now four (reduction of 33%) and the total time for registration was
decreased to 1294.7 minutes (reduction of 36%).
The
second strategy was to change the number of counters after the consultation
(positions REG and DISC). Before changing the number of counters an analysis
was made to analyze the occupation of the counter REG. The result is presented
in Figure 15. It was observed a large idle time.
Considering
the result presented in Figure 15 it was proposed a new simulation reducing the
number of counters. A new simulation was carried out with a single counter. The
result is presented in Figure 16.
It
was observed that one counter is sufficient to attend the demand of patients
that come from the offices. This implies in a reduction of cost to the
hospital.
|
|
Figure 10: Waiting
room: Current situation |
Figure 11: Counter
queue: Current situation |
|
|
Figure 12: Registration:
Current situation |
Figure 13: Waiting
room: Proposed situation (8 offices) |
|
|
Figure 14: Registration:
Proposed situation (8 offices) |
Figure
15: Registration
Counter occupation |
Figure 16: New Registration Counter
occupation
7.2.
Specialties Ambulatory
The
system starts with patients from the General Ambulatory and patients who were
already in the system, for example, a person hospitalized after surgery,
performed previously, awaiting a return visit.
The
first study was carried out on the Discharge position, which is the total time
system simulation for a day, or as soon as the position reaches the number of
28 patients. In Figure 17, it is possible to identify this time as 2845.9
minutes.
After,
the occupation at the waiting room was verified. Figure 18 presents this
occupation. A maximum number of 23 patients was observed.
|
|
Figure 17: Discharge |
Figure 18: Waiting
room |
The
last analysis is related to the counter queue. Unlike the counter queue of the
General Ambulatory, there is no idle time to the counter queue of the
Specialties Ambulatory due the high number of doctors’ offices. There is a
cyclic behavior of the queue, summing 15 patients at the peak. Figure 19
presents this situation.
After
the simulation of the current situation of the Specialties Ambulatory some
proposals were applied in the simulation aiming at improving the performance of
the system. At first, a new counter was inserted in the system since as
presented before the counter queue has a peak of 15 patients. The results did
not bring any significance impact in the current situation. The number of
patients in the waiting room were not modified. The peak of patients in the
counter queue was reduced from 15 to 14 patients.
As
carried out to the General Ambulatory, the number of doctors’ offices was
increased. Increasing one office implied to a reduction of 1 patient in the
waiting room (from 23 to 22) and the peak of the counter queue was increased in
one patient (from 15 to 16).
In
a simulation considering 22 offices, the total time until the last patient out
the system (Discharge) was reduced in 10.8%. In the waiting room, the peak of
the patients achieved a maximum of 19. This condition is presented in Figure
20.
On
the other hand, the counter queue presented a crescent number of patients over
time as presented in Figure 21.
|
|
Figure 19: Counter
queue |
Figure 20: Waiting
room: 22 offices |
Figure 21: Counter queue: 22 offices
This
study showed that the addition of medical offices while benefiting the
distribution of patients in the waiting room and reduce the total simulation
time, overloads the service in the post-consultation counter. Therefore, it is
not justified the increase in the number of medical offices without making any
other changes related to the optimization of the service counters.
Considering
the number of patients in the post-consultation counter new simulations were
carried out considering the insertion of a new post-consultation counter.
The
best situation occurred with 21 doctors’ offices.
Table
5 summarizes the best results from the simulations of the General Ambulatory.
It compares the current real data of the General ambulatory to the best
scenario proposed from the simulations. Table 6 summarizes the best results
from the simulations of the Specialties Ambulatory.
Table 5: General
Ambulatory: Simulation Results
|
Current Situation |
Best Proposal (5 Offices) |
Waiting Room |
12 Patients |
4 Patients |
Counter Queue
(Patients) |
1 Patient |
1 Patient |
Registration |
2010.8 min |
1294.7 min |
Counter Queue
(Idle time) |
38.8 min |
18.5 min |
Table 6: Specialties
Ambulatory: Simulation Results
|
Current Situation
(19 offices – 1 counter) |
Best Proposal (21 Offices – 2
counters) |
Waiting Room |
23 Patients |
21 Patients |
Counter Queue
(Patients) |
15 Patients |
15 Patients |
Registration |
2845.9 min |
2586.1 min |
8.
CONCLUSIONS
This
paper presented a modelling and simulation of a cardiology hospital
ambulatories. The simulation using timed Petri nets showed itself a powerful
tool to analyze the flow of patients into the ambulatories. The simulation used
a free software providing a low-cost solution to the hospital. Two ambulatories
were modelled and simulated: General and Specialties.
The
models are connected since some patients from the General ambulatory can enter
the Specialties ambulatory. After modelling the current situation in both
ambulatories some proposals were made aiming at improving the performance of
the system. It was observed that some simple modifications have a huge impact
on the performance.
The
most impressive results were achieved in the General ambulatory. Increasing the
number of offices from five to eight implied in reduction of the total
patients’ time in the system as well as allowed the reduction of the number of
patients in the waiting room and the idle time of the counters.
Although
the models were constructed considering a specific situation of a Brazilian
hospital the paper contributes with the subject when presenting the possibility
of modelling these kinds of systems with a free software tool. The situations
modelled are typical of these systems so the models proposed could be easily
adapted for other hospitals.
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