Medical Imaging: Exams Planning and Resource Assignment
Hybridization of a Metaheuristic and a List Algorithm
Nathalie Klement
1
, Nathalie Grangeon
2
and Michel Gourgand
2
1
´
Ecole Nationale Sup´erieure d’Arts et M´etiers, LSIS CNRS UMR 7296,
8 boulevard Louis XIV, 59046 Lille Cedex, France
2
LIMOS CNRS UMR 6158, Universit´e Blaise Pascal,
Complexe Universitaire des C´ezeaux, 63178 Aubi`ere Cedex, France
Keywords:
Hybridization, Metaheuristic, List Algorithm, Medical Imaging.
Abstract:
The presented work is about optimization of the hospital system. An existing solution is the pooling of
resources within the same territory. This may involve different forms of cooperation between several hospitals.
Problems of sizing, planning and scheduling may be considered. We define the problem of activities planning
with resource assignment. To solve this problem, we propose a hybridization between a metaheuristic and a
list algorithm. Single based metaheuristics are used. This proposition requires a new encoding inspired by
permutation problems. This method is easy to apply: it combines already known methods. With the proposed
hybridization, the constraints to be considered only need to be integrated into the list algorithm. For big
instances, the solver used as a reference returns only lower and upper bounds. The results of our method
are very promising. It is possible to adapt our method on more complex issues through integration into the
list algorithm of the constraints. It would be particularly interesting to test these methods on real hospital
authorities to assess their significance.
1 INTRODUCTION
Given the current economic situation, everything is
done to move towards a better use of goods and ser-
vices production systems. The hospital system also
follows this trend as much or less resources are allo-
cated to it but it should work more efficiently to meet
a demand that is increasing. To do so, in 2015, the
french government defined the HGT: Hospital Group
of Territory, an evolution of the HCT previously pre-
sented (Gourgand et al., 2014a). It is a coopera-
tion between public institutions, which are at different
places, that implement a common strategy and jointly
manage some functions and activities through delega-
tions or skills transfer between them. Some decision
support tools are needed to manage this new kind of
organization.
The aim of our work is the development of a de-
cision support tool to help to manage HGTs or any
hospital cooperations. This tool should be used at dif-
ferent levels: strategic, tactical or operational, to deal
with problems of sizing, planning, resources assign-
ment or scheduling. It should be used to anticipate
the creation of a new cooperation, to manage this or-
ganization day to day, or to react in case of hazard
or crisis situation. In this paper, we take the prob-
lematic of medical imaging over a HGT as an exam-
ple. Some material resources, such as X-ray, scan-
ner, MRI, are located at different places belonging to
the HGT. Human resources work there and have spe-
cific competences on these material resources. Some
patients need to pass an exam on such a material re-
source. The planning horizon can be some days or
weeks, divided in periods of half-days. Some incom-
patibilities and time constraints are defined. The tac-
tical level will be discussed in this paper: the objec-
tive is to assign the exams to human and material re-
sources during a period. The other levels can easily
be solved by our method which uses some operational
research purposes.
2 STATE OF THE ART
Since the last ten years, many methods of opera-
tional research have been used to solve hospital sys-
tem problems. (Rais and Viana, 2011) referenced
around two hundred and fifty articles about opera-
tional research for hospital system in general. (Car-
260
Klement N., Grangeon N. and Gourgand M.
Medical Imaging: Exams Planning and Resource Assignment - Hybridization of a Metaheuristic and a List Algorithm.
DOI: 10.5220/0006113002600267
In Proceedings of the 10th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2017), pages 260-267
ISBN: 978-989-758-213-4
Copyright
c
2017 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
doen et al., 2010) referenced more than one hundred
and twenty articles about planning and scheduling of
operating theater. (Van den Bergh et al., 2013) made
a literature review about scheduling human resources
and referenced around three hundred articles.
But articles dealing with multi-place system in
hospital network are scarce, or their case study are
quite limited. Planning surgical vacations by specialty
is dealt by (Santib´a˜nez et al., 2007). Availability of
operating theater, beds capacity, surgeons preferences
and waiting list are considered. The proposed model
allocates specialties to operating theater, and is ap-
plied to a Canadian study case, composed by eight
hospitals, over four weeks. (Everett, 2002) developed
a support aid tool to manage the waiting list of pa-
tients who need a surgical act. The system is made
up by several hospitals, working in cooperation. The
waiting list is common for all the hospitals. Each day,
each patient is assigned to one place according to the
availability of the hospitals. If no hospital is available
on one day, patients are assigned the next day. As-
signment of resources is not considered. (VanBerkel
and Blake, 2007) developed a tool to reduce the wait-
ing time and to plan beds capacity in a surgery ser-
vice, over several places. It is a problem of allocation
of the fixed resources, in an other Canadian example.
This tool aims at studying a redistribution of postoper-
ative beds between the places, using simulation tools.
Problem of capacity in intensive care unit can result
in the cancellation of programmed acts, an overload
of medical team or a reject of urgent patients. Thus,
urgent patients could be transferred to further places.
A cooperative solution is studied by (Litvak et al.,
2008), taking into example a case in the Netherlands.
Some hospitals belonging to the same territory share
some beds to urgent patients.
Researchs are done about the pooling of resources.
(Trilling et al., 2006) dealt with the problem of
scheduling human resources over different services
in one hospital. The objective is to share resources
within larger surgical suite, in order to reduce the
costs. At another level, it can be seen as a sharing
of resources from different places within larger orga-
nization such as HGT. In this paper, concerned re-
sources are stretchers and nurses, who are common
resources used for any hospital services and locations.
A lot of researches about hospital system are dedi-
cated. Articles consider three problems: sizing, plan-
ning and scheduling. Most of the papers focuses on
one particular problem. Their models and resolution
methods are not easily reusable. Our proposed model
and tool are generic, so they could be reused as often
as possible.
3 ANALYSIS
To analyze our system, we split the system into three
subsystems: the physical subsystem (physical enti-
ties used to perform all the activities, their geographi-
cal distribution and their interconnections),the logical
subsystem (flows that the system should treat, all ac-
tivities concerning the treatment of these flows and all
entities in the system relating to them) and the deci-
sion subsystem (center of decision which contains all
the decision rules).
3.1 Physical Subsystem
The HGT is composed by several places. There is a
known distance between each place.
On each place, there are one or several material
resources. A material resource belongs to a type (for
instance X-ray, scanner or MRI). Each material re-
source has an opening schedule which defines the
times when the material resource is available over
each period. For example, a given material resource
may only be available five hours on Monday because
it needs a maintenance operation or because an exter-
nal doctor reserved it. Overtime may be allowed but
is limited in time.
Human resources compose a medical team. The
composition of this team depends on the considered
exam. This team should have a specific number of
stretchers, specialist doctors, nurses, etc. Human re-
sources belong to a given place but can work on other
places belonging to the same HGT, allowing a pool-
ing of human resources over the HGT. Moves are not
allowed within the same period, but between two pe-
riods. A time is given to human resources to go from
a place to another. A human resource can use one
or several types of material resource according to its
skills. A skillful human resource, who can work on
several types of material resources, is potentially less
efficient than a human resource who can only work on
one type of material resource, or one particular mate-
rial resource. This efficiency should be translated in
the processing time of the concerned exams. Each
human resource has a planning which defines its reg-
ular work time, taking into account break times and
holidays. Time to move from one place to another is
included in the work time of human resources. Over-
time may be allowed but is limited in time.
3.2 Logical Subsystem
The logical subsystem defines the flow: the set of ex-
ams to plan and assign, and the relationship between
these exams and the resources previously defined.
Medical Imaging: Exams Planning and Resource Assignment - Hybridization of a Metaheuristic and a List Algorithm
261
An exam should be done before a period at the
latest, called a due date. Each exam has a known pro-
cessing time which depends on the assigned human
and material resources. Each exam starts at one pe-
riod and ends at the same one. Each exam has a refer-
ence place, where it should be done, if possible.
An exam needs a given number of human re-
sources and one material resource. All required re-
sources must be compatible with each other. By defi-
nition, an exam is compatible with some material re-
sources, so the assigned material resource must be
compatible with the exam. This material resource be-
longs to a type, so the assigned human resources must
have the needed skill to use this type of material re-
source. The place where the exam is done is deduced
from the one where is located the assigned material
resource.
3.3 Decision Subsystem
The objective is to develop a model which, from a
set of exams, builds a planning associating the triplet
{exam, human resources, material resource} to a pe-
riod. The study is made in a predictive approach, all
the exams can be treated since the beginning of the
planning horizon. The objective of this model is not
to schedule exactly the exams but to assign one pe-
riod to each exam. This planning must optimize some
criteria and respect some constraints.
3.3.1 Criteria
Three categories of criteria can be defined: econom-
ical, about the comfort of the patient, and about the
proper functioning of the HGT.
Concerning the economical aspects, criteria are
about the costs. Occupation rates of each place, each
material resource and each human resource help to
ensure the proper use of these entities. To be the most
economic, these occupation rates have to be maxi-
mized. However, it can be preferable to define a se-
curity margin, so the HGT can be reactive in case
of hazard. All exams are planned during the con-
sidered planning horizon. The makespan is the pe-
riod assigned to the last exam. It ensures that all ex-
ams are assigned as soon as possible. The smaller
the makespan is, more time remains free at the end
of the planning horizon to potentially treat the next
exams. The number of moves of human resources in
the HGT should be considered, as well as overtime of
human and material resources. Overtime and moves
have a cost for the HGT. It is better to minimize them.
But it can be interesting to allow some overtime or
some moves to increase the number of exams during
the considered period.
About the comfort of the patient, the criterion is
the number of exams done at their reference place. If
some exams cannot be done at their reference place,
the distances between the reference places and the ef-
fective ones may be minimized.
About the medical criterion, the number of ex-
ams done before their due dates has to be maximized.
Thus, if a patient needs other exams, the next ones
could be done on time. If an exam is planned after its
due date, the tardiness may be minimized.
3.3.2 Constraints
Constraints that Must Be Respected
Each exam must be assigned to human resources,
one material resource and one period. The consid-
ered human resources must be assigned during the
period at the place where the considered material
resource is located.
Compatibility between the material resource and
the exam: the assignment must satisfy the given
list of incompatibilities between exams and mate-
rial resources.
Compatibility between skill of the human re-
source and the type of the material resource: for
each exam, the human resource must be able to
work on the considered material resource.
If a human resource can move during the plan-
ning horizon, its moves are constrained: a human
resource can only work at one place during one
period.
Constraints that May Be Respected
Exams should be done before their due dates and
at their reference place.
Material resources and human resources may be
used or work during their opening schedule. Oth-
erwise, additional time is considered as overtime.
Overtime is limited in time.
4 CONSIDERED PROBLEMS
The considered problem is defined as follow: exams
planning and assignment of needed material and hu-
man resources. The previous analysis was about the
complete problem. Some hypothesis are made to di-
vide this complete problem into three problems.
4.1 Hypothesis
The following hypothesis are made:
HEALTHINF 2017 - 10th International Conference on Health Informatics
262
Only one human resource and one material re-
source are needed to perform exams. Human re-
sources are compatible with one or several types
of material resources.
Processing time of the exams are given and fixed.
Opening schedules of material resources are equal
in every periods.
To each exam, the release date is equal to the date
of appointment decision. These dates are equal to
zero: all exams are known at the beginning of the
planning.
Distances between places are taken into account
in the time allocated to the human resources to
move from one place to another. This time is as-
sumed to be constant, all places are equidistant to
the others.
Overtime is not allowed.
4.2 Definition of the Considered
Problems
The complete problem is divided into three problems
of increasing difficulty:
Problem 1 is the more basic: human resources are
not considered. Only the material resources are
considered.
Human resources are considered in Problem 2.
They can work on one or several types of mate-
rial resources. They cannot move, they work all
the time at the same place. The assignment of the
human resources at the places is given.
Human resources are mobile in Problem 3. They
can work on several places, they can move from
one place to another. The assignment of the hu-
man resources at the places has to be built by the
model.
Two criteria are used in the following study:
Sum of assigned periods to all exams, which en-
sure that all exams are planned as soon as possi-
ble.
Number of exams assigned before their due date.
4.3 Analogy with the Bin Packing
Problem
Our problem can be seen as a bin packing problem
(Gourgand et al., 2014a). The bin packing problem
considers N items, with a given size, and some bins
with the same capacity. The aim is to pack all the
items in a minimum number of bins. The size of the
packed items has to respect the capacity of the bins.
Each item has to be assigned once and only once.
4.3.1 Without Human Resources
Considering Problem 1, the aim is to assign exams
to a material resource during a period. The planning
horizon is made by couples (resource, period). The
objective is to assign exams to couples (resource, pe-
riod). Exams have to be done as soon as possible: the
aim is to minimize the number of couples, (= the num-
ber of bins). An example is given by Figure 1, where
the assignment of exams to material resources MR
1
,
MR
2
and MR
3
is considered. Table 1 summarizes
analogies between bin packing problem and Problem
1: exams planning with resources assignment.
Time
Bin
Resource
MR
1
MR
2
MR
3
Period
Monday AM
MR
1
MR
2
MR
3
Monday PM
1
6
3
4
2
7
11
5
Opening
schedule
of resources
Caption:
X
Exam
number X
Figure 1: Representation of Problem 1.
Table 1: Analogies between both problems.
Bin packing Problem of exams planning
problem with resources assignment
Data
Item Exam
Bin Couple (resource, period)
Size of an item Processing time of an exam
Capacity of a bin Opening schedule of resources
- Due date
- Reference place
Problem
Assign items Assign exams to one couple
to one bin (resource, period)
Constraints
Capacity of bins Opening schedule of resources
- Constraint of compatibility
Criteria
Minimize the number
-
of used bins
-
Minimize the sum of
assigned periods
4.3.2 With Human Resources
Exams have to be assigned to material and human re-
sources during one period. Analogy is made between
this problem and interdependentbin packingproblem.
Let’s take p
1
and p
2
two bin packing problems,
with a given number of bins. Groups of bins are de-
fined in both problems. A group should be made by
one or several bins. Number of bins can be different
Medical Imaging: Exams Planning and Resource Assignment - Hybridization of a Metaheuristic and a List Algorithm
263
for both problems, but number of groups is the same.
Each item is assigned to one and only one bin in each
problem. Interdependence between both problems is
defined as follow: if an item is assigned to a bin from
group g in problem p
1
, it must be assigned to a bin
from the same group g in problem p
2
. The aim is
to assign items in bins of both problem, by minimiz-
ing the number of used bins, satisfying capacity con-
straints and interdependence between both problems.
In our case, both problems p
1
and p
2
can be de-
fined like this:
p
1
: assignment of each exam to a material re-
source during a period, respecting the opening
schedule of the material resource during the pe-
riod and the compatibility between the exam and
the material resource.
p
2
: assignment of each exam to a human resource
during a period, respecting the work time of the
human resource during the period and the compat-
ibility between the exam and the human resource.
Compatibility between exam and human resource
is not directly defined but can be deduced: an exam
is compatible with a human resource if and only if
this exam is treated by a material resource from one
type and this human resource can work on this type of
material resource.
Thus, group g is the couple (period, type). In
both problems p
1
and p
2
, exam has to be assigned
during the same period to the same type of material
resource. Figure 2 illustrates the interdependent bin
packing problem in the HGT case. The lower portion
of the figure is the assignment of exams to material re-
sources and periods, in the same way as Figure 1. The
upper portion is the assignment of exams to human re-
sources and periods. In both portions, each exam has
to be assigned to the same period and the same type
(according to the type of the material resource and the
competencies of the human resource to use this type).
5 RESOLUTION METHOD
The bin packing problem is NP-Hard (Garey and
Johnson, 1979). Our problems are an extension of the
bin packing problem, so our problems of exams plan-
ning with resources assignment are also NP-Hard. In
the following, approximate methods are used to solve
them.
Our proposed method is a hybridization of a meta-
heuristic and a list algorithm. Our tool is convenient
because one part is generic: it can be used for any
of the considered problems. Only the list algorithm
needs to be specific to the considered problem.
Time
Bin
Type
Material
Resource
X-ray
MR
1
Scanner
MR
2
MR
3
Period
X-ray
MR
1
MR
2
Scanner
MR
3
Monday PM
1
6
3
4
2
7
8
5
Opening
schedule
of material
resources
Time
Bin
Type
Human
Resource
X-ray
HR
1
Scanner
HR
2
Period
X-ray
HR
1
Scanner
HR
2
Monday PM
1
6
3
4
2
7
8
5
Planning
of human
resources
Group 1
Group 2
Monday AM
Monday PM
Figure 2: Interdependent bin packing problem.
5.1 Genericity
The proposed tool, illustrated by Figure 3, uses a hy-
bridization of a metaheuristic and a heuristic, more
precisely a list algorithm. A single solution based
metaheuristic or a population based metaheuristic can
be used. The encoding used by the metaheuristic is
a list Y of exams. The list algorithm L considers
the exams according to their order in list Y to plan
and assign them to the required resources, consider-
ing the problem constraints. This builds a solution
X. The objective function H evaluates the solution
X. According to this evaluation, the solution is cho-
sen or not by the metaheuristic. At the end of the
running, the given solution by the hybridization is the
best listY
of exams: the one which optimizes the ob-
jective function by applying the list algorithm. This
hybridization can be used to solve many problems:
the specificity of a given problem is only considered
in the list algorithm.
5.2 A List Y of Exams
The general scheme of the encoding is given by Equa-
tion (1), with the set of all the lists Y and S the set
HEALTHINF 2017 - 10th International Conference on Health Informatics
264
A list Y of exams
Metaheuristic
List
algorithm
The best list Y
Cost H of
this solution
Solution X?
(assignment
and planning)
Figure 3: Hybridization metaheuristic - List algorithm.
of all the admissible solutions X built by the list algo-
rithm L.
Y
Heuristic L
L(Y) = X S
Criterion H
H(X) (1)
The set is the set of all permutations of exams.
Cardinal of is N! with N the number of exams. One
solution Y is a list of exams. More details about
the encoding are given in (Gourgand et al., 2014b).
5.3 Metaheuristic
The metaheuristic performs in the set of solutions .
An initial solution is randomly computed: a list of ex-
ams randomly sorted between one and the number of
exams. Several metaheuristics have been used: some
single solution based metaheuristics such as iterated
local search or simulated annealing. A neighborhood
system is used to visit the set of solutions, it allows
to go from one solution to another one. Neighbor-
hood system V is a permutation of two exams in the
list Y: the exam at position i permutes with the one
which is at position j. V satisfies the accessibility and
reversibility properties.
5.4 List Algorithm
A list algorithm is used to build the solution X from
the list Y: it assigns the exams to resources and to
periods.
List scheduling algorithms are one-pass heuristics
that are widely used to make schedules. A standard
list scheduling algorithm constructs a schedule by as-
signing each job in listed order to the first machine
that becomes idle (Zhu and Wilhelm, 2006). It is
important to work with a list algorithm, because the
metaheuristic browses the set of solutions. So the
used algorithm needs to consider the order of the list
to assign exams to resources and periods.
Our problem has be analyzed as a bin packing
problem and some list algorithms have been proposed
since the definition of this problem (Johnson, 1973).
So our developed list algorithm is inspired by them.
For instance, considering Problem 1, in which human
resources are not considered, Algorithm 1 is an ex-
tension of the First Fit algorithm for the bin packing
problem. Other list algorithms can be adapted from
Algorithm 1 to solve the cases of Problems 2 and 3,
considering human resources.
Algorithm 1: List Algorithm First Fit HGT.
Data: List of exams (Y
i
)
i∈{1,N}
; opening
schedule of all resources during all
periods; processing time of all exam
1 Occupied time := 0 for all resources and all
periods
2 forall the i do
3 First resource, first period,
assigned := false
4 while (assigned = false) AND current
period max of periods do
5 while (assigned = false) AND current
resource max of resources do
6 if exam Y
i
is compatible with
current resource then
7 if exam Y
i
fits in couple
(resource, period) then
8 Assign exam Y
i
to couple
(resource, period)
9 Update occupied time of
couple (resource, period)
10 assigned := true
11 Next resource
12 Next period
5.5 Objective Function
Solutions are compared according to an objective
function which characterizes the quality of the solu-
tion. In our case, the objective function represents the
timing aspect of our problem. Exams have to be done
as soon as possible, thus the makespan, the period as-
signed to the last exam, should be considered. Be-
cause many solutions may have the same makespan,
we choose instead the sum of assigned periods to all
exams, so the solutions can be dissociated. This cri-
terion is written H
S
. Another criterion is considered
to ensure that most of the exams are assigned before
their due date. This criterion, written H
D
, is computed
as the number of exams assigned after their due date.
The weighed criteria method is used (Coello, 2000).
The objectivefunction is a weighed sum between both
criteria, defined by Equation (2). ω
D
is chosen equal
to 5 because H
S
is always smaller than 10
5
so both
criteria are easily readable. This function has to be
minimized.
H(X) = 10
ω
D
× H
D
(X) + H
S
(X) (2)
Medical Imaging: Exams Planning and Resource Assignment - Hybridization of a Metaheuristic and a List Algorithm
265
5.6 The Best List Y
Algorithm 2 describes the whole method with the ex-
ample of stochastic descent as the used metaheuristic.
Stochastic descent may be used in an iterated local
search. The set of the lists of exams is browsed
thanks to the metaheuristic using neighborhood sys-
tem V. Lists are compared thanks to the list algorithm
L and the objective function H. According to an ac-
ceptance criterion, some lists are selected. At the end,
the metaheuristic gives the best found list Y
.
Algorithm 2: Hybridization between stochastic de-
scent and a list algorithm.
Data: Initial solution Y
1 X := L(Y)
2 while necessary do
3 Choose uniformly and randomly Y
V(Y)
4 X
= L(Y
)
5 if H(X
) H(X) then
6 X := X
7 Y := Y
Result: Y
= Y
6 EXPERIMENTS
The data are randomly generated but the characteris-
tics and the size of the data represent real instances.
The HGT is composed by 3 places. The planning
horizon is made by 8 to 40 periods. As a remind,
one period represents one half-day, thus the planning
horizon is between 4 and 20 days. 4 to 8 resources
are available. 50 to 500 exams need to be planned
and assigned. Incompatibilities between exams and
resources are randomly generated. Each processing
time is between 5 and 100. Each material resource
has an opening schedule equal to 300 minutes.
The results are detailed in Table 2. The host ma-
chine is powered by an Intel Xeon X5687 quad-core
CPU running at 3.6 GHz. The computation has been
stopped after thirty minutes. Each reported result is
the value of the objective function for the best solu-
tion found in less than thirty minutes, but most of the
time, the best solution is found in a few minutes. The
results are presented as a couple of values (H
D
;H
S
)
with H
D
the number of exams assigned after their due
dates, and H
S
the sum of assigned periods to all the
exams. The results compare three methods:
The resolution of the mathematical model with an
exact method by using the solver CPLEX. If no
optimal solution has been found in less than thirty
minutes by the solver, no result is written.
Our results from the method previously published
in (Gourgand et al., 2014a), using two single so-
lution based metaheuristics (iterated local search
and simulated annealing) in a classical way: the
best value found by all these methods is reported.
Our results from our proposed method detailed in
the current paper. The used metaheuristics are dis-
tinguished: iterated local search and simulated an-
nealing, written ILS* and SA*.
The results are promising. Firstly, this problem
has been solved by CPLEX thanks to our mathemat-
ical model previously proposed. The solver finds an
optimal solution only for small size of problems (less
than two hundred exams over four days). The solver
does not find any solutions when the size of the prob-
lem increases. Then, it has been solved with two ap-
proximate methods: in a classical way, and with a
hybridization. Both methods find an optimal solu-
tion for the small instances. For biggest instances,
the hybridization between a metaheuristic and a list
algorithm outperforms our previous method. Simu-
lated annealing seems to work better than iterated lo-
cal search.
7 CONCLUSION AND
PERSPECTIVES
The current hospital context needs to find solutions
to improve efficiency of hospital systems. Hospital
cooperation has emerged, as Hospital Group of Terri-
tory. A pooling of resources may cause a better use
of the different places in a same territory. But this
cooperation needs some decision support tools to im-
prove or optimize their running. In this paper, we de-
fined the general problem of activities planning with
resources assignment in a multi-place hospital con-
text.
Because this problem is NP-Hard, we propose an
approximate method to solve it: a hybridization be-
tween a metaheuristic and a list algorithm. The re-
sults are promising: our method finds good results in a
few minutes. An improvement of the results is in pro-
cess, using a population based metaheuristic: Particle
Swarm Optimization. Using PSO, the results are very
good for small instances: an optimal solution is found
in a few seconds, but the method still needs some tun-
ing for the biggest instances.
Thanks to the hybridization, our method can be
easily reusable. Indeed, to solve other problems, only
the list algorithm needs to be modified. The meta-
heuristic part will still be the same. Any kinds of
planning, assignment or scheduling problem can be
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Table 2: Results: (number of exams assigned after their due dates; sum of assigned periods to all the exams).
Number of exams CPLEX (Gourgand et al., 2014a) ILS* SA*
50 (0;51) (0;51) (0;51) (0;51)
50 (1;150) (10;147) (1;151) (1;150)
100 (0;131) (0;131) (0;131) (0;131)
100 (0;517) (2;535) (1;516) (0;518)
200 (0;266) (0;266) (0;266) (0;266)
200 - (3;1197) (0;1154) (0;1135)
300 - (0;548) (0;537) (0;534)
400 (0;830) (0;890) (0;841) (0;835)
500 - (0;1350) (0;1241) (0;1234)
500 - (194;8218) (19;6382) (18;6659)
solved thanks to this tool by changing the list algo-
rithm: for instance, it has been used to solve an in-
dustrial problem (Silva et al., 2016). Problems with
human resources can easily be solved by developing
some new list algorithms dedicated to them. Then, a
direct application to a hospital system could be envis-
aged. Other applications in the hospital field could be
done, in other hospital services, with other resources,
etc. We could extend our current work about med-
ical imaging to medical surgeries. More constraints
about medical team should be considered. The next
problematic is to consider patients with several ex-
ams or surgeries, by taking into account precedence
constraints between them.
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