Eurasian Journal of Health Technology Assessment
Corresponding Author: Mehmet ERDEM ,Vol. 2, No. 1
A literature review on Home Healthcare Routing and Scheduling Problem
Mehmet Erdem*,**‡, Serol Bulkan**
*Department of Industrial Engineering, Faculty of Engineering, Atilim University, Incek, 06836, Ankara, Turkey
**Department of Industrial Engineering, Faculty of Engineering Marmara University, Kadikoy, 34722, Istanbul, Turkey
‡
Corresponding Author; Address: Department of Industrial Engineering, Faculty of Engineering, Atilim University, Incek,
06836, Ankara, Turkey Tel: +90 312 586 83 26, Fax: +90 312 586 80 91, e-mail: mehmet.erdem@atilim.edu.tr
Abstract- The Home Healthcare Routing and Scheduling Problem (HHCRSP) involves some of the features of vehicle routing
and nurse rostering problem. Home healthcare is a part of health services, which can be defined as providing the necessary
services to the patients and their families within their familiar environments. Some of the issues such as aging population,
increasing diseases, shortage of workforce, economic reasons, innovation in medical technologies, preferences etc. increase the
importance and the need of Home healthcare. Furthermore, solution procedures for these routing and scheduling problems are
varied according to the assumptions. In this review, the most common characteristics of the problem and an overview of recent
works related to the HHCRSP are discussed.
Keywords- Literature Review, Home Healthcare, Operation Research, Vehicle Routing, Nurse Scheduling.
1. Introduction
Home healthcare (HHC) covers a set of
medical, therapeutic, and nonmedical services for
patients at their familiar environments. Generally,
it is considered as cost efficient, convenient, and as
effective as the care that the patients get in a
hospital. Ageing population, shortage of
workforce, economic reasons, innovation in
medical technologies, preferences of patients and
nurses, etc. that increase the demand/need for
HHC services in the near future as it is today
(Medicine, 2017). In the US, 9 million people
demand care services from regulated providers in
2014. The number of HHC agencies was 9024 in
2007 (Statista, 2015) and this figure was 12400 in
2014 (CDC, 2017). According to a report (R&M,
2017) the volume of HHC services reached $86
billion in 2016. In Europe, more than $20 billion
increase is expected in the volume of the HHC and
nursing care services, and this volume will reach
$232 billion in 2020. ın addition, 65 years or over
made up a 19.2% share of the EU-28’s population
and this group will rise and account for 29.1% by
2080 (Eurostat, 2017). Globally, estimations show
that in 2050 aged 80 years or over will number 434
million, which was 125 million in 2015 (Colombo
and et al.) (UN, 2015). Therefore, the increase in
elderly population leads to an increase number of
people living with chronic illnesses and disabilities
especially
in
developed
societies.
The
sustainability of HHC system is important in this
regard.
The decisions of Operations Management (OM)
can be divided into four level with respect to the
time horizon. These are strategic (1-5 years),
tactical (6-12 months), operational (weeksmonths), and detailed operational levels (hoursdays) (Matta et al., 2014). Furthermore, each of the
level has its own variety of scheduling,
assignment, and routing decision in the HHC
operations. Heterogeneous nurses and clients who
scattered in different geographical areas have a set
19
Erdem, M., Bulkan, S., (2017). A literature review on Home Healthcare Routing and Scheduling Problem , Eurasian
Journal of Health Technology Assessment, Vol. 2, No. 1, 19-33
Eurasian Journal of Health Technology Assessment
Corresponding Author: Mehmet ERDEM ,Vol. 2, No. 1
of characteristics, demands, and preferences. For
an appropriate solution, each side of concern
should be satisfied as much as possible. This is a
time consuming activity for experts who develop a
plan manually. Therefore, creating a suitable plan
in the predetermined planning horizon with a
minimum cost or a minimum deviation from
preferences is a necessity.
There are many studies exists in the fields of
Operations Research (OR) (Cissé et al., 2017;
Milburn, 2012) and OM (Fikar and Hirsch, 2017)
which are related to the HHCRSP. Many
researchers proposed a series of different models
dealt with the HHCRSP. These existing models
involve a set of various objectives and constraints.
Furthermore, solution procedures for these routing
and scheduling problems are varied according to
the assumptions, problem dimension, regulations,
etc. Consequently, the definition of this problem
and the meaning of terms can change in the
literature. The aim of this review is not only to
give insight about existing related literature, but
also to make classification/comparisons between
proposed (performance measures) models. Some
of the review papers (Braekers et al., 2016; Cissé
et al., 2017; Fikar and Hirsch, 2017; Mankowska
et al., 2014; Maya Duque et al., 2015) tackled with
the same issue and we consider these as a basis for
our work.
This review paper organized as follows: Section 2
introduces a brief description of the HHCRSP.
Section 3 gives the relevant and important
performance measures of the problem. Section 4
analyses existing publications according to their
constraints. Exact and metaheuristics solutions are
investigated in Section 5. Section 6 covers
conclusions and future research directions of the
HHCRSP.
2. Home Healthcare Routing and Scheduling
Problem
The Home Healthcare Routing and Scheduling
Problem (HHCRSP) involves some of the features
of vehicles routing problem with time windows
(VRPTW) and nurse rostering problem (NRP).
These are known as combinatorial optimization
problems. HHC is a part of the health services,
which can be defined as providing the necessary
services to the patients and their families within
their living environments. The aim of the HHC is
to increase the level of access to the maximum
treatment with minimum interruption of daily
living, to minimize the effects of the diseases and
the disabilities, and to raise the living conditions
(Karabağ, 2007). This problem concerns the
assignment, routing, and scheduling decisions for a
set of patients in different geographical locations
who demand care with different qualification
levels from a set of heterogeneous healthcare
workers. Furthermore, while allocation these
workers to the clients, time windows, preferences,
features, workload, continuity of care, quality of
service level, regulations, etc. should be
considered during planning horizon. The issues,
modes of transportation, working and waiting
times of nurses should not be ignored in this
perspective.
The HHC services offer many advantages such as
(Ellenbecker et al., 2008; Karabağ, 2007; Marak,
2016):
Caring a patient in the hospital costs higher
than the HHC services.
A client has the opportunity to recover in
her/his own home. This allows freedom
and independence. Moreover, it provides
more effective psychological support.
The HHC services are designed as clientcentred care.
Family and friends can be involved in ones’
care.
Caring at a client’s home is a safer place
than caring at hospital for contagious
infections.
The HHC services improve the quality of
care.
It can reduce and prevent the unplanned
hospital admissions/hospitalizations.
Insurance.
The most common characteristics of the
HHCRSP are summarized in this section. Some of
these are defined clearly and considered as the
20
Erdem, M., Bulkan, S., (2017). A literature review on Home Healthcare Routing and Scheduling Problem , Eurasian
Journal of Health Technology Assessment, Vol. 2, No. 1, 19-33
Eurasian Journal of Health Technology Assessment
Corresponding Author: Mehmet ERDEM ,Vol. 2, No. 1
natural dimension of the problem (Castillo-Salazar
et al., 2014).
Healthcare workers: This is the basic
component of the healthcare system. Healthcare
workers consist of nurses, assistants, and unskilled
workers. In the real world cases, a list of
competencies is specified based upon experience
level and educational level of the workers. Each
worker has a specified working time window, a
specified home location (latitude-longitude), and a
set of features such as gender, speaking language,
pet allergy, smoking habit, etc.
Jobs: The citizens/clients who are elderly or
handicapped receive care from the healthcare
system. They can demand more than one job on
the scheduling horizon, and these jobs can be
carried out by more than one nurse. All of the jobs
must be serviced by nurse(s) for the satisfaction of
clients. For each job, a time window, preferred
starting time, and duration are determined by the
healthcare providers or clients. Therefore, each job
must be performed within a predetermined time
window and the preferred starting time of the job
should be taken into consideration as much as
possible. The graphical representation of a job with
its route and time window is illustrated in Figure 1,
where circular and square nodes correspond to
nurse and job, respectively. Above part of Figure 1
summarizes job j is carried out by nurse n. In order
to perform job j, nurse n must be wait if s/he
arrives before the starting time and job j should be
covered before the ending time of the job.
Time windows: Working time windows can be
considered tight or flexible with respect to
contractual arrangements. Moreover, in some
cases, employees work annually hours without
considering time windows. In the flexible cases,
employees can work overtime. In some case
(Erdem and Bulkan, 2017), a nurse is not assigned
a job before starting working time, and if a nurse
starts to perform a job within her/his working time
windows, the job must be covered without
considering ending working time.
Time window of each job can be considered as
being soft and hard. In the first case, when the
employees can start work as soon as they arrive.
The violation of a soft time window results higher
penalty costs. In the second case, nurses cannot
start to achieve job before starting time and must
complete before ending time. The concept of a
time window is presented in Figure 2 (Bertels and
Fahle, 2006). If a nurse arrives before hard-starting
time it means that, this roster yields waiting time.
Similarly, if a nurse arrives after a hard-ending
time, which means this roster is infeasible.
Penalty
Waiting time
100 %
Infeasible
solution
0%
Hard-starting Soft-starting
Soft-ending Hard-ending
Time
Fig. 2. The penalty concept of a time window
(Bertels and Fahle, 2006)
Healthcare organizations deal with a variety of
demands, hence the duration of jobs differs
depending on the staff member and performing
tasks. In some of the cases, the duration of jobs is
less and equal to the difference of ending and
starting time. When the duration is greater than to
the difference, it is necessary to be considered as
being soft. In order to relax the time windows, a
penalty term can be used according to the existing
fields of the VRPTW (Bräysy and Gendreau,
2005a, 2005b).
Mode of transport: It means that nurses can use
different modes of transportation like cars, bikes,
public transport or else they can walk (Erdem and
Bulkan, 2017; Fikar and Hirsch, 2015; Hiermann
et al., 2015). It is assumed that travelling time and
the cost of transportation differ between two
locations.
Start and end locations: All healthcare workers
can start at the office (Eveborn et al., 2006) or each
nurse may start from her/his home. Moreover, in
some cases, executives force staff to start work at
the office, but they can return home after achieving
the last job. In our case, the home location of
21
Erdem, M., Bulkan, S., (2017). A literature review on Home Healthcare Routing and Scheduling Problem , Eurasian
Journal of Health Technology Assessment, Vol. 2, No. 1, 19-33
Eurasian Journal of Health Technology Assessment
Corresponding Author: Mehmet ERDEM ,Vol. 2, No. 1
nurses defined by latitude and longitude is
considered as starting and ending points.
Skills and qualifications: Some of the works
require different abilities to perform tasks. In
literature, there are two different approaches. (1) A
homogeneous group means having the same skills
and qualifications. (2) A heterogeneous group
means having different levels of proficiencies. In
the two cases, both have pros and cons. Employing
homogenous workers usually unpractical and it
leads to higher costs. The assignment of qualified
employees to the right tasks is also a different
challenge for organizations. As mentioned earlier,
each nurse has a set of skills that is represented by
the qualification levels. These levels are employed
to satisfy a series of customer needs with wellqualified nurses.
Connected activities: It corresponds to the
interdependence of activities (Figure 3). One
activity must be achieved before or after another,
which is called sequential dependency. Rasmussen
et al. (2012) proposed a series of temporal
(Figure 3-II). In other words, the second (bottom)
job must start when the first job has finished.
Minimum difference dependency, i.e. a nurse starts
a job at a client’s home and a following nurse
(perhaps the same nurse) finishes the same job at
the same client home. Maximum difference
dependencies built a starting time limit for the
second job with respect to the start of the first job.
In this temporal dependency, there is at least an
overlap between the two jobs. The min-max
difference can be accomplished by employing time
windows dependency and it is also shown in
Figure 3-V. The dotted line and the dashed-dotted
line correspond to the earliest and latest feasible
start time for the bottom of the job in Figure 3-V,
respectively.
Teaming: In order to achieve a job sometimes a
group work necessitates because of the special
case of the work. When members of the team are
fixed, then it is assumed that they are treated as a
single entity; hence, it is perceived that they
achieve the jobs at the same time. On the other
hand, team synchronization is necessary to
perform the jobs. Here, synchronization
corresponds to the staffs not to activities. If the
members of the groups change regularly, then skill
matching must be considered to achieve multiple
jobs.
Clusterisation is sometimes reasonable to
apply. For instance, it can decrease the travelled
distance of the staff member. The assignment of
employees in a certain region is more preferable
for the organizations. It can be also used to
decrease the size of the problem (Erdem and
Bulkan, 2017).
Fig. 3. Temporal dependencies (Rasmussen et al., 2012)
dependencies. Synchronization occurs, i.e. when
the two jobs are required to start at the same time.
Overlap means activities happen simultaneously
In the literature, most publications deal with
deterministic and static problems, all problem
parameters are known beforehand. In dynamic
problems, at least one of the input is unknown and
revealed dynamically. Similar to the dynamic
problems, in stochastic problems part or all of the
inputs are unknown in advance and revealed
during the optimization process. The difference
between the two are stochastic knowledge (Pillac
et al., 2013). In contrast to the deterministic
problems, some authors also tackle with dynamic
(Bennett and Erera, 2011; Bowers et al., 2015;
22
Erdem, M., Bulkan, S., (2017). A literature review on Home Healthcare Routing and Scheduling Problem , Eurasian
Journal of Health Technology Assessment, Vol. 2, No. 1, 19-33
Eurasian Journal of Health Technology Assessment
Corresponding Author: Mehmet ERDEM ,Vol. 2, No. 1
Koeleman et al., 2012) and stochastic (Carello and
Lanzarone, 2014; Lanzarone and Matta, 2014;
Rodriguez et al., 2015; B. Yuan et al., 2015)
problems.
3. Objectives
The performance measure and objectives of the
HHCRSP are classified in Table 1 and Table 2.
These works are sorted in the first column by date
instead of alphabetically as in the works of Cissé et
al. (2017); Fikar and Hirsch (2017). The rest
column represents the measures. The meanings of
the abbreviations in the tables are given under the
tables. Table 1 and Table 2 involves 36 singleperiod and 29 multi-period works, respectively.
Many of the deterministic publications involve an
extension of VRP, and travelling salesman
problem (TSP) (Allaoua et al., 2013) and dial-aride-problem (DARP) (Fikar and Hirsch, 2015)
based models also developed.
The most common objectives are the
Table 1. Objectives of the single-period HHCRSP (Fikar and Hirsch, 2017)
Table 2. Objectives of the multi-period HHCRSP (Fikar and Hirsch, 2017)
Paper
H T C D WT OT BW PR NJ NN NU CV SM PRI CC
Fernandez et al. (1974)
S T C D
+ WT OT BW PR NJ NN NU CV SM PRI CC
Paper
H
Chengetand
(1998)
S ++ + +
Begur
al. Rich
(1997)
M
Hindle et al. (2000)
S
+
+
De Angelis (1998)
M
+
Bertels and Fahle (2006)
S
+
+
+
Borsani et al. (2006)
M
+
+
+
Eveborn et al. (2006)
S
+
Steeg
and Schröder
(2008)
M
+ ++
+
Akjiratikarl
et al. (2007)
S
Hertz
and Lahrichi
(2009)
M
+
+
+
Bredström
and Rönnqvist
S
+
+
+
(2008) et al. (2011)
Bachouch
M
+
Elbenania
al. (2008)
S
+
+
Bennett
andetErera
(2011)
M
+
Yannick Kergosien et al.
S
+
Barrera et al. (2012)
M
+
+
(2009)
Cattafi
M
+
+
Bräysyetetal.
al.(2012)
(2009)
S
+
Gamst
and
Jensen
(2012)
M
+
+
+
+
Dohn et al. (2009)
S
+
Hindle et al.
(2009)
S
+
Koeleman
et al.
(2012)
M
+
Misir
et
al.
(2010)
S
+
+
+
Nickel et al. (2012)
M
+
+
+
+
Redjem
et (2012)
al. (2011)
S
++
+
Shao
et al.
M
+
Trautsamwieser and
Bennett-Milburn
and Hirsch
Spicer
S
++
+
+
+
+
M
+
+
(2011)
(2013)
Trautsamwieser
et al. (2011) S
+
+
+
+
+
Cappanera
and Scutellà
M
+
Rasmussen et al. (2012)
S
+
+
+
(2013)
Rendl
et al. (2012)
S ++ + +
+
+
+
Y.
Kergosien
et al. (2014)
M
Allaoua
et et
al.al.
(2013)
S
+
Bard
Shao
(2014)
M
+
+
Coppi
et
al.
(2013)
S
+
Bard, Shao et al. (2014)
M
+
+
Liu et al. (2013)
S
+
Carello and Lanzarone (2014) M
+
+
Di Mascolo et al. (2014)
S
+
Di Gaspero and Urli (2014)
M +
+
+
+
Castillo-Salazar et al. (2014) S
+ +
+
+
Ramos
et
al.
(2014)
M
+
Lanzarone and Matta (2014) S
+
+
Trautsamwieser and Hirsch
Mankowska et al. (2014)
S ++
+ +
+
+
M
(2014)
Mutingi and Mbohwa (2014) S
+
+
+
Bowers et al. (2015)
M +
+
Fikar and Hirsch (2015)
S
+
+
Cappanera and Scutellà
M
+
Issaoui et al. (2015)
S
+
(2015)
Hiermann
et
al.
(2015)
S
+
+
+
Maya Duque et al. (2015)
M
+
++
Mısır et al. (2015)
S
+
+
+
+
+
Rodriguez et al. (2015)
M
+
B. Yuan et al. (2015)
S
+
+
+
Z. Yuan and Fügenschuh
M
+ +
++
+
Braekers
et
al.
(2016)
S
+
+
+
(2015)
Redjem and
Marcon
S
+
+
Wirnitzer
et al.
(2016)(2016) M
+
+
23
Rest
and
Hirsch
(2016)
S
+
+
+
Yalçındağ, Cappanera et al.
Erdem,
M.,
Bulkan,
S.,
(2017).
A
Mliterature
+ review on Home
+ Healthcare Routing and Scheduling Problem , Eurasian
Yalçındağ, Matta et al. (2016) S
+
+
(2016)
Journal
of
Health
Technology
Assessment,
Vol.
2,
No.
1,
19-33
H:
Horizon
Time:T,
Waiting:WT,
Balance
of the workload:BW,
Erdem
and (S:single-M:multi),
Bulkan (2017)
S
+ Cost:C,
+ + Distance:D,
+
+ Overtime:OT,
+
+
+
Patient-Staff
preferences:PR,
Number
of
patients
or
jobs:NJ,
Number
of
nurses:NN,
Uncovered
CV:
H: Horizon (S:single-M:multi), Time:T, Cost:C, Distance:D, Waiting:WT, Overtime:OT, Balance of thevisits:NU,
workload:BW,
Violations
of constraints
,Skill matching:SM,
Priority:PRI,
Continuity
of care:CC.
Patient-Staff
preferences:PR,
Number of patients
or jobs:NJ,
Number
of nurses:NN, Uncovered visits:NU, CV:
Violations of constraints ,Skill matching:SM, Priority:PRI, Continuity of care:CC.
Eurasian Journal of Health Technology Assessment
Corresponding Author: Mehmet ERDEM ,Vol. 2, No. 1
minimization of travelling time and distance.
Furthermore, some of the works include overtime
work and waiting/idle time of workers. Generally,
allocating minimum number of nurses is
considered in the long or multi-period
publications. Furthermore, the deviations of a set
of hard and soft constraints are also taken into
account as objectives (Hiermann et al., 2015).
Many of the works utilize the multi-objective
function in which weights represent different
priorities/precedence. The determination of
weights is a crucial process and generally
computations of these lead to an obstacle for
computational comparisons. In contrast to the
Table 2. Objectives of the multi-period HHCRSP (Fikar and Hirsch, 2017)
Paper
H T C D WT OT BW PR NJ NN NU CV SM PRI CC
Begur et al. (1997)
De Angelis (1998)
Borsani et al. (2006)
M +
+
M
M
+
Steeg and Schröder (2008)
Hertz and Lahrichi (2009)
Bachouch et al. (2011)
Bennett and Erera (2011)
Barrera et al. (2012)
Cattafi et al. (2012)
M
M
M
M
M
M
+ +
+
+
+
+
+
+
+
+
+
+
+
+
+
Gamst and Jensen (2012)
M + +
+
+
Koeleman et al. (2012)
M
+
Nickel et al. (2012)
M
+
+
+
+
Shao et al. (2012)
M
+
+
Bennett-Milburn and Spicer
M
+
+
+
(2013)
Cappanera and Scutellà
M
+
(2013)
Y. Kergosien et al. (2014)
M + + +
Bard Shao et al. (2014)
M
+
+
Bard, Shao et al. (2014)
M
+
+
Carello and Lanzarone (2014) M
+
+
Di Gaspero and Urli (2014)
M +
+
+
+
Ramos et al. (2014)
M +
Trautsamwieser and Hirsch
M +
+
(2014)
Bowers et al. (2015)
M +
+
Cappanera and Scutellà
M
+
(2015)
Maya Duque et al. (2015)
M
+
+
Rodriguez et al. (2015)
M
+
Z. Yuan and Fügenschuh
M +
+
+
(2015)
Wirnitzer et al. (2016)
M
+
+
Yalçındağ, Cappanera et al.
M
+
+
(2016)
H: Horizon (S:single-M:multi), Time:T, Cost:C, Distance:D, Waiting:WT, Overtime:OT, Balance of the workload:BW,
Patient-Staff preferences:PR, Number of patients or jobs:NJ, Number of nurses:NN, Uncovered visits:NU, CV:
Violations of constraints ,Skill matching:SM, Priority:PRI, Continuity of care:CC.
24
Erdem, M., Bulkan, S., (2017). A literature review on Home Healthcare Routing and Scheduling Problem , Eurasian
Journal of Health Technology Assessment, Vol. 2, No. 1, 19-33
Eurasian Journal of Health Technology Assessment
Corresponding Author: Mehmet ERDEM ,Vol. 2, No. 1
single-period models, workload balance and
continuity of care terms are the most common
features discussed in the multi-period models.
When Table 1 and Table 2 are investigated
further, the terms such as balancing workload (also
named as fairness of schedule), skill matching,
preferences of clients’ and nurses, continuity of
care are taken into consideration. The number of
nurses and patients or jobs and also minimizing the
number of unscheduled jobs are used as objectives.
4. Constraints
The existing literature can be divided into two
groups such as single-period and multi-period.
However, the most observed constraints are time
windows, skill matching, working regulations, and
synchronization without considering scheduling
horizon.
As mentioned before, nurses and clients are
crucial components of the problem and each side
has different characteristics. Nurses have different
types of qualification levels and clients can request
a series of services at different levels. In addition
to this, the allocation of nurse to the patients
predetermined a variety of features, which should
be considered for an appropriate assignment.
These features can be language, gender, pet
ownership/allergy, smoking habit, etc. (Erdem and
Bulkan, 2017; Hiermann et al., 2015;
Trautsamwieser and Hirsch, 2011, 2014). The
downgrading of the competence is also taken into
account in some publications (Trautsamwieser and
Hirsch, 2011, 2014).
In order to perform some types of jobs, more
than one nurse can be required. This issue is
generally defined as the term temporal
dependency. The single-period works (Bredström
and Rönnqvist, 2008; Dohn et al., 2009; Eveborn
et al., 2006) (Rasmussen et al., 2012) and the
multi-period works (Bachouch et al., 2011) take
into this account in their models. ın most of the
reviewed publications, synchronized jobs are
considered in the HHC services.
As previously mentioned, nurses should visit
all assigned jobs within a variety of predetermined
time windows. In addition to this, within the time
windows, each patient can demand services
desired starting times. In these cases, deviations
from the time windows and desired starting time
can be defined in the constraint set and penalized
in the objective function (Erdem and Bulkan,
2017; Hiermann et al., 2015).
The single-period works (Fikar and Hirsch,
2015; Trautsamwieser et al., 2011; Trautsamwieser
and Hirsch, 2011) and the multi-period (Rodriguez
et al., 2015; Trautsamwieser and Hirsch, 2014)
works employ a series of constraints for satisfying
the mandatory working and breaks regulations.
There are two types of breaks defined (Cissé et al.,
2017). Nurses have a break either within a
predetermined time interval or according to the
length of the travelled time/distance.
Overtime work means any time worked
beyond normal working hours (UK, 2017). In
general, nurses work within the working time
windows which is determined by contractual
agreements. When nurse exceed the predetermined
time windows, the additional compensation is paid
for the overtime work. In other words, this yields
infeasible solutions. In the model that employed
soft working time windows, violations are
penalized with a higher cost in the objective as the
deviation of job or visiting time windows.
Furthermore, the upper limit can be added for the
overtime work (Bertels and Fahle, 2006).
Visiting pattern is also another temporal issue
of the multi-period publications. Throughout
planning horizon, nurses visit clients either on the
predetermined days or times. In the first case,
clients determine visiting days (i.e. Tuesday and
Sunday) on each week. In the second case visiting
times (i.e. two time a week or everyday visit) is
determined.
In order to guarantee the fairness of the
schedule and to evaluate workload balance many
authors propose measurements. The single-period
works (Bredström and Rönnqvist, 2008;
Lanzarone and Matta, 2014; Mankowska et al.,
2014) and the multi-period works (Hertz and
Lahrichi, 2009) (Barrera et al., 2012; Cappanera
and Scutellà, 2013)focus on the workload balance
25
Erdem, M., Bulkan, S., (2017). A literature review on Home Healthcare Routing and Scheduling Problem , Eurasian
Journal of Health Technology Assessment, Vol. 2, No. 1, 19-33
Eurasian Journal of Health Technology Assessment
Corresponding Author: Mehmet ERDEM ,Vol. 2, No. 1
issue. Moreover, the workload of nurses
regulates/limits according to the daily and weekly
working hours which depend on each country. For
instance, the number of daily working hours is
limited to 7.5 h in the UK and 8 h in Finland
(Akjiratikarl et al., 2007; Cissé et al., 2017).
The continuity of care is used for the person
oriented consistency (Cissé et al., 2017) between
nurses and clients. The aim is to assign the
minimum number of different nurses to the same
client during planning horizon. It is also defined as
loyalty (Nickel et al., 2012) and regularity (Gamst
and Jensen, 2012).
5. Solution Methods
In order to deal with the HHCRSP, the
reviewed works focus on exact and metaheuristic
solution procedures. The review paper dealing
with metaheuristics (Cissé et al., 2017) can be
divided into three local search-based (Mankowska
et al., 2014; Rest and Hirsch, 2016), population
based (Akjiratikarl et al., 2007; Cheng and Rich,
1998; Mutingi and Mbohwa, 2014), and hybrid
(Bertels and Fahle, 2006; Bredström and
Rönnqvist, 2008; Hiermann et al., 2015) methods.
There are no benchmark instances available;
hence, Cissé et al. (2017) compared the existing
some of the publications dealing with
metaheuristics to winning strategies proposed by
(Vidal et al., 2013). The majority of single-period
works propose a procedure based on the
metaheuristics.
On the other hand, in order to deal with the
small-size of the HHCRSPs, branch-and bound
algorithms (Dohn et al., 2009; Rasmussen et al.,
2012; B. Yuan et al., 2015) are mostly used.
Moreover, set portioning problem (SPP) (Allaoua
et al., 2013; Eveborn et al., 2006; Fikar and
Hirsch, 2017) is also implemented.
Hybrid methods generally start with a feasible
solution. Then metaheuristics improve the initial
generated solution. In each phase different
decisions such as assignment and routing can be
performed. The combination of exact and heuristic
methods is applied to obtain more improve
solutions (Bertels and Fahle, 2006; Braekers et al.,
2016; Bredström and Rönnqvist, 2008; Hiermann
et al., 2015; Rendl et al., 2012).
While commonly used population-based
algorithms are genetic algorithm (GA) (Cheng and
Rich, 1998; Liu et al., 2013; Yalçındağ, Matta et
al., 2016), particle swarm optimization (PSO)
(Akjiratikarl et al., 2007; Mutingi and Mbohwa,
2014), memetic algorithm (MA) (Hiermann et al.,
2015), the local search-based algorithms are tabu
search (TS) (Bertels and Fahle, 2006; Elbenania et
al., 2008; Liu et al., 2013; Rest and Hirsch, 2016),
simulated annealing (SA) (Hiermann et al., 2015),
and variable neighbourhood search (VNS) (Erdem
and Bulkan, 2017; Hiermann et al., 2015; Issaoui
et al., 2015; Rendl et al., 2012; Trautsamwieser et
al., 2011; Trautsamwieser and Hirsch, 2011).
In contrary to Cissé et al. (2017) single-period
problems grouping, the multi-period problems are
classified as construction-based (Bard Shao et al.,
2014; Shao et al., 2012), local search-based (Hertz
and Lahrichi, 2009), and hybrid (Steeg and
Schröder, 2008; Trautsamwieser and Hirsch, 2014)
methods.
The BP (Gamst and Jensen, 2012) and branchprice-and-cut (BPC) (Trautsamwieser and Hirsch,
2014) algorithms are also implemented for multiperiod problems.
In order to deal with the multi-period
HHCRSP, a construction-based algorithms called
greedy randomized adaptive search procedure
(GRASP) (Bard Shao et al., 2014; Shao et al.,
2012) is employed. The local search-based
algorithms are TS (Hertz and Lahrichi, 2009;
Yannick Kergosien et al., 2009), VNS(Y.
Kergosien et al., 2014), and adaptive large
neighbourhood search (ALNS) (Nickel et al.,
2012; Steeg and Schröder, 2008) heuristics.
In the literature, some of the multi-period
works concern that some of the parameters are
unknown throughout the planning horizon.
Stochastic parameters such as travelling time, the
duration of services, the demands of a varied
services, etc. are considered in this framework.
Hence, dynamic (Bennett and Erera, 2011) and
stochastic (Bowers et al., 2015; Koeleman et al.,
26
Erdem, M., Bulkan, S., (2017). A literature review on Home Healthcare Routing and Scheduling Problem , Eurasian
Journal of Health Technology Assessment, Vol. 2, No. 1, 19-33
Eurasian Journal of Health Technology Assessment
Corresponding Author: Mehmet ERDEM ,Vol. 2, No. 1
2012; Rodriguez et al., 2015) problems are
proposed in the field of multi-period HHC.
6. Conclusions
This review paper evaluates 65 publications
related to the HHCRSP which combines nurse
scheduling and vehicle routing. In order to solve
this problem, mixed integer programming (MIP),
integer programming (IP), stochastic programming
(SP), constraint programming (CP) using SPP and
network flow models are applied. Moreover, local
search-based metaheuristics such as VNS, TS, SA,
etc. and population-based metaheuristics such as
GA, PSO, MA, etc. implemented. The publications
that involve stochastic setting focuses on the
limited real world stochastic parameters. In other
words, these consider simplified version of real
world problems and did not involve all decisions
such as routing, assignment, and scheduling. And
these are tested on synthesis data or employing
mathematical proof of lemma, theorem, and
proposition. Based on the classification, the
majority of the model considers multi-objective
function, which employs minimization of cost,
working time, and distance. In terms of
constraints, most research focus on time windows,
skill matching, and regulations. Furthermore,
preferences, temporal dependency, especially
synchronization, workload, and continuity of care
are used in many recently proposed problems.
In terms of solution technique, in the HHCRSP
literature, there is no work dealing with graphical
processing units (GPU) and/or parallel computing.
The advantage of these can reduce the runtime of
the optimization process.
The majority of publications is based upon the
deterministic parameter setting; hence, the issues
covering uncertainty in some types of
emergencies, traffic conditions, etc., should not be
ignored in terms of HHC services. The choice of a
suitable mode pf transportation is another crucial
issue because of its direct relationship with the
energy consumption. Switching between the
modes of transportation can be a new direction for
the HHCRSP. Moreover, in term of (economic)
sustainability the healthcare workers can use green
or electrical vehicles. In this case, in addition to
the assignment, scheduling, and routing decisions,
a new recharging strategy should be determined.
Therefore, the HHCRSP can cover a set of
constraints for these vehicles such as refuelling of
green vehicles or full/partial recharge strategies for
electrical vehicles.
References
Akjiratikarl, C., Yenradee, P., & Drake, P. R. (2007).
PSO-based algorithm for home care worker scheduling
in the UK. Computers & Industrial Engineering, 53(4),
559-583. doi:10.1016/j.cie.2007.06.002
Allaoua, H., Borne, S., Létocart, L., & Wolfler Calvo,
R. (2013). A matheuristic approach for solving a home
health care problem. Electronic Notes in Discrete
Mathematics,
41,
471-478.
doi:10.1016/j.endm.2013.05.127
Bachouch, R. B., Guinet, A., & Hajri-Gabouj, S.
(2011). A Decision-Making Tool for Home Health
Care Nurses’ Planning. Supply Chain Forum: An
International
Journal,
12(1),
14-20.
doi:10.1080/16258312.2011.11517250
Bard, J. F., Shao, Y., & Jarrah, A. I. (2014). A
sequential GRASP for the therapist routing and
scheduling problem. Journal of Scheduling, 17(2), 109133. doi:10.1007/s10951-013-0345-x
Bard, J. F., Shao, Y., Qi, X., & Jarrah, A. I. (2014). The
traveling
therapist
scheduling
problem.
IIE
Transactions,
46(7),
683-706.
doi:10.1080/0740817X.2013.851434
Barrera, D., Velasco, N., & Amaya, C. A. (2012). A
network-based approach to the multi-activity combined
timetabling and crew scheduling problem: Workforce
scheduling for public health policy implementation.
Computers & Industrial Engineering, 63(4), 802-812.
doi:http://dx.doi.org/10.1016/j.cie.2012.05.002
Begur, S. V., Miller, D. M., & Weaver, J. R. (1997). An
Integrated Spatial DSS for Scheduling and Routing
Home-Health-Care Nurses. Interfaces, 27(4), 35-48.
doi:doi:10.1287/inte.27.4.35
Bennett-Milburn, A., & Spicer, J. (2013). Multiobjective home health nurse routing with remote
monitoring devices. Int J Plan Sched, 1(4), 242-263.
27
Erdem, M., Bulkan, S., (2017). A literature review on Home Healthcare Routing and Scheduling Problem , Eurasian
Journal of Health Technology Assessment, Vol. 2, No. 1, 19-33
Eurasian Journal of Health Technology Assessment
Corresponding Author: Mehmet ERDEM ,Vol. 2, No. 1
Bennett, A. R., & Erera, A. L. (2011). Dynamic
periodic fixed appointment scheduling for home health.
IIE Transactions on Healthcare Systems Engineering,
1(1), 6-19. doi:10.1080/19488300.2010.549818
Bertels, S., & Fahle, T. (2006). A hybrid setup for a
hybrid scenario: combining heuristics for the home
health care problem. Computers & Operations
Research,
33(10),
2866-2890.
doi:http://dx.doi.org/10.1016/j.cor.2005.01.015
Borsani, V., Matta, A., Beschi, G., & Sommaruga, F.
(2006, Oct. 2006). A Home Care Scheduling Model For
Human Resources. Paper presented at the 2006
International Conference on Service Systems and
Service Management.
Bowers, J., Cheyne, H., Mould, G., & Page, M. (2015).
Continuity of care in community midwifery. Health
Care Management Science, 18(2), 195-204.
doi:10.1007/s10729-014-9285-z
Braekers, K., Hartl, R. F., Parragh, S. N., & Tricoire, F.
(2016). A bi-objective home care scheduling problem:
Analyzing the trade-off between costs and client
inconvenience. European Journal of Operational
Research,
248(2),
428-443.
doi:http://dx.doi.org/10.1016/j.ejor.2015.07.028
Bräysy, O., Dullaert, W., & Nakari, P. (2009). The
potential of optimization in communal routing
problems: case studies from Finland. Journal of
Transport
Geography,
17(6),
484-490.
doi:http://dx.doi.org/10.1016/j.jtrangeo.2008.10.003
Bräysy, O., & Gendreau, M. (2005a). Vehicle Routing
Problem with Time Windows, Part I: Route
Construction and Local Search
Algorithms.
Transportation
Science,
39(1),
104-118.
doi:10.1287/trsc.1030.0056
Bräysy, O., & Gendreau, M. (2005b). Vehicle Routing
Problem with Time Windows, Part II: Metaheuristics.
Transportation
Science,
39(1),
119-139.
doi:10.1287/trsc.1030.0057
Bredström, D., & Rönnqvist, M. (2008). Combined
vehicle routing and scheduling with temporal
precedence and synchronization constraints. European
Journal of Operational Research, 191(1), 19-31.
doi:10.1016/j.ejor.2007.07.033
Cappanera, P., & Scutellà, M. G. (2013). Home Care
optimization: impact of pattern generation policies on
scheduling and routing decisions. Electronic Notes in
Discrete
Mathematics,
41,
53-60.
doi:10.1016/j.endm.2013.05.075
Cappanera, P., & Scutellà, M. G. (2015). Joint
Assignment, Scheduling, and Routing Models to Home
Care Optimization: A Pattern-Based Approach.
Transportation
Science,
49(4),
830-852.
doi:doi:10.1287/trsc.2014.0548
Carello, G., & Lanzarone, E. (2014). A cardinalityconstrained robust model for the assignment problem in
Home Care services. European Journal of Operational
Research,
236(2),
748-762.
doi:http://dx.doi.org/10.1016/j.ejor.2014.01.009
Castillo-Salazar, J. A., Landa-Silva, D., & Qu, R.
(2014). Workforce scheduling and routing problems:
literature survey and computational study. Annals of
Operations Research, 1-29. doi:10.1007/s10479-0141687-2
Cattafi, M., Herrero, R., Gavanelli, M., Nonato, M.,
Malucelli, F., & Ramos, J. J. (2012). Improving Quality
and Efficiency in Home Health Care: an application of
Constraint Logic Programming for the Ferrara NHS
unit. Paper presented at the Technical Communications
of the 28th International Conference on Logic
Programming
(ICLP'12).
http://drops.dagstuhl.de/opus/volltexte/2012/3641/
CDC. (2017). Home Health Care.
Retrieved from
https://www.cdc.gov/nchs/fastats/home-health-care.htm
Cheng, E., & Rich, J. L. (1998). A home health care
routing and scheduling problem.
Cissé, M., Yalçındağ, S., Kergosien, Y., Şahin, E.,
Lenté, C., & Matta, A. (2017). OR problems related to
Home Health Care: A review of relevant routing and
scheduling problems. Operations Research for Health
Care. doi:http://dx.doi.org/10.1016/j.orhc.2017.06.001
Colombo, F., ., & et al. Help Wanted? : OECD
Publishing.
Coppi, A., Detti, P., & Raffaelli, J. (2013). A planning
and routing model for patient transportation in health
care. Electronic Notes in Discrete Mathematics, 41,
125-132. doi:10.1016/j.endm.2013.05.084
28
Erdem, M., Bulkan, S., (2017). A literature review on Home Healthcare Routing and Scheduling Problem , Eurasian
Journal of Health Technology Assessment, Vol. 2, No. 1, 19-33
Eurasian Journal of Health Technology Assessment
Corresponding Author: Mehmet ERDEM ,Vol. 2, No. 1
De Angelis, V. (1998). Planning Home Assistance for
AIDS Patients in the City of Rome, Italy. Interfaces,
28(3), 75-83. doi:doi:10.1287/inte.28.3.75
Di Gaspero, L., & Urli, T. (2014). A CP/LNS Approach
for Multi-day Homecare Scheduling Problems. In M.
Blesa, et al. (Eds.), Hybrid Metaheuristics (Vol. 8457,
pp. 1-15): Springer International Publishing.
Di Mascolo, M., Espinouse, M.-L., & Ozkan, C. E.
(2014). Synchronization Between Human Resources in
Home Health Care Context. In A. Matta, et al. (Eds.),
Proceedings of the International Conference on Health
Care Systems Engineering (pp. 73-86). Cham: Springer
International Publishing.
Dohn, A., Kolind, E., & Clausen, J. (2009). The
manpower allocation problem with time windows and
job-teaming constraints: A branch-and-price approach.
Computers & Operations Research, 36(4), 1145-1157.
doi:http://dx.doi.org/10.1016/j.cor.2007.12.011
Elbenania, B., Ferland, J. A., & Gascon, V. (2008).
Mathematical Programming Approach for Routing
Home Care Nurses. Paper presented at the Industrial
Engineering and Engineering Management, 2008.
IEEM 2008.
Ellenbecker, C. H., Samia, L., Cushman, M. J., &
Alster, K. (2008). Chapter 13-Patient Safety and
Quality in Home Health Care. In R. G. Hughes (Ed.),
Patient Safety and Quality: An Evidence-Based
Handbook for Nurses. Rockville Agency for Healthcare
Research and Quality.
Erdem, M., & Bulkan, S. (2017). A Two-Stage
Solution Approach For The Large-Scale Home
Healthcare Routing And Scheduling Problem. The
South African Journal of Industrial Engineering, 28
(4), 133-149. doi:http://dx.doi.org/10.7166/28-4-1754
Eurostat. (2017). Population structure and ageing
Retrieved from http://ec.europa.eu/eurostat/statisticsexplained/index.php/Population_structure_and_ageing
Eveborn, P., Flisberg, P., & Rönnqvist, M. (2006). Laps
Care—an operational system for staff planning of home
care. European Journal of Operational Research,
171(3), 962-976. doi:10.1016/j.ejor.2005.01.011
Fernandez, A., Gregory, G., Hindle, A., & Lee, C. A.
(1974). A Model for Community Nursing in a Rural
County. Journal of the Operational Research Society,
25(2), 231-239. doi:10.1057/jors.1974.40
Fikar, C., & Hirsch, P. (2015). A matheuristic for
routing real-world home service transport systems
facilitating walking. Journal of Cleaner Production,
105, 300-310. doi:10.1016/j.jclepro.2014.07.013
Fikar, C., & Hirsch, P. (2017). Home health care
routing and scheduling: A review. Computers &
Operations
Research,
77,
86-95.
doi:http://dx.doi.org/10.1016/j.cor.2016.07.019
Gamst, M., & Jensen, T. S. (2012). A branch-and-price
algorithm for the long-term home care scheduling
problem. In D. Klatte, et al. (Eds.), Operations
Research Proceedings 2011 (pp. 483-488): Springer
Berlin Heidelberg.
Hertz, A., & Lahrichi, N. (2009). A patient assignment
algorithm for home care services. Journal of the
Operational Research Society, 60(4), 481-495.
doi:10.1057/palgrave.jors.2602574
Hiermann, G., Prandtstetter, M., Rendl, A., Puchinger,
J., & Raidl, G. (2015). Metaheuristics for solving a
multimodal home-healthcare scheduling problem.
Central European Journal of Operations Research,
23(1), 89-113. doi:10.1007/s10100-013-0305-8
Hindle, T., Hindle, A., & Spollen, M. (2000). Resource
Allocation Modelling for Home-Based Health and
Social Care Services in Areas Having Differential
Population Density Levels: A Case Study in Northern
Ireland Health Serv Manage Res, 13(3), 164-169.
doi:10.1177/095148480001300304
Hindle, T., Hindle, G., & Spollen, M. (2009). Travelrelated costs of population dispersion in the provision
of domiciliary care to the elderly: a case study in
English Local Authorities Health Serv Manage Res,
22(1), 27-32. doi:10.1258/hsmr.2008.008012
Issaoui, B., Zidi, I., Marcon, E., & Ghedira, K. (2015).
New Multi-Objective Approach for the Home Care
Service Problem Based on Scheduling Algorithms and
Variable Neighborhood Descent. Electronic Notes in
Discrete
Mathematics,
47,
181-188.
doi:10.1016/j.endm.2014.11.024
Karabağ, H. (2007). Evde Sağlik Bakim Hizmetlerinin
Türkiye’de Uygulanabilirliğine İlişkin Hekimlerin
Görüşleri Ve Kardiyoloji Hastalari İçin Hastane
29
Erdem, M., Bulkan, S., (2017). A literature review on Home Healthcare Routing and Scheduling Problem , Eurasian
Journal of Health Technology Assessment, Vol. 2, No. 1, 19-33
Eurasian Journal of Health Technology Assessment
Corresponding Author: Mehmet ERDEM ,Vol. 2, No. 1
Destekli Evde Bakim Hizmetleri Modeli Önerisi.
(Master Thesis), Gazi University, Ankara.
Kergosien, Y., Lenté, C., & Billaut, J.-C. (2009). Home
health care problem: An extended multiple Traveling
Salesman Problem. Paper presented at the Proceedings
of the 4th Multidisciplinary International Scheduling
Conference: Theory and Applications (MISTA 2009),
Dublin, Ireland.
Kergosien, Y., Ruiz, A., & Soriano, P. (2014). A
Routing Problem for Medical Test Sample Collection
in Home Health Care Services. In A. Matta, et al.
(Eds.), Proceedings of the International Conference on
Health Care Systems Engineering (pp. 29-46). Cham:
Springer International Publishing.
Koeleman, P. M., Bhulai, S., & van Meersbergen, M.
(2012). Optimal patient and personnel scheduling
policies for care-at-home service facilities. European
Journal of Operational Research, 219(3), 557-563.
doi:10.1016/j.ejor.2011.10.046
Lanzarone, E., & Matta, A. (2014). Robust nurse-topatient assignment in home care services to minimize
overtimes under continuity of care. Operations
Research
for
Health
Care,
3(2),
48-58.
doi:http://dx.doi.org/10.1016/j.orhc.2014.01.003
Liu, R., Xie, X., Augusto, V., & Rodriguez, C. (2013).
Heuristic algorithms for a vehicle routing problem with
simultaneous delivery and pickup and time windows in
home health care. European Journal of Operational
Research,
230(3),
475-486.
doi:10.1016/j.ejor.2013.04.044
Mankowska, D. S., Meisel, F., & Bierwirth, C. (2014).
The home health care routing and scheduling problem
with interdependent services. Health Care Management
Science, 17(1), 15-30. doi:10.1007/s10729-013-9243-1
Marak, C. (2016). Benefits of Home Care. Retrieved
from
http://www.homehealthcareagencies.com/resources/ben
efits-of-home-care/
Matta, A., Chahed, S., Sahin, E., & Dallery, Y. (2014).
Modelling home care organisations from an operations
management perspective. Flexible Services and
Manufacturing
Journal,
26(3),
295-319.
doi:10.1007/s10696-012-9157-0
Maya Duque, P. A., Castro, M., Sörensen, K., & Goos,
P. (2015). Home care service planning. The case of
Landelijke Thuiszorg.
European Journal of
Operational
Research,
243(1),
292-301.
doi:10.1016/j.ejor.2014.11.008
Medicine, U. S. N. L. o. (2017). Home Care Services
Retrieved
from
https://medlineplus.gov/homecareservices.html
Milburn, A. B. (2012). Operations Research
Applications in Home Healthcare. In R. Hall (Ed.),
Handbook of Healthcare System Scheduling (pp. 281302). Boston, MA: Springer US.
Mısır, M., Smet, P., & Vanden Berghe, G. (2015). An
analysis of generalised heuristics for vehicle routing
and personnel rostering problems. Journal of the
Operational Research Society, 66(5), 858-870.
doi:10.1057/jors.2014.11
Misir, M., Verbeeck, K., De Causmaecker, P., &
Berghe, G. V. (2010, 18-23 July 2010). Hyperheuristics with a dynamic heuristic set for the home
care scheduling problem. Paper presented at the
Evolutionary Computation (CEC), 2010 IEEE
Congress on.
Mutingi, M., & Mbohwa, C. (2014). Home Healthcare
Staff Scheduling: A Clustering Particle Swarm
Optimization Approach. Paper presented at the
International Conference on Industrial Engineering and
Operations Management, Bali, Indonesia,.
Nickel, S., Schröder, M., & Steeg, J. (2012). Mid-term
and short-term planning support for home health care
services. European Journal of Operational Research,
219(3), 574-587. doi:10.1016/j.ejor.2011.10.042
Pillac, V., Gendreau, M., Guéret, C., & Medaglia, A. L.
(2013). A review of dynamic vehicle routing problems.
European Journal of Operational Research, 225(1), 111. doi:https://doi.org/10.1016/j.ejor.2012.08.015
R&M. (2017). Europe Home Healthcare and
Residential Nursing Care Services Market Report 2017.
Retrieved
from
https://www.researchandmarkets.com/research/xjwcsf/e
urope_home
Ramos, A. F. T., Lizarazo, E. H. A.-., Rubiano, L. S.
R.-., & Araújo, C. L. Q. (2014). Mathematical Model
for the Home Health Care routing and scheduling
30
Erdem, M., Bulkan, S., (2017). A literature review on Home Healthcare Routing and Scheduling Problem , Eurasian
Journal of Health Technology Assessment, Vol. 2, No. 1, 19-33
Eurasian Journal of Health Technology Assessment
Corresponding Author: Mehmet ERDEM ,Vol. 2, No. 1
problem with multiple treatment and time windows.
Paper presented at the Mathematical Methods in
Science and Engineering, Athens.
Rasmussen, M. S., Justesen, T., Dohn, A., & Larsen, J.
(2012). The Home Care Crew Scheduling Problem:
Preference-based visit clustering and temporal
dependencies. European Journal of Operational
Research,
219(3),
598-610.
doi:10.1016/j.ejor.2011.10.048
Redjem, R., Kharraja, S., & Marcon, E. (2011).
Collaborative model for planning and scheduling
caregivers’ activities in homecare. IFAC World
Congress,
Volume
18,
2877-2882.
doi:10.3182/20110828-6-IT-1002.01043
Redjem, R., & Marcon, E. (2016). Operations
management in the home care services: a heuristic for
the caregivers’ routing problem. Flexible Services and
Manufacturing
Journal,
28(1),
280-303.
doi:10.1007/s10696-015-9220-8
Rendl, A., Prandtstetter, M., Hiermann, G., Puchinger,
J., & Raidl, G. (2012). Hybrid Heuristics for
Multimodal Homecare Scheduling. In N. Beldiceanu, et
al. (Eds.), Integration of AI and OR Techniques in
Contraint
Programming
for
Combinatorial
Optimzation Problems (Vol. 7298, pp. 339-355):
Springer Berlin Heidelberg.
Rest, K.-D., & Hirsch, P. (2016). Daily scheduling of
home health care services using time-dependent public
transport. Flexible Services and Manufacturing
Journal, 28(3), 495-525. doi:10.1007/s10696-0159227-1
Rodriguez, C., Garaix, T., Xie, X., & Augusto, V.
(2015). Staff dimensioning in homecare services with
uncertain demands. International Journal of
Production
Research,
53(24),
7396-7410.
doi:10.1080/00207543.2015.1081427
Shao, Y., Bard, J. F., & Jarrah, A. I. (2012). The
therapist routing and scheduling problem. IIE
Transactions,
44(10),
868-893.
doi:10.1080/0740817X.2012.665202
Statista. (2015). Number of home health agencies in the
U.S.
1967-2015.
Retrieved
from
https://www.statista.com/statistics/195318/number-ofmedicare-home-health-agencies-in-the-us/
Steeg, J., & Schröder, M. (2008). A Hybrid Approach
to Solve the Periodic Home Health Care Problem. In J.
Kalcsics & S. Nickel (Eds.), Operations Research
Proceedings 2007 (Vol. 2007, pp. 297-302): Springer
Berlin Heidelberg.
Trautsamwieser, A., Gronalt, M., & Hirsch, P. (2011).
Securing home health care in times of natural disasters.
OR Spectrum, 33(3), 787-813. doi:10.1007/s00291011-0253-4
Trautsamwieser, A., & Hirsch, P. (2011). Optimization
of daily scheduling for home health care services.
Journal of Applied Operational Research, 3, 124-136.
Trautsamwieser, A., & Hirsch, P. (2014). A BranchPrice-and-Cut approach for solving the medium-term
home health care planning problem. Networks, 64(3),
143-159. doi:10.1002/net.21566
UK. (2017). Overtime: your rights. Retrieved from
https://www.gov.uk/overtime-your-rights.
UN. (2015). World Population Ageing 2015 Retrieved
from
http://www.un.org/en/development/desa/population/pu
blications/pdf/ageing/WPA2015_Report.pdf
Vidal, T., Crainic, T. G., Gendreau, M., & Prins, C.
(2013). Heuristics for multi-attribute vehicle routing
problems: A survey and synthesis. European Journal of
Operational
Research,
231(1),
1-21.
doi:https://doi.org/10.1016/j.ejor.2013.02.053
Wirnitzer, J., Heckmann, I., Meyer, A., & Nickel, S.
(2016). Patient-based nurse rostering in home care.
Operations Research for Health Care, 8, 91-102.
doi:http://dx.doi.org/10.1016/j.orhc.2015.08.005
Yalçındağ, S., Cappanera, P., Grazia Scutellà, M.,
Şahin, E., & Matta, A. (2016). Pattern-based
decompositions for human resource planning in home
health care services. Computers & Operations
Research,
73,
12-26.
doi:http://dx.doi.org/10.1016/j.cor.2016.02.011
Yalçındağ, S., Matta, A., Şahin, E., & Shanthikumar, J.
G. (2016). The patient assignment problem in home
health care: using a data-driven method to estimate the
travel times of care givers. Flexible Services and
Manufacturing
Journal,
28(1),
304-335.
doi:10.1007/s10696-015-9222-6
31
Erdem, M., Bulkan, S., (2017). A literature review on Home Healthcare Routing and Scheduling Problem , Eurasian
Journal of Health Technology Assessment, Vol. 2, No. 1, 19-33
Eurasian Journal of Health Technology Assessment
Corresponding Author: Mehmet ERDEM ,Vol. 2, No. 1
Yuan, B., Liu, R., & Jiang, Z. (2015). A branch-andprice algorithm for the home health care scheduling and
routing problem with stochastic service times and skill
requirements. International Journal of Production
Research,
53(24),
7450-7464.
doi:10.1080/00207543.2015.1082041
Yuan, Z., & Fügenschuh, A. (2015). Home Health Care
Scheduling A Case Study. Paper presented at the
MISTA.
32
Erdem, M., Bulkan, S., (2017). A literature review on Home Healthcare Routing and Scheduling Problem , Eurasian
Journal of Health Technology Assessment, Vol. 2, No. 1, 19-33