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Kocsis, Tibor and Negny, Stéphane and Floquet, Pascal and Meyer, Xuân-Mi and
Rév, Endre Case-based reasoning system for mathematical modelling options and resolution
methods for production scheduling problems: case representation, acquisition and retrieval.
(2014) Computers & Industrial Engineering, 77. 46-64. ISSN 0360-8352
OATAO
Case-Based Reasoning system for mathematical modelling options and
resolution methods for production scheduling problems: Case
representation, acquisition and retrieval
Tibor Kocsis
a,b, Stéphane Negny
a,⇑, Pascal Floquet
a, Xuân Meyer
a, Endre Rév
ba
Université de Toulouse, LGC UMR 5503 – INPT ENSIACET, 4 allée Emile Monso, BP 44 362, 31030 Toulouse Cedex 4, France b
Budapest University of Technology and Economics, Department of Chemical and Environmental Process Engineering, Budafoki út 8, 1111 Budapest, Hungary
a r t i c l e
i n f o
Keywords:
Decision-support system Process scheduling Case Based Reasoning
Classification and notation system Case retrieval
a b s t r a c t
Thanks to a wide and dynamic research community on short term production scheduling, a large number of modelling options and solving methods have been developed in the recent years both in chemical pro duction and manufacturing domains. This trend is expected to grow in the future as the number of pub lications is constantly increasing because of industrial interest in the current economic context. The frame of this work is the development of a decision support system to work out an assignment strategy between scheduling problems, mathematical modelling options and appropriate solving methods. The system must answer the question about which model and which solution method should be applied to solve a new scheduling problem in the most convenient way. The decision support system is to be built on the foundations of Case Based Reasoning (CBR). CBR is based on a data base which encompasses pre viously successful experiences. The three major contributions of this paper are: (i) the proposition of an extended and a more exhaustive classification and notation scheme in order to obtain an efficient sched uling case representation (based on previous ones), (ii) a method for bibliographic analysis used to per form a deep study to fill the case base on the one hand, and to examine the topics the more or the less examined in the scheduling domain and their evolution over time on the other hand, and (iii) the prop osition of criteria to extract relevant past experiences during the retrieval step of the CBR. The capabilities of our decision support system are illustrated through a case study with typical constraints related to process engineering production in beer industry.
1. Introduction
This research is focused on the issue of capitalizing simulation modelling knowledge to efficiently develop relevant models for short term scheduling applications. Indeed, the supply chain of a company is a complex network which involves the integration of information, transportation, procurement of raw materials, inven tory, transformation into finished products, warehousing, material handling and distribution of finished products to end users. The goal is to reach a high end user satisfaction level at a low cost.
One of the main functions in the supply chain is the production which aims to use available production capacities to produce the desired products. The coordination of the production is one way to achieve high efficiency with low cost. This can be done through the production planning. But planning refers to a wide range of activities with different decision levels and different time scales. Among them, scheduling is a crucial step which is a short term planning dealing with the allocation of resources to tasks (assign ments and sequencing of tasks to units) over time with one or var ious objectives to optimize.
However, the growing worldwide competition in the current context imposes new industrial strategies based on more and more flexible processes affording a greater reactivity to remain compet itive in the global marketplace. Indeed, for the manufacture of chemicals or materials, the production process or the demand pat tern is likely to change. The inherent operational flexibility of industrial plants provides the platform for great saving in good Abbreviations: AI, Artificial Intelligence; BBT, bright beer tank; CBR, Case Based
Reasoning; CTR, continuous time representation; MILP, Mixed Integer Linear Programming; MINLP, Mixed Integer Non Linear Programming; NMF, non negative matrix factorization; PSE, process system engineering; RBT, raw beer tank; RTN, Resource Task Network; STN, State Task Network; USTE, Unit Specific Time Events.
⇑Corresponding author.
production schedu
l
es as
it
is the core of production
manag
eme
nt.
This
flexibility is
incr
eased
because of the demand for greater prod
uct customization and diversification. As a consequence produc
tion processes become more complex with multi
p
roducts
or
m
u
l
tipurpose plants with batch
mixing
/spli
tt
ing,
m
u
l
ti units,
m
u
lti
recipes for products constructions and an
incr
eas
ing
set of produc
tion constraints. Moreover, processes
n
eed
reengineering to
respect
n
ew constraints coming
from
the legislative world
( e
n
v
i
ronmenta
l
, security constraints) or
from
the e
nt
e
rpris
e
its
elf (cost
reduction, production centralizationi
F
urthermore, the application
of process eng
in
ee
ring
towards
n
ew
areas, such as food, biotechno
logica
l
, electro
n
ic or pha
rmac
eutica
l
ind
ust
r
ies is generating
n
ew
production and scheduling problems with additiona
l
resource con
straints, batching decisions, process restrictions, handling mixing
and splitting streams.
T
o address a
ll
of these scheduling issues,
the p
roc
ess system e
ngin
ee
ring
community
has
developed severa
l
mod
e
ls
, and resolution
m
et
hods.
Th
e
r
esea
rch
area on scheduling
has
been broadly studied by
both the
industry
and the academia world
r
esu
l
ting
in
significant
advances
in
relevant modelling and solution techniques. Numer
ous research studies
ha
ve been
mad
e of this area, e
.g.
(
Blazewicz,
Ecker, Pesch, Schmidt,
&Weglarz, 2007; Esquirol
&Lopez, 1999;
Maravelias,
2012
i
Scheduler show
in
ve
nt
ive
n
ess
to propose
n
ew
mod
e
llin
g options and
impro
ved
math
e
mat
ica
l
m
et
hods
to address
to these complex highly combinatoria
l
problems.
Th
e inc
r
eas
ing
number
of research articles dedicated to short term scheduling
problems bears out this trend. Accordingly, plenty of possibilities
of association between
mod
e
llin
g options, and between
mod
e
l
s
and
r
eso
lut
io
n
methods are thus ava
il
able.
More
and more difficult
and
larg
e
r
problems than those studied years ago can be
now
solved, sometimes eve
n
to optimality
in
a
r
easonable time thanks
to
mor
e efficient
int
egrated
math
ematica
l
fram
eworks
. This impor
tant achievement comes mainly
from hug
e advances
in
mode
llin
g
techniques, a
l
gorithmic solutions and computationa
l
technologies.
This r
esu
lts in
different possibilities to mode
l
a scheduling prob
tern, but a
l
so
mult
ip
l
e
math
e
matical
formulations for the same
mod
e
l.
Th
e
diversification of
mod
e
llin
g options, the combination
and creation of resolution methods are
incr
eas
ing
and w
ill
going
to grow
in
the fo
ll
owing years
in
order to e
nlarg
e the
class
es and
the size of the problems treated.
F
or
instanc
e
in
Sundaramoorthy
and
Maravelias
(2008)
the
number
and size of batches are
now
included
as decision variables (
mat
e
rial
based approach)
in
a job
shop problem whereas before they were fixed
(batch
based
approach).
T
o show the richness of the
mod
e
llin
g options developed to
dea
l
with the
incr
eas
ing
complexity of problems, we ca
ll
r
efe
r
e
nce
h
ere
to the we
ll
known and widely used
exa
mpl
e
:
the chemica
l
process problem proposed by
Kondili, Pantelides, and Sargent
(1993)
.
Asshown
in
Fig. 1
, three
raw
materials
(A,B
and
C)are
required, three
int
ermediates and two fina
l
products are produced
through five stages: heating, reactions 1 3, and separation.
In
their work
Kondili et al. (1993)
hav
e solved this problem by
applying a discrete time representation mode
l
with the following
assumptions: process times are
invariab
le and
ind
epe
nd
e
nt
of size,
products of the same task can arrive
in
different times, a
ll
transit/
changeover times are
included into
process times or
n
eg
l
ected
.
Other models
hav
e been successfu
ll
y applied to the same problem
by
Maravelias and Grossmann (2003)
and
lerapetritou and Floudas
(1998)
with the assumptions that products of the same task arrive
in
the same time, and process times can be size dependant.
Th
ey
applied a globa
l
and a unit specific time eve
nt
based mode
l
respec
tively.
Pan,
Li,and Qian (2009)
r
eused
the Kondili
problem
and
applied six different
mod
e
ls
successfu
ll
y.
Th
ey
also tested the
problem with different objectives: makespan minimization and
profit
maxim
izatio
n r
espect
iv
e
ly. Th
ey performed a comparative
Product 1 lntAB Reaction 2 A lnt BC lmpE Separation Product 2 B Reaction 1 Reaction 3 C
Fig. 1. Example of Kondili et al. {1993}
analysis ofthis example, showing that
num
erous
mod
e
ls
are ava
il
able to the same problem, without a unique "best one".
Table 1
summarized some of the above research studies but the
list
is far
from
being ex
haustiv
e,
not m
e
nt
io
ning
yet the different
possible solving methods:
Hegyhati and Friedler (2011)
precise
that
most
of the published approaches are based on a
mixed int
e
ger prog
ramm
i
ng
formulation and they analyze the combinatoria
l
natur
e of batch scheduling problems.
Th
e
r
efore, this
m
ere example
underlines that
in
order to choose between mode
llin
g options and
solving
m
et
hods
strategies, we need a decision support system,
especia
ll
y as the process and manufacturing
industri
es gather a
wide range of applications lead
ing
to a variety of processing char
acteristics and constraints to take
into
account. Accordingly, the
number
of research papers has
increased
to develop
n
ew
mod
e
l
options and
num
e
rical
methods to account for these specific con
straints, reinforcing the
n
eed for a decision support system.
Th
e
goa
l
of this decision support system is to help user
in
choosing
the mode
llin
g options and the appropriate solving methods thanks
to a detailed description of the faced scheduling problem.
B
ut
in
front
of the difficulty to build such a system and the huge
int
e
r
est
of the process
eng
in
ee
rin
g community to
mathemat
ica
l
approaches,
in
the
r
est of the study we voluntary
limit
this work
to a decision support dedicated to
math
ematica
l
approaches.
Zhou, Son, Chen, Zhang, and MA (2007)
have explained that the
mod
e
l
development is a time consuming and knowledge
int
e
ns
e
activity that require skills
from
three different fields: domain
expertise,
mod
e
llin
g and simulation, and
impl
eme
ntat
io
n
F
or the
development of models,
Meyer
(2004)
has
formalized a
p
roc
ess
commonly used
in
process system e
ngin
ee
rin
g
(
PSE
),
Fig. 2
.
T
his
process clearly demonstrates that the development of a
mod
e
l
is
an activity which
r
elies
on the sk
il
ls and experiences of a working
group composed of expe
rts
with diverse background and know
l
edge: domain of application (fo
r instanc
e physics, chemistry, bio
l
ogy), PS
E
, computer science.
Ind
eed, to facilitate the resolution
it
is
often
n
ecessary to
r
ea
liz
e a
pre
liminary
work for structu
rin
g the
system of equations or to give
it
a specific form to easy
initializa
tion and have a stable, accurate and robust resolution
Moreov
e
r
,
as
Zhou, Chen, He, and Chen (2010)
hav
e underlined
most
of sim
ulation models developed are often customized and specific ones
Table 1
Different solution strategies to the Kondili-problem.
Paper
Kondili et al (1993)
Assumptions
Process times are invariable and independent from size Products of the same task can arrive in different times
Model (type)
Discrete time representation, based on time intervals of equal lengths ( MlLP)
No transit/changeover, but sequence/frequency dependant cleaning are considered
Maravelias and Grossmann (2003)
Process times depend on the quantity of material Sequence dependent changeover times Utility constraints are considered
Process times depend on the quantity of material
Continuous time representation based on global time events ( Ml LP)
lerapetritou and Floudas
(1998) No transit/changeover, but clean-up requirements and multiple due dates are considered
Continuous time representation based on unit-specific time events
(MlLP)
Sundaramoorthy and Karimi (2005)
Storage and idle waiting are considered as special tasks Continuous time representation, based on time intervals (slots) of variable lengths (MlLP)
Pan et al. (2009) Profit maximization and makespan minimization are considered Six different continuous time representation models ( MlLP)
.
Process for Model Development
1-Identification of the principal purpose of the modeling
2-Characterisation of the system studied: kinetics, thermodynamic ...
3-Identification of the principal phenomenon (limiting phenomenon ... )
4-Selection of a theorical basis: model assumptions 5- Equations formulation
6-Degree of freedom analysis 7- Choice of the resolution method
8-Parameters estimation
9- Model validation with experimental data
10-Model documentation
11- Model implementation in a simulation environment
12-Future model developments
Fig. 2. Model development.
I
but
PSE
experts
try to
develop generic
models that
can be easily
reused
and/or adapted. Consequently
PSE
experts continuously
propose new inventive mode
lli
ng
opt
i
ons and solv
i
ng methods to
increase
reusability and
to
dea
l
with the
increasing
complexity of
the
prob
l
ems treated.
A mode
l
is
richer in knowledge
than the one exp
r
essed through
the system of equat
i
ons.
This knowledge
is
not
always
clearly
exp
r
ess but is
crucia
l
to
reach relevant mode
l
and solut
i
ons.
The
cha
ll
enge is
to
ensure
knowledge
engineer
i
ng in
order to
reuse
we
ll
known
and optim
i
zed
past
exper
i
ences to
increase
quality
of solut
i
on and
mode
lli
ng
decis
i
on, decrease the time of
mode
l
deve
l
opment.
Bes
i
des,
in mode
l
development
knowledge
and skills
of experts are difficult to
formalize
and capitalize because of their
unstructured
nature. However,
some
Almethods
seem
to
be appro
priate
to construct such a decis
i
on a
i
d system.
Among Al methods
for knowledge management,
we dec
i
de
to
use Case
Based Reason
ing
(
CBR) to capitalize and reuse
past
experiences of
PSE
expert
because of
its
ability and facility for
knowledge
formu
l
at
i
on,
knowledge
acquisit
i
on, and
knowledge maintenance.
I
n
order to e
l
aborate such a decis
i
on support system the exist
ing knowledge has
to be extracted,
modelled,
adapted, diffused,
maintained
and actualized. Some
Artificia
l
Intelligence
(
Al) meth
ods were deve
l
oped to
manage knowledge
used and dep
l
oyed
in
a domain and to
prov
i
de assistance to a
p
r
ocess engineer
in
the
deve
l
opment and the
resolut
i
on of short term scheduling
models.
Accordingly,
the
purpose
of this art
i
cle is twofold.
F
irst it presents
the basis of a decis
i
on support system to
propose
relevant and suit
ab
l
e
mode
lli
ng
opt
i
ons and
resolut
i
on
method
for scheduling
prob
)
em.
This implies
the development of a classificat
i
on scheme of the
mode
lli
ng
approaches
to
describe genera
l
problem.
Consequently,
the second
purpose
dea
l
s w
i
th the
creat
i
on and operat
i
on of a past
exper
i
ences
memory
to solve
new prob
l
ems.
T
he remainder
of this art
i
cle
is structured as fo
ll
ows:
the
second
part
presents and discusses
the
existing
Al
app
r
oaches and espe
da
ll
y CBR to dea
l
with a computer a
i
ded system.
In
this
part
a
clas
sificat
i
on and a
notat
i
on are proposed to
rep
r
esent a scheduling
prob
l
em and
its
associated solut
i
on
in
terms of scheduling opt
i
ons
and solut
i
on
methods. In
the subsequent part,
the
issue of case
base
fi
lli
ng
is discussed and a
method
for bib
li
ographic analysis
is proposed
in
order to extract
relevant research past
experiences.
Part
4 dea
l
s with the
prob
l
em of case retr
i
eva
l
and
more precisely
the sim
il
arity
measurement
and
introduces
the concept of adapt
ability.
Before
to
draw
the conclus
i
on,
in part
5, a case study
re
l
ated to beer p
r
oduct
i
on is
proposed to
ill
ustrate the
main
steps
of the approach.
2. Basic co
n
ce
p
ts of the
d
ecis
i
o
n
-su
pport
sys
t
e
m
2.1. Artificial Intelligence approaches in scheduling
Artificia
l
Intelligence
(Al)is the
mimicking
of
human taught
and
cognitive
p
r
ocesses to solve complex
problems.
Aluses techniques
and bu
il
ds
tools
to represent,
cap
i
talize,
manipulate
and
reuse
knowledge. The
genera
l
desire of
Alapp
r
oaches is to
make
use of
past
exper
i
ences, and every
knowledge
based system
tries to
record
and
reuse
an earlier episode where a
prob
l
em was tota
ll
y
or part
i
a
ll
y solved.
Most
of
Alapproaches encapsulate
knowledge
gained
from human
experts and apply
it
automatica
ll
y to
make
decis
i
ons.
T
he process
of acquiring expert
knowledge
and to
man
age
i
t
requires
cons
i
derab
l
e sk
ill
s
to
perform successfu
ll
y. Among
A
l
app
r
oaches, expert systems
imitate human
reasoning, consider
ing it
as being decomposab
l
e
into
elementary steps. An expert sys
tern is
made
up of a base of
ru
l
es and a base of facts
regrouping
the
propert
i
es that are "true"; condit
i
on and a consequence part
(
IF
THEN
rules).
Then
an
inference
engine
permits
to determine the
condition parts of
rules that
are satisfied and the consequences
that can be deduced. Severa
l
attempts
have
been
made in
order
to
mode
l
the knowledge
on the domain of scheduling or on a given
workshop.
T
hese experiences
have met
two great difficu
l
ties:
li
ttle
genera
l
knowledge
seems to exist about this area and
the
deve
l
op
ment
of a base of knowledge
needs important
effort. Addit
i
ona
ll
y,
the
knowledge
app
li
ed to scheduling
prob
l
em does
not
seem to
rea
ll
y
fit
to a binary schema such as the "simp
l
e"
p
r
oduct
i
on
ru
l
es.
Expert
systems sound a
l
so
inappropriate
because of
its
difficu
l
ty to
Th
ere were also a
t
tempts w
i
t
h n
eura
l
n
etworks
. T
he goa
l
is
n
ot
to
i
m
i
tate t
h
e huma
n r
easo
nin
g but t
h
e capab
ili
t
i
es to
l
ea
rn
o
f
t
h
e
h
uma
n
bra
in. Th
e "k
n
ow
l
edge" is stored
in
t
h
e co
nn
ectio
n
weig
ht
s
.
Th
e comp
l
ex
i
ty o
f
t
h
e decis
i
o
n
p
r
ocess makes
i
t
diffi
cu
l
t to bu
il
d a
su
ffi
cie
n
t
l
y comp
l
ex
n
eura
l
n
etwork to
m
ode
l
t
h
e reso
l
ut
i
o
n
strat
egy
t
oo
.
C
B
R is a
n
a
l
te
rn
at
i
ve to
r
u
l
e based systems
.
C
B
R t
r
i
es to fi
nd
a
so
l
ut
i
o
n
to a g
i
ve
n
prob
l
e
m
w
i
t
h
t
h
e
h
e
l
p o
f
t
h
e so
l
ut
i
o
n
o
f
a s
im
il
a
r
prob
l
em, so
l
ved
in
t
h
e past.
I
n
t
h
is approac
h
t
h
e ce
n
t
r
a
l
e
l
e
me
n
t is a case, wh
i
ch
r
ep
r
ese
n
ts a co
n
textua
l
expe
ri
e
n
ce
composed o
f
t
h
e problem desc
ri
pt
i
o
n
, t
h
e so
l
ut
i
o
n
des
cri
pt
i
o
n
a
nd
the e
n
v
i
ro
n
me
n
t o
f
a prob
l
em
.
Numerous cases a
r
e sto
r
e
d in
a case
m
e
m
ory,
i.
e
.
case base
. Th
en, when a
n
ew problem is
m
et,
t
h
e so
l
ut
i
o
n
o
f
a
r
et
ri
eved case is adapted
i
n orde
r
to match more
p
r
ecise
l
y w
i
t
h
t
h
e
ini
t
i
a
l
prob
l
em
. Th
e C
B
R assu
m
es
:
•
T
o be ab
l
e to forma
li
ze t
h
e k
n
ow
l
edge by some para
m
eters
in
o
r
de
r
to desc
ri
be a case
.
•
T
o deter
m
i
n
e a s
imil
a
ri
ty fu
n
ct
i
o
n
per
m
i
t
t
in
g to extract a rele
va
n
t case to so
l
ve t
h
e face
d
prob
l
em
.
•
T
o be able to adapt t
h
e retr
i
eved so
l
ut
i
o
n.
•
T
o sto
r
e e
n
ough cases
in
t
h
e memory to have t
h
e max
i
ma
l
cov
e
r
age o
f
t
h
e prob
l
ems a
n
d so
l
ut
i
o
n
s spaces to e
n
su
r
e C
B
R
e
ffi
cie
n
cy
.
Th
ese A
l
approaches are
m
ore approp
ri
ated to
m
ode
l
loca
l
k
n
ow
l
edge
in
o
r
de
r
to
i
m
i
tate t
h
e huma
n
behav
i
ou
r
to make
c
h
o
i
ce o
n m
ore efficien
t
m
et
h
ods, e
.
g
.
co
n
stra
in
ts progra
m
m
in
g
.
Acco
rdin
gly, t
h
ese met
h
ods a
r
e ma
inl
y used to just
if
y p
ri
o
ri
ty
c
h
o
i
ces
in
a spe
ci
fic co
n
text o
r
to set some genera
l
va
ri
ab
l
es o
f
t
h
e sc
h
edu
lin
g prob
l
em
. B
ut t
h
ey are also use
d
to c
r
eate a corn
p
l
ete so
l
ut
i
o
n
to a schedu
lin
g prob
l
e
m.
As ex
p
l
a
in
ed befo
r
e, due to cu
r
re
n
t mat
h
ematica
l
,
n
ume
r
i
ca
l
a
n
d computer evo
l
ut
i
o
n
s t
h
ere is a g
l
oba
l
tre
n
d to develop a
n
d
so
l
ve
Mi
xed
In
tege
r Lin
ea
r P
rog
r
amm
in
g
(
M
IL
P
)
a
n
d
Mi
xed
In
tege
r
No
n Lin
ea
r P
rog
r
amm
in
g
(
M
I
N
L
P
)
models fo
r
sc
h
edu
lin
g prob
l
ems
bot
h in m
a
n
ufactu
rin
g a
n
d
in
chemica
l
p
r
ocesses commu
ni
t
i
es
. In
t
h
is co
n
text, A
l
approac
h
es ca
n
a
l
so be use
d
as met
h
od to c
r
eate a
decis
i
o
n
a
i
ded system dedicated to t
h
e first steps o
f
t
h
e
m
ode
l
e
l
abo
r
at
i
o
n:
assumpt
i
o
n
s, t
i
me
r
ep
r
ese
n
tat
i
o
n
, object
i
ve fu
n
ct
i
o
n
,
n
umerica
l
m
et
h
ods
. T
o create such a dec
i
s
i
o
n
a
i
ded system, C
B
R
is
r
eleva
n
t because
i
t deals w
i
t
h
a symbolic
r
ep
r
ese
n
tat
i
o
n
w
hi
l
e
n
eu
r
a
l
n
etworks used
n
u
m
erica
l
o
n
e
. In
C
B
R systems t
h
is task
requ
ir
es s
i
g
ni
fica
n
t
l
y
l
ess k
n
ow
l
edge acquis
i
t
i
o
n
effo
rt
s
in
ce
i
t
sea
r
ches to co
ll
ect a set o
f
past exper
i
e
n
ces w
i
t
h
out try
in
g to fo
r
mu
t
ate a doma
i
n mode
l
fr
om t
h
ese o
n
es
.
CBR is also su
i
tab
l
e
because
n
u
m
erous
m
ode
llin
g opt
i
o
n
s become recu
rr
ent a
n
d past
expe
r
i
e
n
ces ca
n
eas
il
y be
r
eused to reduce s
i
g
ni
fica
n
t
l
y t
h
e mode
l
e
l
aborat
i
o
n. M
oreover, C
B
R has t
h
e adva
n
tage to
m
ake k
n
ow
l
edge
eas
il
y access
i
b
l
e, u
n
dersta
n
dab
l
e a
n
d reusab
l
e
.
In
t
h
e
li
terature t
h
e applicat
i
o
n
o
f
C
B
R
in
sc
h
edu
lin
g sta
rt
s w
i
t
h
t
h
e works o
f Miyashita (1995)
a
n
d
Schmidt (1996), Schmidt (1998)
w
h
o t
ri
ed to find a so
l
ut
i
o
n
fo
r
a schedu
lin
g prob
l
em assig
nin
g jobs
over t
im
e to
m
ach
in
es a
n
d poss
i
bly add
i
t
i
o
n
a
l
resources
. D
esp
i
te
t
h
ese wo
r
ks gave t
h
e fi
r
st bu
il
d
in
g b
l
ocks fo
r
a C
B
R system, t
h
ey
were
limi
ted
in
ter
m
s o
f
practica
l
applicat
i
o
n.
W
i
t
h
t
h
e sa
m
e a
im
to e
l
aborate a comp
l
ete sc
h
edu
l
e but fo
r
project,
Dzeng and Lee
(2004)
proposed a genera
li
zed
fr
a
m
ework to
r
eprese
n
t schedu
l
e
k
n
ow
l
edge to a
n
a
l
yze project schedul
in
g a
n
d to g
i
ve co
rr
ective
advise o
n
a pote
n
t
i
a
l
e
rr
ors
. Dzeng and Tommelein (2004)
deve
l
oped a too
l
to he
l
p project sc
h
edu
l
e
r
to
r
et
ri
eve a
nd r
euse pa
rt
s
o
f
exist
in
g sc
h
edu
l
e to ge
n
e
r
ate new one
.
More
r
ece
n
t
l
y
Mikulakova, Konig, Tauscher, and Beucke (2010)
developed a
k
n
ow
l
edge system based o
n
C
B
R fo
r
project schedu
l
e ge
n
erat
i
o
n
but t
h
ey go deeper by
in
clud
in
g a
n
eva
l
uat
i
o
n m
odu
l
e to he
l
p
t
h
e choice amo
n
g a
l
te
r
nat
i
ve
.
A
n
ot
h
er way to use C
B
R
in
p
r
oduct
i
o
n
sc
h
edu
lin
g is to fi
n
d t
h
e
promis
in
g seque
n
ce o
f
jobs p
r
ocess
in
g as
in
t
h
e wo
r
k o
f Dong and
Kitaoka (1994).
Priore, de la Fuente, Puente, and Parreno (2006)
compa
r
ed C
B
R a
nd ind
uct
i
ve
l
ea
rnin
g a
n
d back propagat
i
o
n n
eura
l
n
etworks to extract t
h
e "best" d
i
spatch
in
g
r
ules to dy
n
a
m
i
ca
ll
y
sc
h
edu
l
e jobs
in
flex
i
b
l
e ma
n
ufactu
rin
g systems
.
Chang, Hsieh,
and Liu (2006)
have prese
n
ted a genetic a
l
go
ri
t
h
m a
nd
C
B
R hyb
r
i
d
i
zat
i
o
n
for a s
in
g
l
e
m
ach
i
ne w
i
t
h r
elease t
im
e to
minim
i
ze t
h
e tota
l
weig
h
ted comp
l
et
i
o
n
t
i
me
.
Whe
n
a
n
ew prob
l
em eme
r
ges, the C
B
R
ret
r
i
eved cases that a
r
e used to be pa
r
t o
f
t
h
e
ini
t
i
a
l
popu
l
at
i
o
n
a
nd
in
je
cted
d
u
rin
g generat
i
o
n
s to t
h
e poo
l
o
f
chromoso
m
es
in
t
h
e
ge
n
etic a
l
go
ri
t
h
m
.
C
B
R is a
l
so used to t
h
e para
m
eter
i
zat
i
o
n
o
f m
etaheu
ri
stics for
t
h
e reso
l
ut
i
o
n
o
f d
y
n
amic schedu
lin
g prob
l
ems because paramete
r
t
u
nin
g is
n
ot obv
i
ous
.
As t
h
e va
l
ue for
m
eta
h
eu
r
istic pa
r
a
m
ete
r
s
depe
nd
ma
inl
y o
n
the prob
l
em, t
h
e sea
r
ch t
i
me to so
l
ve
i
t, t
h
e
requ
ir
ed qua
li
ty o
f
t
h
e so
l
ut
i
o
n
,
Pereira and
Madureira
(2013) h
ave
estab
li
shed a
l
ea
rnin
g modu
l
e, based o
n
C
B
R, fo
r
a
n
auto
n
omous
pa
r
ameter
i
zat
i
o
n.
2.2. Case Based Reasoning
D
i
ff
ere
n
t
m
ode
l
s were proposed to represent
t
h
e various
seque
n
t
i
a
l
steps
(
k
n
ow
l
edge represe
n
tat
i
o
n
, k
n
ow
l
edge
r
easo
nin
g,
k
n
ow
l
edge
in
terpretat
i
o
n
a
n
d
r
eus
in
g
)
o
f
t
h
e C
B
R process
:
(
Allen,
1994; Hunt, 1995; Leake, 1996).
Cu
r
re
n
t
l
y t
h
e R
5cycle proposed
by
Finnie and Sun (2003)
is commo
nl
y accepted,
Fig. 3. Th
is cycle
is a
n
extens
i
o
n
o
f
t
h
e R
4m
ode
l
in
troduced by
Aamodt and Plaza
(1994).
In
t
h
e
CB
R cycle, o
n
ce t
h
e
n
ew prob
l
em desc
ri
bed
in
t
h
e Rep
r
e
se
n
tat
i
o
n
step, t
h
e most s
i
m
il
a
r
cases to t
h
e
n
ew prob
l
em spec
i
fi
cat
i
o
n
s a
r
e ret
r
i
eved
fr
om t
h
e case base w
i
t
h
t
h
e he
l
p o
f
a
s
i
mila
ri
ty fu
n
ct
i
o
n. T
he Reuse step is t
h
e copy o
r
t
h
e mod
i
ficat
i
o
n
o
f
t
h
e so
l
ut
i
o
n
o
f
t
h
e retr
i
eved cases w
i
t
h
t
h
e a
im
to so
l
ve t
h
e
ini
t
i
a
l
prob
l
em
. T
he Revis
i
o
n
step is t
h
e adaptat
i
o
n
o
f
t
h
e reuse
d
case
to w
i
t
h
draw the rema
in
ing
d
iscrepa
n
cies
. T
he Reta
in
step is t
h
e
in
co
rp
o
r
at
i
o
n
o
f
t
h
e
n
ew case
in
to t
h
e exist
i
ng case base o
n
ce
i
t
h
as bee
n
co
n
fi
r
med or validated
(
Pal & Shiu, 2004
)
.
Eac
h
o
f
these
steps
in
vo
l
ves a
n
u
m
ber o
f m
ore specific a
n
d complex sub pro
cesses, fo
r in
sta
n
ce
r
eta
in i
mplies
: in
teg
r
ate
(
r
etu
rn
prob
l
em,
update genera
l
k
n
ow
l
edge, a
n
d adjust
in
dexes
)
,
in
dex
(
ge
n
era
li
ze
Learned Case Confirmed Solution New Case Previous Cases General/Domain Knowledge Revision Retrieved Case Suggested Solution
