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Resources,
Conservation
and
Recycling
104
(2015)
391–404
Contents
lists
available
at
ScienceDirect
Resources,
Conservation
and
Recycling
jo
ur
nal
home
p
age:
www.elsevier.com/locate/resconrec
Full
length
article
Stochastic
reverse
logistics
network
design
for
waste
of
electrical
and
electronic
equipment
Berk
Ayvaza,
Bersam
Bolatb,
Nezir
Aydınc,∗
aDepartment
of
Industrial
Engineering,
Istanbul
Commerce
University,
Küc¸
ükyalı,
Istanbul
34840,
Turkey
bDepartment
of
Management
Engineering,
Istanbul
Technical
University,
Besiktas,
Istanbul
34367,
Turkey
cDepartment
of
Industrial
Engineering,
Yıldız
Technical
University,
Besiktas,
Istanbul
34349,
Turkey
a
r
t
i
c
l
e
i
n
f
o
Article
history:
Received
30
December
2013
Received
in
revised
form
22
June
2015
Accepted
8
July
2015
Available
online
1
August
2015
Keywords:
Reverse
Logistics
Network
Design
Waste
of
electrical
and
electronic
equipment
(WEEE)
Stochastic
programming
Sample
average
approximation
Uncertainty
a
b
s
t
r
a
c
t
In
recent
years,
Reverse
Logistics
has
received
increasing
attentions
in
supply
chain
management
area.
The
reasons
such
as
political,
economic,
green
image
and
social
responsibility
etc.
force
firms
to
develop
strategies
to
their
current
systems.
The
aim
of
this
study
is
to
propose
a
generic
Reverse
Logistics
Network
Design
model
under
return
quantity,
sorting
ratio
(quality),
and
transportation
cost
uncertainties.
We
present
a
generic
multi-echelon,
multi-product
and
capacity
constrained
two
stage
stochastic
programing
model
to
take
into
consideration
uncertainties
in
Reverse
Logistics
Network
Design
for
a
third
party
waste
of
electrical
and
electronic
equipment
recycling
companies
to
maximize
profit.
We
validated
developed
model
by
applying
to
a
real
world
case
study
for
waste
of
electrical
and
electronic
equipment
recycling
firm
in
Turkey.
Sample
average
approximation
method
was
used
to
solve
the
model.
Results
show
that
the
developed
two
stage
stochastic
programming
model
provides
acceptable
solutions
to
make
efficient
decisions
under
quantity,
quality
and
transportation
cost
uncertainties.
©
2015
Published
by
Elsevier
B.V.
1.
Introduction
In
recent
years,
product
recovery
has
received
growing
attention
in
the
world,
due
to
driving
factors
such
as
social,
environmen-
tal,
and
economic
reasons.
The
factors
such
as
regulation
pressure,
economic,
green
image
and
social
responsibility
force
firms
to
evolve
strategies
to
their
current
systems.
Many
manufacturers
have
adapted
the
practice
of
recovering
value
from
returned
prod-
ucts
and
integrated
product
recovery
activities
into
their
processes
(Lee
and
Dong,
2009).
Reverse
logistics
(RL)
is
the
concept
of
reusing
used
products
to
reduce
wastes
and
to
increase
an
indus-
try’s
environmental
performance
(Diabat
et
al.,
2013).
In
term
of
sustainability,
RL
can
be
defined
as
a
business
strategy
that
acts
as
the
driving
force
of
putting
recovery
activities
in
action
effectively
in
order
to
increase
sustainability.
The
recovery
options
in
RL
are
remanufacturing,
repairing,
refurbishing,
cannibalizing,
and
recycling
(Zhou
and
Wang,
2008).
It
is
widely
applicable
for
the
products
like
computers,
vehi-
cle
engines,
electrical
appliances,
electronic
equipment,
copiers,
single-use
cameras,
cellular
phones,
paper,
carpets,
plastics,
∗Corresponding
author.
Tel.:
+90
212
383
3029;
fax:
+90
212
258
5928.
E-mail
address:
nzraydin@yildiz.edu.tr
(N.
Aydın).
medical
equipment,
tires,
and
batteries
(Srivastava,
2008a;
Sasikumar
et
al.,
2010).
The
reason
of
product
return
in
the
supply
can
be
listed
such
as;
manufacturing
returns,
commercial
returns
(B2B
and
B2C),
product
recalls,
warranty
returns,
service
returns,
end-of-use
returns,
end-
of-life
returns.
(De
Brito,
2002;
Du
and
Evans,
2008).
Decisions
in
RL
can
be
taken
for
long-term
such
as
those
about
facility
location,
layout,
capacity
and
design;
or
medium
term
such
as
those
related
to
integrating
operations
or
deciding
about
which
information
and
communication
technologies
systems
support
the
return
handling
or
short-term
decisions
about
inventory
hand-
ling,
vehicle
routing,
remanufacturing
scheduling,
etc.
(Srivastava,
2008b).
Studies
in
the
literature
associated
with
RL
have
been
concluded
on
different
aspects
such
as
network
design,
return
forecasting,
eco-
nomic
and
environmental
performance,
lot
sizing,
vehicle
routing,
etc.
The
design
of
product
recovery
networks
is
one
of
the
challeng-
ing
RL
problems
(De
Brito,
2002;
Chanintrakul
et
al.,
2009).
A
Reverse
Logistics
Network
Design
(RLND)
is
complicated
by
the
needs
for
testing
and
grading
of
return
products,
addressing
uncertainty
of
return
products
in
terms
of
quantity,
quality
and
supply
timing,
integrating
and
coordinating
different
forward
and
reverse
flows.
A
high
level
of
uncertainty
is
one
of
the
characteristics
of
RL
networks
(Fleischmann
et
al.,
2000).
Espe-
cially
the
impact
of
uncertainty
in
terms
of
quantity,
quality
and
http://dx.doi.org/10.1016/j.resconrec.2015.07.006
0921-3449/©
2015
Published
by
Elsevier
B.V.
392
B.
Ayvaz
et
al.
/
Resources,
Conservation
and
Recycling
104
(2015)
391–404
timing
is
the
most
popular
issue
in
RLND
(Chanintrakul
et
al.,
2009).
Deterministic
models
for
RLND
lack
the
ability
to
incorporate
such
uncertainty
factors
as
variances
of
return
amount,
timing,
and
lead
time
through
the
network
(Lee,
2009).
Kall
and
Wallace
(1994)
claim
that
stochastic
programming
techniques
present
more
flex-
ibility
to
cope
with
uncertainty.
So,
in
order
to
deal
with
this
uncertainty,
researchers
developed
various
stochastic
models
(Ilgin
and
Gupta,
2010).
The
aim
of
this
study
is
to
propose
a
RLND
model
under
return
quantity,
quality,
and
transportation
cost
uncertainties
and
solve
with
a
well-known
solution
algorithm,
Sample
average
approx-
imation
(SAA),
for
Stochastic
Programming
(SP)
problems.
We
present
a
multi-stage,
multi-echelon,
multi-product
and
capacity
constrained
two
stage
stochastic
programing
model
to
take
into
consideration
uncertainties
in
RLND.
We
validate
the
developed
generic
model
by
applying
to
a
real
world
case
study
of
waste
of
electric
and
the
waste
of
electrical
and
electronic
equipment
(WEEE)
third
party
recycling
company
in
Turkey.
SAA
schema
is
applied
in
solution
process.
The
contributions
of
this
paper
are
as
follows:
First,
this
study
is
the
first
appliance,
in
WEEE
literature
for
RLND
under
uncertain
parameters,
such
as,
amount
of
WEEE,
quality
of
collected
WEEE
and
transportation
costs.
Second,
the
RLND
network
is
modeled
as
a
SP
model
and
it
is
solved
by
SAA.
Third,
the
proposed
model
is
a
generic
RLND
for
third
party
reverse
logistic
companies.
Lastly,
the
proposed
model
is
easy
and
effective
to
support
establishing
RLND
decisions
for
managers
and
decision
makers.
In
the
literature,
many
researchers
showed
increasingly
interest
in
the
RLND
problem.
Some
of
the
studies
are
briefly
explained
as
follows:
Barros
et
al.
(1998)
presented
a
multi-level
capacitated
facility
location
problem
for
sand
recycling
in
the
Netherlands.
They
devel-
oped
a
mixed
integer
program
(MILP)
model
when
the
volume
and
the
locations
of
the
demand
are
uncertain.
They
determined
the
optimal
number,
capacities
and
locations
of
the
depots
and
clean-
ing
facilities
for
recycling
sand
from
construction
waste.
Krikke
et
al.
(1999)
developed
a
MILP
model
for
a
multi-echelon
RLND
for
a
copier
manufacturer
in
the
Netherlands.
Shih
(2001)
devel-
oped
a
MILP
model
for
design
of
an
optimal
collection
and
recycling
system
for
end-of-life
computers
and
home
appliances.
Jayaraman
et
al.
(2003)
developed
an
MILP
model
as
a
two-echelon
capacitated
facility
location
problem
with
limited
collection
and
refurbish-
ing
facilities.
Heuristic
methods
were
also
developed
to
solve
the
model.
Min
et
al.
(2006)
addressed
the
multi-echelon
RLND
prob-
lem
for
product
returns
and
developed
a
single-objective,
nonlinear
mixed-integer
programming
model
that
determines
the
optimal
number
and
locations
of
collecting
points
as
well
as
centralized
return
centers
while
taking
the
shipping
costs,
closeness
of
the
col-
lection
points
and
in-transit
inventory
into
consideration.
A
genetic
algorithm
is
developed
to
solve
the
problem.
Lu
and
Bostel
(2007)
addressed
a
two-level
location
problem
with
three
types
of
facility
to
be
located
in
a
specific
reverse
logistics
system.
For
this
problem,
they
developed
mixed
integer
programming
model,
considering
simultaneously
“forward”
and
“reverse”
flows.
They
used
langrage
heuristic
to
solve
the
problem.
Pati
et
al.
(2008)
developed
a
mixed
integer
goal
programming
model.
The
model
addressed
the
inter-relationship
between
multiple
objectives
of
a
recycled
paper
distribution
network.
The
objectives
were
the
reverse
logistics
cost,
a
non-relevant
wastepaper
target
and
a
wastepaper
recovery
tar-
get.
Du
and
Evans
(2008)
presented
a
bi-objective
MILP
model
for
designing
a
closed-loop
logistics
network
for
third-party
logistics
providers.
The
objectives
of
the
model
are
the
minimization
of
total
costs
and
the
tardiness.
Kannan
et
al.
(2012)
presented
a
mixed
integer
linear
model
for
a
carbon
footprint
based
RLND.
The
developed
model
aims
to
min-
imize
the
costs
involved
in
the
reverse
logistics
network
model,
and
it
considers
the
carbon
footprint
involved
both
in
transporta-
tion
and
reverse
logistics
operations
(collection)
costs.
It
employs
reverse
logistics
activities
to
recover
used
products,
hence
includ-
ing
the
location/transportation
decision
problem.
The
presented
model
is
applied
to
a
plastic
sector.
Achillas
et
al.
(2012)
presented
multiple
objective
linear
programming
(MOLP).
The
main
goal
of
a
MOLP
model
is
the
weighted
optimization
of
different
objectives.
The
developed
MOLP
approach
minimizes
total
logistics
costs,
con-
sumption
of
fossil
fuel
and
production
of
emissions.
The
uncertainty
is
an
important
characteristic
of
product
recov-
ery
(Fleischmann
et
al.,
2000).
Design
of
reverse
and
closed-loop
supply
chain
networks
involves
generally
high
degree
of
uncer-
tainty,
especially
associated
with
quality
and
quantity
of
the
returned
products,
as
well
as
the
time,
delay
and
location
of
recov-
ery
and
redistribution
(Chouinard
et
al.,
2008;
Ilgin
and
Gupta,
2010;
Pishvaee
et
al.,
2011).
The
quantity
and
quality
of
used
prod-
ucts
are
more
difficult
to
control
and
estimate
(Qin
and
Ji,
2010).
Diabat
et
al.
(2013)
developed
a
multi-echelon
reverse
logistics
network
for
product
returns
to
minimize
the
total
reverse
logis-
tics
cost,
which
consists
of
renting,
inventory
carrying,
material
handling,
setup,
and
shipping
costs.
In
their
study,
a
mixed
integer
non-linear
programming
(MINLP)
model
is
developed
to
find
out
the
number
and
location
of
initial
collection
points
and
centralized
return
centers.
Two
solution
approaches,
namely
genetic
algorithm
and
artificial
immune
system,
are
implemented
and
compared.
The
usefulness
of
the
proposed
model
and
algorithm
are
illustrated
by
an
illustrative
example.
Listes
(2002)
presented
a
generic
stochastic
model
for
the
design
of
networks
organized
in
a
closed
loop
system.
This
model
con-
siders
one
echelon
forward
network
combined
with
two
echelon
reverse
network.
The
uncertainty
is
handled
in
a
stochastic
formu-
lation
by
means
of
discrete
alternative
scenarios.
Listes¸
and
Dekker
(2005)
proposed
two
formulations
using
stochastic
optimization
for
the
network
design
of
recycling
sand
under
demand
and
sup-
ply
uncertainties.
The
first
formulation
is
a
two-stage
stochastic
optimization
with
locational
uncertainty
of
demand.
The
second
formulation
involves
both
demand
and
supply
uncertainty
via
a
three-stage
stochastic
optimization
model.
Listes¸
(2007)
presented
a
generic
stochastic
model
for
the
design
of
integrated
real-world
RL
network.
They
considered
uncertainty
under
return
quantity.
The
objective
is
to
maximize
profit.
Decomposition
method
based
on
the
branch-and-cut
known
as
the
integer
L-shaped
method
is
developed
to
solve
the
problem.
Salema
et
al.
(2007)
devel-
oped
a
generic
reverse
logistics
network
model
which
includes
multi-product
management
and
uncertain
product
demands
and
returns.
A
mixed
integer
formulation
is
developed.
They
solve
their
model
with
standard
branch-and-bound
(BB)
techniques
rather
than
using
a
decomposition
method.
Chouinard
et
al.
(2008)
con-
sidered
the
uncertainties
related
with
recovery,
processing
and
demand
volumes
in
a
closed-loop
supply
chain
design
problem
by
developing
a
stochastic
programming
model.
Sample
average
approximation-based
heuristic
is
developed
to
solve
the
problem.
Lee
and
Dong
(2009)
considered
a
stochastic
approach
for
the
dynamic
RLND
under
demand
and
return
uncertainties.
A
two-
stage
stochastic
programming
model
is
developed
by
which
a
deterministic
model
for
dynamic
RLND
can
be
extended
to
con-
sider
uncertainties.
Pishvaee
et
al.
(2009)
presented
a
stochastic
programming
model
for
single
period,
single
product,
multi-stage
integrated
forward/Reverse
Logistics
Network
Design
to
cope
with
the
uncertainty
associated
with
the
quantity
and
quality
of
returned
products,
demands
and
variable
costs.
First,
an
efficient
deterministic
MILP
model
is
developed
for
integrated
logistics
net-
work
design
to
avoid
the
sub-optimality
caused
by
the
separate
design
of
the
forward
and
reverse
networks.
Then
the
stochastic
counterpart
of
the
proposed
MILP
model
is
developed
by
using
scenario-based
stochastic
approach.
B.
Ayvaz
et
al.
/
Resources,
Conservation
and
Recycling
104
(2015)
391–404
393
Fonseca
et
al.
(2010)
presented
a
comprehensive
model
for
RL
planning
in
which
they
considered
many
real-world
features
such
as
the
existence
of
multi-echelons,
multi-commodities,
choices
of
technology,
and
uncertainties
associated
with
transportation
costs
and
waste
generation.
Moreover,
they
presented
a
two-stage
stochastic
dual-objective
mixed-integer
programming
formulation
in
which
strategic
decisions
are
considered
in
the
first
stage
and
tac-
tical
and
operational
decisions
in
the
second.
The
two
objectives
considered
are
the
total
cost
and
the
total
obnoxious
effect.
El-
Sayed
et
al.
(2010)
proposed
a
Stochastic
MILP
model
for
integrated
logistics
network
design
including
demand
and
return
uncertain-
ties.
The
objective
is
the
total
profit
maximization.
Kara
and
Onut
(2010)
developed
a
two-stage
stochastic
programming
model
to
determine
a
long
term
strategy
including
optimal
facility
locations
and
optimal
flow
amounts
for
large
scale
reverse
supply
chain
net-
work
design
problem
under
uncertainty.
In
this
study,
the
first
stage
decisions
correspond
to
the
location
decisions
that
must
be
made
for
opening
facilities
before
the
values
of
the
random
parameters
become
known
and
the
second
stage
decisions
correspond
to
the
flow
amount
decisions
through
the
established
network
after
the
values
of
the
random
parameters
become
known.
Gomes
et
al.
(2011)
extended
the
model
proposed
by
Salema
et
al.
(2010)
to
handle
the
uncertainty
related
to
the
quality
of
the
returned
products,
which
at
this
stage
is
modeled
by
a
two-
stage
scenario-based
stochastic
approach.
Ramezani
et
al.
(2013)
proposed
a
stochastic
multi-objective
model
for
forward/reverse
logistic
network
design
under
a
uncertain
environment
includ-
ing
three
echelons
in
forward
direction
(i.e.,
suppliers,
plants,
and
distribution
centers)
and
two
echelons
in
backward
direction
(i.e.,
collection
centers
and
disposal
centers).
They
demonstrated
a
method
to
evaluate
the
systematic
supply
chain
configura-
tion
maximizing
the
profit,
customer
responsiveness,
and
quality
as
objectives
of
the
logistic
network.
The
set
of
Pareto
optimal
solutions
is
obtained
and
also
financial
risk
relevant
to
them
is
computed
in
order
to
show
the
tradeoff
between
objectives.
The
results
give
important
insight
for
fostering
the
decision
making
pro-
cess.
In
their
study,
uncertainties
are
associated
with
quantity
of
price,
production
costs,
operating
costs,
collection
costs,
disposal
costs,
demands
and
return
rates
and
are
described
by
the
set
of
scenarios.
Demirel
et
al.
(2014)
presented
a
mixed
integer
linear
pro-
gramming
model
for
network
design
including
the
different
actors
taking
part
in
end-of-life
vehicles
(ELVs)
recovery
sys-
tem
in
order
to
comply
with
related
regulations
and
manage
the
recovery
of
end-of-life
vehicles
efficiently.
The
proposed
frame-
work
is
justified
by
a
real
case
performed
in
Ankara.
They
also
presented
a
modeling
approach
for
the
projection
of
car
owner-
ship
and
number
of
end-of-life
vehicles
and
generated
scenario
analyzes
based
on
the
long-term
changing
in
the
number
of
end-
of-life
vehicles.
Suyabatmaz
et
al.
(2014)
presented
two
hybrid
simulation-analytical
modeling
approaches
for
the
RLND
of
the
third-party
logistics.
Hatefi
and
Jolai
(2014)
proposed
a
robust
and
reliable
mixed-integer
linear
programing
model
for
design-
ing
an
integrated
forward–reverse
network,
which
can
cope
with
the
parameters’
uncertainty
in
the
customer
demand,
the
quantity
and
quality
of
returned
products
and
facility
disruptions,
simulta-
neously.
To
present
the
behavior
of
the
robustness
and
reliability
of
the
network,
numerical
examples
are
conducted.
Ferri
et
al.
(2015)
proposed
a
reverse
logistics
network
for
the
management
of
munic-
ipal
solid
waste
considering
the
recent
legal
requirements
of
the
Brazilian
Waste
Management
Policy.
The
presented
mathematical
model
allows
the
determination
of
the
number
of
facilities
required
for
the
reverse
logistics
network,
their
location,
capacities,
and
waste
flows
between
these
facilities.
Zhou
and
Zhou
(2015)
pro-
posed
a
nonlinear
integer
programming
model
for
determining
the
locations
and
numbers
of
recycling
stations
and
plants,
in
order
to
minimize
the
total
cost.
A
case
study
of
selected
sites
along
the
Xueyuan
Road
in
Beijing
is
conducted
to
illustrate
the
presented
model.
Kilic
et
al.
(2015)
developed
a
reverse
logistics
system
for
WEEE
in
Turkey.
They
used
a
mixed
integer
linear
programming
model
in
order
to
provide
solutions.
Ten
scenarios
are
taken
into
consideration
related
to
different
collection
rates.
The
optimum
locations
and
flows
are
determined
for
each
scenario
via
the
pro-
posed
MILP
model.
Roghanian
and
Pazhoheshfar
(2014)
addressed
multi-product,
multi-stage
reverse
logistics
network
problem
for
the
return
products.
They
presented
a
probabilistic
mixed
integer
linear
programming
model
for
the
design
of
a
reverse
logistics
net-
work
to
handle
the
degree
of
uncertainty
in
terms
of
the
capacities,
demands
and
quantity
of
products.
To
solve
the
proposed
model,
priority
based
genetic
algorithm
is
used.
The
proposed
model
is
applied
to
a
numerical
example.
Ene
and
Öztürk
(2015)
developed
a
mathematical
programming
model
for
managing
reverse
flows
in
end-of-life
vehicles’
recovery
network.
The
objectives
of
the
pro-
posed
model
are
to
maximize
revenue
and
minimize
pollution
in
end
of-life
product
operations.
Table
1
gives
an
overview
of
some
important
models’
char-
acteristics.
The
result
of
literature
review
shows
clearly
that
deterministic
models
commonly
ignore
uncertainty
associated
with
RLND
process;
the
stochastic
models
account
for
the
uncer-
tainties
in
terms
of
returned
products
quantity,
quality
and
time.
The
uncertainty
in
RL
literature
is
still
scarce.
As
a
result,
there
are
some
gap
research
areas
related
to
RLND
such
as
combining
of
multiple
objectives,
multiple
commodities,
multiple
echelons,
real
life
cases
and
uncertainty.
Therefore
in
this
study,
we
present
multi-echelon
and
multi-product
SP
for
RLND
under
return
product
quantity,
quality
(sorting
ratio),
and
trans-
portation
costs.
2.
Problem
statement
and
methodology
The
RLND
problem
that
is
addressed
in
this
paper
is
an
open
loop,
multi-echelon,
multi-product,
capacity
constrained
under
return
quantity,
return
quality
(sorting
ratio)
and
transportation
cost
uncertainties.
It
is
known
that
deterministic
programming
is
unable
to
handle
uncertainties
parameters.
Therefore
stochastic
programming
is
used
to
cope
with
the
uncertain
parameters.
Stochastic
Programming
(SP)
is
a
framework
to
model
opti-
mization
problems
which
involve
uncertain
parameters
(Bidhandi
and
Yusuff,
2011).
It
is
assumed
that
the
probability
distribution
functions
of
uncertain
parameters
are
known
and
decision
makers
optimize
the
expected
value
of
the
objective
function
(Hosseini
and
Dullaert,
2011).
The
most
widely
applied
SP
models
are
two-stage
linear
and
mixed
integer
linear
programs.
A
two
stage
SP
model
is
proposed
by
Birge
and
Louveaux
(1997)
that
take
into
account
ran-
domness.
The
first
stage
variables
are
those
that
have
to
be
decided
before
the
actual
realization
of
the
uncertain
parameters
becomes
available.
Subsequently,
once
the
random
events
have
presented
themselves,
further
design
or
operational
policy
improvements
can
be
made
by
selecting,
at
a
certain
cost,
the
values
of
the
second
stage
or
recourse
variables.
The
objective
is
to
choose
the
first
stage
vari-
ables
in
a
way
that
the
sum
of
the
first
stage
costs
and
the
expected
value
of
the
random
second
stage
or
recourse
costs
are
minimized
(Ayvaz
and
Bolat,
2014).
We
present
two
stage
stochastic
programming
model
to
deter-
mine
the
number
of
collecting
centers,
sorting
centers,
and
recycling
centers
to
maximize
the
profit.
The
presented
model
includes
collecting
centers,
sorting
centers,
recycling
centers,
refin-
ery
centers,
raw
material
markets,
and
disposal
centers.
As
shown
in
Fig.
1,
returned
products
are
collected
from
customer
zones
which
are
electronic
markets,
municipality,
electronic
distributers
etc.,
and
transported
to
the
collecting
centers
then
they
are
sent
to
sorting
centers
in
order
to
preprocessing;
it
is
divided
into
394
B.
Ayvaz
et
al.
/
Resources,
Conservation
and
Recycling
104
(2015)
391–404
Table
1
Review
of
reverse
logistic
network
design
literature.
References
Model
Objectives
Type
of
network
Number
of
product
Uncertain
parameters
Barros
et
al.
(1998)
MILP
C
Open-loop
Multi
–
Krikke
et
al.
(1999) MILP
C
Open-loop
Single
–
Shih
(2001)
MIP
P
Open-loop
Multi
RR
Jayaraman
et
al.
(2003)
MIP
C
Open-loop
Single
–
Min
et
al.
(2006)
MINLP
C
Open-loop
Single
–
Du
and
Evans
(2008)
MILP
C,
TT
Close-loop
Multi
–
Pati
et
al.
(2008)
MIGP
C,
NWT,
WRT
Open-loop
Single
D
Lu
and
Bostel
(2007)
MIP
C
Close-loop
Single
–
Achillas
et
al.
(2012) MOLP
C,
E,
FOpen-loop
Single
–
Kannan
et
al.
(2012)
MILP
C
Close-loop
Single
–
Diabat
et
al.
(2013)
MINLP
C
Open-loop
Single
–
Listes
(2002)
SMILP
C
Close-loop
Single
D,
R
Listes¸
and
Dekker
(2005)
SMILP
P
Open-loop
Single
D,
R
Listes¸
(2007)
SMILP
P
Close-loop
Single
D,
R
Chouinard
et
al.
(2008)
SMIP
C
Close-loop
Multi
D,
Rec,
Pro
Salema
et
al.
(2007)
SMIP
C
Close-loop
Multi
D,
TC,
R
Lee
and
Dong
(2009)
SMILP
C
Close-loop
Multi
D,
R
Pishvaee
et
al.
(2009) SMILP
C
Close-loop
Single
R,
Q,
VC
Fonseca
et
al.
(2010)
SMILP
C,
TOE
Open-loop
Multi
TC,
R
El-Sayed
et
al.
(2010)
SMILP
P
Close-loop
Single
D,
R
Kara
and
Onut
(2010)
SMILP
P
Open-loop
Single
D,
R
Gomes
et
al.
(2011)
SMILP
C
Open-loop
Multi
Q
Ramezani
et
al.
(2013)
SMILP
P,
CR,
SQ
Close-loop
Multi
Pr,
PC,
OC,
CC,
DC,
D,
RR
Diabat
et
al.
(2013)
MINLP
C
Open-loop
Single
–
Demirel
et
al.
(2014) MILP
C
Open-loop
Single
–
Suyabatmaz
et
al.
(2014)
MILP
C
Open-loop
Single
R
Hatefi
and
Jolai
(2014)
RO
C
Close-loop
Single
D,
R,
Q
Ferri
et
al.
(2015)
MILP
P
Close-loop
Multi
–
Roghanian
and
Pazhoheshfar
(2014)
PMILP
C
Open-loop
Multi
CAP,
D,
R
Zhou
and
Zhou
(2015) MINLP
C
Open-loop
Single
–
Kilic
et
al.
(2015)
MILP
C
Open-loop
Multi
–
Ene
and
Öztürk
(2015) SMILP
P,
Pol
Open-loop
Single
R
MILP:
mixed
integer
linear
programming,
PMILP:
probabilistic
mixed
integer
linear
programming,
NLP:
non
linear
programming,
SMILP:
stochastic
mixed
integer
linear
programming,
MIGP:
mixed
integer
goal
programming,
MINLP:
mixed
integer
non
linear
programming,
MOLP:
multi
objectives
linear
programming,
RO:
robust
optimization,
C:
cost
min.,
P:
profit
max.,
TT:
total
tardiness
min.,
E:
minimize
emissions,
F:
minimize
fossil
fuel,
Pol:
pollution
min.,
NWT:
a
non-relevant
wastepaper
target,
WRT:
a
wastepaper
recovery
target,
D:
demand
quantity,
R:
return
quantity,
Rec:
recovery
volumes,
Pro:
processing
volumes,
TC:
transportation
costs,
Q:
return
quality,
VC:
variable
cost,
TOE:
total
obnoxious
effect,
CR:
customer
responsiveness,
SQ:
service
quality,
Pr:
price,
PC:
production
costs,
OC:
operating
costs,
CC:
collection
costs,
DC:
disposal
costs,
RR:
return
rates,
CAP:
capacity.
recoverable
products
and
scrapped
products.
The
recoverable
prod-
ucts
are
transported
to
the
recycling
centers
and
scrapped
products
are
sent
to
disposal
centers.
As
a
result,
recycled
materials
are
sent
to
raw
material
markets,
some
hazardous
material
are
sent
to
dis-
posal
center,
and
products,
which
cannot
be
processing
such
as
gold,
are
sent
to
refinery
center(s).
2.1.
Two-stage
stochastic
programming
model
The
aim
of
the
RLND
is
to
determine
the
location
of
collecting,
sorting
and
recycling
centers,
and
to
find
the
quantity
of
flow
between
the
network
facilities.
The
proposed
model
considers
the
following
assumptions:
-
Inventory
costs
are
ignored.
-
There
is
no
any
safety
stock
in
collecting
and
recycling
centers.
-
There
are
capacity
constraints
of
collecting
centers,
sorting
cen-
ters,
and
recycling
centers.
-
All
costs
except
transportation
cost,
and
allocation
rates
of
prod-
ucts
and
materials
are
known
in
advance.
-
Possible
locations
of
collecting
centers,
sorting
centers,
recycling
centers
and
capacities
are
known.
-
Locations
of
refinery,
markets
disposal
centers
are
known
in
advance.
Fig.
1.
Presented
reverse
logistic
network.
B.
Ayvaz
et
al.
/
Resources,
Conservation
and
Recycling
104
(2015)
391–404
395
For
the
clearness,
for
the
rest
of
this
study,
we
will
refer
to
waste
as
‘product’.
According
to
above
descriptions,
the
stochas-
tic
programming
model
under
quantity,
quality,
and
transportation
cost
uncertainties
can
be
defined
and
the
presented
model,
which
includes
the
following
sets,
parameters
and
decision
variables
are
as
follows:
Sets
Indices
and
superscripts
R:
set
of
regions
where
waste
occurs
r:
region
index,
r
∈
R
CC:
set
of
possible
facility
locations
for
collecting
processes
i:
collecting
center
index,
i
∈
CC
SC:
set
of
possible
facility
locations
for
sorting
processes
j:
sorting
center
index,
j
∈
SC
RC:
set
of
possible
facility
locations
for
recycling
processes
k:
recycling
center
index,
k
∈
RC
RFC:
set
of
refinery
locations
rf:
refinery
index,
rf
∈
RFC
MC:
set
of
market
locations
h:
market
index,
h
∈
MC
DC:
set
of
facility
locations
for
disposing
processes
b:
disposal
center
index,
b
∈
DC
Pr:
set
of
products p:
product
index,
p
∈
Pr
Com:
set
of
commodities
c:
commodity
index,
c
∈
Com
S:
set
of
scenarios
s:
scenario
index,
s
∈
S
Parameters,
constants,
and
coefficients
FCCi:
fixed
cost
for
locating
a
collecting
center
at
location
i,
i
∈
CC
FSCj:
fixed
cost
for
locating
a
sorting
center
at
location
j,
j
∈
SC
FRCk:
fixed
cost
for
locating
a
recycling
center
at
location
k,
k
∈
RC
trp,s
r,i :
cost
of
transporting
one
unit
of
product
p
from
region
r
to
collecting
center
i
in
scenario
s,
r
∈
R,
i
∈
CC,
p
∈
Pr,
s
∈
S
tcp,s
i,j :
cost
of
transporting
one
unit
of
product
p
from
collecting
center
i
to
sorting
center
j
in
scenario
s,
i
∈
CC,
j
∈
SC,
p
∈
Pr,
s
∈
S
tsp,s
j,k :
cost
of
transporting
one
unit
of
product
p
from
sorting
center
j
to
recycling
center
k
in
scenario
s,
j
∈
SC,
k
∈
RC,
p
∈
Pr,
s
∈
S
tsdp,s
j,b :
cost
of
transporting
one
unit
of
product
p
from
sorting
center
j
to
disposing
center
b
in
scenario
s,
j
∈
SC,
b
∈
DC,
p
∈
Pr,
s
∈
S
trcp,s
k,rf :
cost
of
transporting
one
unit
of
product
p
from
recycling
center
k
to
refinery
rf
in
scenario
s,
k
∈
RC,
rf
∈
RFC,
p
∈
Pr,
s
∈
S
trcdp,s
k,b:
cost
of
transporting
one
unit
of
product
p
from
recycling
center
k
to
disposing
centre
b
in
scenario
s,
k
∈
RC,
b
∈
DC,
p
∈
Pr,
s
∈
S
trcmc,s
k,h:
cost
of
transporting
one
unit
of
commodity
c
from
recycling
center
k
to
market
h
in
scenario
s,
k
∈
RC,
h
∈
MC,
c
∈
Com,
s
∈
S
PCCp
i:
processing
cost
of
collecting
one
unit
of
product
p
at
collecting
center
i,
i
∈
CC,
p
∈
Pr
PSCp
j:
processing
cost
of
sorting
one
unit
of
product
p
at
sorting
center
j,
j
∈
SC,
p
∈
Pr
PRCp
k:
processing
cost
of
recycling
one
unit
of
product
p
at
recycling
center
k,
k
∈
RC,
p
∈
Pr
PDCp
b:
processing
cost
of
disposing
one
unit
of
product
p
at
disposing
center
b,
b
∈
DC,
p
∈
Pr
InPp:
income
from
one
unit
of
product
p,
p
∈
Pr
InCc:
income
from
one
unit
of
commodity
c,
c
∈
Com
˚p,s
r:
amount
of
product
p
occurred
at
region
r
in
scenario
s,
r
∈
R,
p
∈
Pr,
s
∈
S
ap,s:
percentage
of
product
p
that
worth
to
be
recycled
in
scenario
s,
p
∈
Pr,
s
∈
S
p:
percentage
of
product
p
that
is
transported
to
refinery,
p
∈
Pr
p:
percentage
of
product
p
that
is
transported
to
markets,
p
∈
Pr
c,p:
percentage
of
product
p
that
consists
commodity
c,
c
∈
Com,
p
∈
Pr
CapCCi:
capacity
of
collecting
center
i,
i
∈
CC
CapSCp
j:
capacity
of
sorting
center
j
for
product
p,
j
∈
SC,
p
∈
Pr
CapRCp
k:
capacity
of
recycling
center
k
for
product
p,
k
∈
RC,
p
∈
Pr
s:
probability
of
scenario
s,
s
∈
S
Decision
variables
xi:
1
if
collecting
center
i
is
located,
0
otherwise,
i
∈
CC
yj:
1
if
sorting
center
j
is
located,
0
otherwise,
j
∈
SC
zk:
1
if
recycling
center
k
is
located,
0
otherwise,
k
∈
RC
wi,j:
1
if
collecting
center
i
is
assigned
to
sorting
center
j,
0
otherwise,
i
∈
CC,
j
∈
SC
˛p,s
r,i :
amount
of
product
p
transported
from
region
r
to
collected
center
i
in
scenario
s,
r
∈
R,
i
∈
CC,
p
∈
Pr,
s
∈
S
ˇp,s
i,j :
amount
of
product
p
transported
from
collecting
center
i
to
sorting
center
j
in
scenario
s,
i
∈
CC,
j
∈
SC,
p
∈
Pr,
s
∈
S
p,s
j,k :
amount
of
product
p
transported
from
sorting
center
j
to
recycling
center
k
in
scenario
s,
j
∈
SC,
k
∈
RC,
p
∈
Pr,
s
∈
S
ıp,s
j,b :
amount
of
product
p
transported
from
sorting
center
j
to
disposing
center
b
in
scenario
s,
j
∈
SC,
b
∈
DC,
p
∈
Pr,
s
∈
S
p,s
k,rf :
amount
of
product
p
transported
from
recycling
center
k
to
refinery
rf
in
scenario
s,
k
∈
RC,
rf
∈
RFC,
p
∈
Pr,
s
∈
S
ωp,s
k,b:
amount
of
product
p
transported
from
recycling
center
k
to
disposing
center
b
in
scenario
s,
k
∈
RC,
b
∈
DC,
p
∈
Pr,
s
∈
S
c,s
k,h:
amount
of
commodity
c
transported
from
recycling
center
k
to
market
h
in
scenario
s,
k
∈
RC,
h
∈
MC,
c
∈
Com,
s
∈
S
We
now
model
our
RLND
as
two-stage
stochastic
program
with
recourse.
The
uncertain
parameters
in
this
formulation
are
the
amount
of
collected
WEEE,
the
quality
of
collected
WEEE
and
trans-
portation
costs.
Objective
function
[maximize]
=
income
−
(transportation
costs
between
nodes
+
fixed
costs
of
locating
centers
+
processing
costs
of
collecting,
sorting,
recycling
and
disposing)
Maximize
k∈RC
rf
∈RFC
p∈Pr
s∈S
sInPp−
trcp,s
k,rf p,s
k,rf
+
k∈RC
h∈MC
c∈Com
s∈S
sInCc−
trcmc,s
k,bc,s
k,h
−
i∈CC
FCCixi−
j∈SC
FSCjyj
−
k∈FRC
FRCkzk−
r∈R
i∈CC
p∈Pr
s∈S
sPCCp
i+
trp,s
r,i ˛p,s
r,i
−
i∈CC
j∈SC
p∈Pr
s∈S
sPSCp
j+
tcp,s
i,j ˇp,s
i,j
−
j∈SC
k∈RC
p∈Pr
s∈S
sPRCp
k+
tsp,s
j,k p,s
j,k
−
j∈SC
b∈DC
p∈Pr
s∈S
sPDCp
b+
tsdp,s
j,b ıp,s
j,b
−
k∈RC
b∈DC
p∈]
s∈S
sPDCp
b+
trcdp,s
k,bωp,s
k,b
(1)
Subject
to
i∈CC
˛p,s
r,i ≤
˚p,s
r∀r
∈
R,
p
∈
Pr,
s
∈
S
(2)
ˇp,s
i,j ≤
CapSCp
jwi,j ∀i
∈
CC,
j
∈
SC,
p
∈
Pr,
s
∈
S
(3)
j∈SC
wi,j ≤
1
∀i
∈
CC
(4)
j∈SC
ˇp,s
i,j =
r∈R
˛p,s
r,i ∀i
∈
CC,
p
∈
Pr,
s
∈
S
(5)
k∈RC
p,s
j,k =
i∈CC
ap,sˇp,s
i,j ∀j
∈
SC,
p
∈
Pr,
s
∈
S
(6)
b∈DC
ıp,s
j,b =
i∈CC 1
−
ap,sˇp,s
i,j ∀j
∈
SC,
p
∈
Pr,
s
∈
S
(7)
h∈MC
c,s
k,h =
j∈SC
p∈Pr
˝pc,pp,s
j,k ∀k
∈
RC,
c
∈
Com,
s
∈
S
(8)
rf
∈RFC
p,s
k,rf =
j∈SC
pp,s
j,k ∀k
∈
RC,
p
∈
Pr,
s
∈
S
(9)
b∈DC
ωp,s
k,b =
j∈SC 1
−
˝p−
pp,s
j,k ∀k
∈
RC,
p
∈
Pr,
s
∈
S
(10)
396
B.
Ayvaz
et
al.
/
Resources,
Conservation
and
Recycling
104
(2015)
391–404
r∈R
p∈Pr
˛p,s
r,i ≤
CapCCixi∀i
∈
CC,
s
∈
S
(11)
i∈CC
ˇp,s
i,j ≤
CapSCp
jyj∀j
∈
SC,
p
∈
Pr,
s
∈
S
(12)
j∈SC
p,s
j,k ≤
CapRCp
kzk∀k
∈
RC,
p
∈
Pr,
s
∈
S(13)
xi,
yj,
zk,
wi,j ∈0,
1i
∈
CC,
j
∈
SC,
k
∈
RC
(14)
˛p,s
r,i ,
ˇp,s
i,j ,
p,s
j,k ,
ıp,s
j,b ,
p,s
k,rf ,
ωp,s
k,b,
c,s
k,h ≥
0
r
∈
R,
i
∈
CC,
j
∈
SC,
k
∈
RC,
b
∈
DC,
rf
∈
RFC,
h
∈
MC,
p
∈
Pr,
c
∈
Com,
s
∈
S
(15)
The
objective
function
in
(1)
is
the
sum
of
the
first
stage-costs
and
the
expected
second-stage
costs
and
income.
The
first
stage
costs
represent
the
costs
of
opening
collecting
centers,
sorting
centers
and
recycling
centers.
The
second
stage
costs
represent
expected
total
transporting
costs,
processing
costs
of
collecting,
sorting,
recycling
and
disposing,
and
expected
total
income
from
markets
and
refineries.
Constraints
(2)
prevent
that
the
total
trans-
ported
products
to
collecting
center
is
less
than
or
equal
to
the
total
occurred
products
in
the
regions.
Constraints
(3)
are
the
assignment
constraints
and
prevent
any
transportation
from
a
collecting
center
to
a
sorting
center
if
the
specified
collecting
center
is
not
assigned
to
that
sorting
center.
Constraints
(4)
ensure
that
each
collecting
center
is
assigned
to
at
most
one
sorting
center.
Constraints
(5)
equalize
the
inflow
to
outflow
of
products
for
each
collecting
cen-
ter.
Constraints
(6)
and
(7)
determine
the
flow
from
each
sorting
center
to
recycling
centers
and
disposing
centers,
respectively.
Con-
straints
(8)–(10)
determine
the
flow
from
each
recycling
center
to
markets,
refineries
and
disposing
centers,
respectively.
Constraints
(11)–(13)
take
care
of
capacity
restrictions
for
collecting
centers,
sorting
centers
and
recycling
centers,
respectively.
Constraints
(14)
and
(15)
are
the
non-negativity
constraints.
As
a
solution
methodology
one
of
the
most
known
solution
algo-
rithm,
Sample
average
approximation
(SAA),
is
used
to
determine
an
accurate
solution
to
the
problem.
SAA
method
uses
exterior
sampling
and
has
become
a
popular
technique
in
solving
large-
scale
SP
problems.
This
is
primarily
due
to
its
ease
of
application.
It
has
been
shown
that
the
solutions
obtained
by
the
SAA
converge
to
the
optimal
solution
when
the
sample
size
is
sufficiently
large
(Ahmed
and
Shapiro,
2002a,b;
Aydin
and
Murat,
2013).
2.2.
Sample
average
approximation
(SAA)
Sampling
based
methods
are
usually
used
when
the
stochastic
problem
is
too
large
or
difficult
to
solve
by
exact
solution
tech-
niques.
The
objective
function
is
approximated
through
a
random
sample
of
scenarios
via
the
sampling
based
methods.
Typically
sampling
based
approaches
are
classified
into
two:
Interior
samp-
ling
and
exterior
sampling
methods
(Verweij
et
al.,
2003).
In
interior
sampling
methods,
sampling
is
performed
inside
a
cho-
sen
algorithm
with
new
(independent)
samples
generated
during
the
iterative
solution
process.
In
the
exterior
sampling
approach,
a
sample
of
scenarios
is
generated
from
possible
realizations,
and
then
deterministic
optimization
problem
is
developed
from
the
generated
samples
and
then
it
is
solved.
This
procedure
(generat-
ing
samples
and
solving
deterministic
problems)
repeated
several
times.
SAA
is
one
of
the
exterior
type
sampling
based
method
and
is
a
Monte
Carlo
simulation
based
sampling
method,
in
which
the
expected
value
of
objective
function
of
stochastic
program
is
approximated
by
solving
the
problem
for
a
sample
of
scenarios.
In
network
models
usually
parameters
such
as
demand,
travel
cost,
and
link
costs
are
uncertain
and
difficult
to
forecast
accurately
(Patil
and
Ukkusuri,
2011).
In
this
study,
we
consider
quantity,
quality,
and
transportation
costs
as
uncertain,
such
as
transportation
cost
from
a
location
i.e.
collecting
center
to
another
i.e.
sorting
center,
and
quantity
that
is
transported
between
centers,
etc.
SAA
can
be
defined
through
a
number
of
steps;
random
samples
are
gener-
ated,
a
sample
average
function
is
applied
to
the
selected
random
samples
to
approximate
the
expected
value
function.
Some
advantages
of
SAA
are
listed
as
following:
Ease
of
numer-
ical
implementation,
often
one
can
use
existing
software,
good
convergence
properties,
well
developed
statistical
inference
(vali-
dation
and
error
analysis,
stopping
rules),
easily
amendable
to
variance
reduction
techniques
and
ideal
for
parallel
computations
(Shapiro,
2004).
SAA
procedure
includes
following
steps:
Step
1:
Generate
M
independent
samples
of
sizes
i
=
1,.
.
.,N,
(1,.
.
.,N).
For
each
sample
solve
the
corresponding
SAA
problem.
min cTy
+1
N
N
n=1
Qy,
n
j
vj
Nand ˆ
yj
Nbe,
respectively,
the
corresponding
optimal
objective
value
and
an
optimal
solution
for
the
samples
j
=
1,.
.
.,M.
Step
2:
Calculate
the
statistical
lower
bound
based
on
the
average
optimal
objective
value
obtained
from
samples
j
=
1,.
.
.,M
in
step1.
¯vN,M:=1
M
M
J=1
vj
N
Then
the
variance
of
this
estimate
can
be
estimated
as:
2
¯
vN,M :=1
(M
−
1)M
M
j=1vj
N−
¯vN,M2
Step
3:
Choice
a
feasible
solution ¯
y
among
those
obtained
in
step
1.
Estimate
the
value
of
the
objective
function
with
a
sample
of
size
N,
much
larger
than
N,
by
solving
˜
fN(¯
y):=cT¯
y
+1
N
N
n=1
Q¯
y,
n
The
value
of ˜
fN(¯
y),
is
an
estimated
upper
bound
of
the
“true”
problem
objective
function.
Then
the
variance
of
this
estimate
can
be
estimated
as:
2
N(¯
y):=1
(N−
1)N
N
n=1cT¯
y+
Q¯
y,
n−˜
fN(¯
y)2
Step
4:
Calculate
an
estimate
of
the
optimality
gap
of
the
solution
¯
y:
gapN,M,N(¯
y)=˜
fN(¯
y)−
¯vN,M
The
variance
of
this
estimate
can
be
estimated
as:
2
gap =
2
N(¯
y)+
2
¯
vN,M
The
confidence
interval
for
the
optimality
gap
is
then
calculated
as
following.
˜
fN(¯
y)−
¯vN,M +
z˛2
N(¯
y)+
2
¯
vN,M 1/2
with
Z˛:=˚−1(1
−
˛)where
˚(z)is
the
cumulative
distribution
function
of
the
standard
normal
distribution.
B.
Ayvaz
et
al.
/
Resources,
Conservation
and
Recycling
104
(2015)
391–404
397
When
the
estimated
gap
is
judged
as
unreasonable,
additional
samples
or
increased
sample
size
N
must
be
tested
(Chouinard
et
al.,
2008).
Note
that
quality
of
a
solution
to
stochastic
programming
based
sampling
methods
depends
on
several
criteria
such
as,
sam-
ple
size,
convergence
rate,
and
stopping
rules
(criterion).
Bayraksan
and
Morton
(2009)
in
their
tutorial
introduced
a
procedure
that
shapes
an
interval
estimator
on
the
optimality
gap
of
a
certain
solution.
They
provide
methods
reducing
the
variance
and
compu-
tational
effort
of
the
estimator
they
introduced.
Also,
they
discussed
ways
to
increase
sample
size
without
hurting
computational
effort
in
a
smart
way
what
they
call
“sequential
sampling
procedure”.
Researches
similar
to
the
sequential
sampling
procedure
are
done
both
in
simulation
and
statistics
(Chow
and
Robbins,
1965;
Law
and
Kelton,
1982).
If
the
decision
variables
are
continuous,
it
has
been
proven
that
an
optimal
solution
of
the
SAA
problem
provides
exact
solution
of
the
true
problem
with
probability
approaching
to
one
expo-
nentially
fast
as
N
increases
(Shapiro
and
Homem-de-Mello,
2000;
Ahmed
and
Shapiro,
2002a,b).
Many
studies
are
conducted
to
deter-
mine
the
required
sample
size.
Kleywegt
et
al.
(2002)
applied
the
SAA
method
to
stochastic
discrete
optimization
problems,
i.e.,
knapsack
problem.
They
noted
that
the
complexity
of
the
SAA
methods
usually
increases
exponentially,
at
least
linearly,
in
terms
of
sample
size
selected.
Selecting
the
sample
size
is
needed
to
con-
sider
the
tradeoff
between
the
bounds
on
the
optimality
gap
and
the
quality
of
an
optimal
solution
of
a
SAA
problem
and
the
com-
putational
performance.
They
expressed
that
selecting
sample
size
should
dynamically
change
depending
on
the
previous
results
that
are
computed
and
the
more
proficient
gap
estimator
of
the
approx-
imated
value
function
improves
the
performance
of
SAA
method
applied
to
the
algorithm.
Problem
definition
and
methodology
that
is
used
in
this
study
is
presented
schematically
as
in
Fig.
2.
3.
Case
study
and
data
acquisition
Recycled
WEEE
is
a
very
valuable
material
for
Turkey
and
it
is
noted
that
the
collection
rates
of
WEEE
increases
fast
in
the
last
decade.
It
is
difficult
to
obtain
statistical
data
of
WEEE
uti-
lization
and
recycling
rates.
In
this
study,
proposed
general
RLND
model
is
applied
with
the
data
of
the
waste
electrical
and
elec-
tronic
equipment
collecting
and
recycling
facility
which
operates
in ˙
Izmit-Turkey.
It
is
one
of
the
biggest
WEEE
recycling
companies
in
Turkey.
The
company
plans
to
develop
a
new
RL
network
considering
already
functioning
system
to
lead
the
market.
The
company
has
a
limited
process
centers:
such
as
collecting,
sorting
and
recycling
centers.
The
constructed
network
is
a
type
of
multi
echelon
and
it
has
several
steps:
E-wastes
are
collected
from
regions,
including
distributors,
original
equipment
manufacturers,
and
municipal-
ities.
In
this
study,
region
refers
to
a
city
or
a
district
where
waste
occurs.
In
total
28
cities
are
selected
as
regions
and
are
as
follows:
Adana,
Afyon,
Ankara,
Antalya,
Aydın,
Balıkesir,
Bursa,
C¸
anakkale,
Diyarbakır,
Edirne,
Erzurum,
Eskis¸
ehir, ˙
Istanbul, ˙
Izmir,
˙
Izmit,
Kırıkkale,
Konya,
Kütahya,
Manisa,
Mersin,
Mu˘
gla,
Ni˘
gde,
Sakarya,
Samsun,
Tekirda˘
g,
Trabzon,
Yalova,
and
Zonguldak.
Even
though
there
are
ten
types
of
WEEE
based
on
European
Commission
WEEE
Directive
(EC,
2003),
in
this
study
only
four
types
of
E-waste
are
considered
because
other
six
types
of
E-waste
are
not
collected
at
an
adequate
amount
in
Turkey.
These
four
types
are
large
house-
hold
appliances,
IT
and
telecommunications
equipment,
lighting
equipment
and
Small
household
appliances,
respectively.
In
col-
lecting
centers
waste
is
collected
based
on
its
type
as
specified
above.
In
this
study,
ten
possible
locations
are
considered
as
collecting
centers
and
are
as
follows:
Adana,
Ankara,
Antalya,
Bursa,
Eskis¸
ehir,
Istanbul,
Izmir,
Izmit,
Sakarya,
and
Tekirdag.
Waste
is
transported
from
collecting
centers
to
sorting
centers
in
order
to
eliminate
invaluable
parts.
There
are
seven
potential
sorting
centers,
Antalya,
Erzurum,
Gaziantep,
Kayseri,
Kocaeli,
Tekirda˘
g,
and
Zonguldak,
respectively.
Lastly,
five
cities
are
considered
as
possible
locations
to
build
recycling
center(s).
These
cities
are:
Adana,
Ankara,
Izmir,
Kocaeli,
and
Samsun.
Since
the
company
already
has
a
functioning
disposing
center
and
no
further
disposing
center
are
needed,
the
management
of
the
company
decided
not
to
change
the
disposing
center’s
location.
The
disposing
center
is
located
in
Gebze/Kocaeli.
Also,
the
company
sends
the
recycled
products
to
Bursa,
as
a
mar-
ket.
After
recycling
process
some
raw
materials
(commodities)
are
acquired.
These
commodities,
i.e.,
gold,
are
sent
to
refinery
where
is
located
in
Belgium,
because
the
companies
in
Turkey
do
not
have
required
license
for
recycling
such
metals.
Potential
facility
sites
are
shown
in
Fig.
3.
The
flow
of
the
WEEE
for
Turkey
through
the
network
is
shown
in
Fig.
4.
In
this
study,
the
data
is
acquired
as
following.
The
data
is
ana-
lyzed
for
44
monthly
time
periods
for
four
different
types
of
waste
which
is
collected
from
28
regions.
Based
on
our
statistical
analy-
sis
we
concluded
that
the
data
fits
exponential
distribution
for
all
types
of
products
with
different
mean
()
values:
211.1
for
product
1,
1300.5
for
product
2,
52.8
for
product
3
and
158.3
for
product
4.
The
parameter
p,s
r(amount
of
product
p
occurred
at
region
r
in
sce-
nario
s)
is
randomly
generated
from
exponential
distributions
for
each
product,
region
and
scenario.
Please
note
that
the
SAA
requires
the
equal
occurrence
probability
for
scenarios.
Thus,
each
scenario
is
taken
with
the
same
probability
occurrence
and
s∈S
s=
1.
The
amount
of
waste
is
the
first
uncertain
parameter
in
the
model.
In
addition,
two
different
uncertain
parameters
are
considered,
such
as
the
quality
of
waste
and
the
transportation
cost.
The
quality
of
the
waste
is
related
to
the
percentage
of
the
waste
that
is
recy-
clable.
This
percentage
is
determined
during
the
sorting
process.
During
the
sorting
process
the
invaluable
part
(1
−
ap,s,
p
∈
Pr,
s
∈
S)
of
the
waste
is
sent
to
disposal
center
and
the
rest
of
the
waste
(ap,s)
is
sent
to
recycling
centers.
The
ap,s determines
the
percent-
age
of
the
valuable
waste
that
is
sent
to
recycling
centers.
Based
on
the
information
gathered
from
the
company‘s
historical
data,
ap,s is
randomly
generated
from
uniform
distribution
which
ranges
from
0.8
to
0.9.
Furthermore,
the
transportation
costs
are
randomly
gen-
erated
from
uniform
distribution
which
ranges
from
0.64
$
and
1.0
$
per
kilometer
per
ton
of
waste.
The
data
related
to
distances
in
terms
of
km
between
regions
and
collecting
centers,
collecting
centers
and
sorting
centers,
sorting
centers
and
recycling
centers
and
recycling
centers
and
market,
disposing
center
and
refinery
are
presented
in
Appendices
A1,
A2,
A3,
and
A4,
respectively.
The
distance
data
are
obtained
from
the
General
Directorate
of
Highways
of
Turkey
(www.kgm.gov.tr).
3.1.
Results
and
analysis
The
calculations
are
carried
out
on
a
Windows
7
Home
Premium,
running
Intel(R)
Core(TM)
i7-3612QM
with
2.10
GHz
processor
and
12
GB
RAM.
The
solution
scheme
is
implemented
in
IBM
Ilog
CPLEX
and
MATLAB
(R2010b)
is
used
for
statistical
calculations.
We
choose
to
solve
the
problem
with
three
different
sizes
of
replications:
M
=
5,
10
and
20
SAA
problems.
For
the
SAA
problems,
we
use
sample
sizes
of
N
=
20,
40,
60
and
100
scenarios.
Each
SAA
problem
is
solved
to
optimality.
The
best
feasible
solution
of
SAA
is
then
stored
as
a
candidate
solution
for
evaluation
in
the
refer-
ence
sample.
The
size
of
the
reference
sample
is
set
to
N=
1000
scenarios.
A
single
scenario
sub
problem
has
1.725
decision
variables
while
92
of
them
are
binary
and
621
constraints.
The
accumulated
398
B.
Ayvaz
et
al.
/
Resources,
Conservation
and
Recycling
104
(2015)
391–404
Fig.
2.
Schematically
representation
of
model.
problems
with
20
scenarios
have
32.752
decision
variables
and
12.230
constraints.
Further,
accumulated
problems
with
40,
60
and
100
scenarios
have
65.412,
98.072
and
163.392
decision
variables,
whilst,
24.450,
36.670
and
61.110
constraints,
consecutively.
Testing
a
given
first-stage
solution
in
the
reference
sample
provides
a
statistical
upper
bound
on
the
optimal
objective
func-
tion
value
of
the
original
problem.
For
the
accumulated
problem
instances,
the
average
of
M
optimal
objective
function
values
of
the
SAA
problems
provides
the
statistical
lower
bound
on
the
objective
function
value
of
the
original
problem.
The
statistical
lower
and
upper
bounds
and
the
best
solutions
and
performances
of
the
best
solutions
in
the
reference
sample
are
presented
in
Table
2.
The
first
and
second
columns
in
Table
2
show
number
of
replications
and
sample
sizes,
respectively.
The
third
and
fourth
columns
show
average
of
the
objective
function
val-
ues
and
standard
deviation
of
the
upper
bound
while
the
fifth
and
B.
Ayvaz
et
al.
/
Resources,
Conservation
and
Recycling
104
(2015)
391–404
399
Fig.
3.
Potential
facility
sites
for
RLND.
Fig.
4.
Network
and
decision
variables
of
RLND.
Table
2
Solutions,
statistical
lower
and
upper
bound
of
the
SAA
problems
with
N=
1000.
Best
solution
Upper
bound
Lower
bound
Collecting
centers
Sorting
centers
Recycling
centers
M
N
Average
(UB)
Average
(LB)
Objective
520
1.425.276
6.286
1.406.662
84.128
2,
5,
6,
8,
9,
10
5,
6,
7
2,
4
1.426.028
40
1.424.187 7.243
1.412.373
74.575
2,
4,7,
8,
9,
10
5,
6,
7
2,
4
1.427.831
60
1.426.125
6.034
1.410.959
74.973
2,
8,
9,
10
5,
6,
7
2,
4
1.429.352
100
1.426.638
5.823
1.437.073
59.203
2,
3,
4,
6,
8,
9,
10
1,
5,
6,
7
2,
3,
4
1.429.464
10 20
1.424.789
6.124
1.440.859
91.118
2,
5,
6,
8,
9,
10
5,
6,
7
2,
4
1.426.028
40
1.423.336
6.257
1.412.737
79.399
2,
4,
7,
8,
9,
10
5,
6,
7
2,
4
1.427.831
60
1.426.533
2.881
1.425.921
69.212
2,
3,
4,
6,
8,
9,
10
1,
5,
6,
7
2,
3,
4
1.429.464
100
1.425.607
2.639
1.435.860
64.271
2,
3,
8,
9,
10
1,
5,
6,
7
2,
3,
4
1.431.764
20 20
1.424.116
5.923
1.446.223
75.954
2,
5,
6,
8,
9,
10
5,
6,
7
2,
4
1.426.028
40
1.425.727
3.106
1.411.103
72.600
2,
6,
8,
9,
10
5,
6,
7
2,
4
1.427.946
60
1.427.399
2.295
1.417.800
69.316
2,
3,
4,
6,
8,
9,
10
1,
5,
6,
7
2,
3,
4
1.429.464
100
1.427.228
2.350
1.427.048
68.388
2,
3,
8,
9,
10
1,
5,
6,
7
2,
3,
4
1.431.764
400
B.
Ayvaz
et
al.
/
Resources,
Conservation
and
Recycling
104
(2015)
391–404
Table
3
Average
optimality
gap
and
confidence
interval.
Average
optimality
gap
90%Confidence
interval
M
N
Gap
%
(gap)
Min
%
Max
%
520
18.614
1.32
42.191
−43.196
−3.07
80.424
5.72
40
11.814
0.84
37.424
−43.011
−3.05
66.640
4.72
60
15.166
1.07
37.628
−39.959
−2.83
70.290
4.98
100
−10.435 −0.73 29.780
−54.062
−3.76
33.192
2.31
10 20
−16.070
−1.12
30.542
−60.813
−4.22
28.674
1.99
40
10.599
0.75
26.657
−28.454
−2.01
49.651
3.51
60
612
0.04
23.283
−33.497
−2.35
34.721
2.43
100
−10.253
−0.71
21.694
−42.034
−2.93
21.528
1.50
20 20
−22.107 −1.53 17.739 −48.095 −3.33 3.880 0.27
40
14.625 1.04 16.998 −10.278
−0.73
39.528
2.80
60
9.600
0.68
16.239
−14.191
−1.00
33.390
2.36
100
180
0.01
16.017
−23.284
−1.63
23.644
1.66
sixth
columns
show
these
values
for
the
lower
bound.
Columns
7–9
present
the
best
solutions
while
the
last
column
shows
the
perfor-
mance
of
the
best
solutions
in
the
reference
sample.
First,
we
note
that
the
upper
bound
improved
with
the
incremental
in
sample
size
and
the
number
of
replications.
Further,
the
improvement
is
more
significant
when
the
sample
size
increased.
Second,
standard
devi-
ation
is
getting
narrower
simultaneously
with
the
improvement
in
upper
bound.
We
can
see
the
same
improvement
in
standard
devi-
ation
of
the
lower
bound
as
well.
Third,
we
note
that
the
more
or
the
less
number
of
opened
facilities
do
not
mean
the
better
per-
formance
in
the
reference
sample.
The
solution
that
gives
the
best
performance,
i.e.
1.431.764,
in
the
reference
sample
is
opening
the
collecting
centers
2,
3,
8,
9,
10,
sorting
centers
1,
5,
6,
7
and
recycling
centers
2,
3,
4.
In
Table
3,
we
present
the
estimator
for
the
optimality
gap
as
well
as
the
upper
and
lower
limit
of
the
90%
confidence
interval
for
the
best
solution
by
solving
the
SAA
problems
with
different
number
of
replications
and
sample
sizes.
The
estimator
for
the
opti-
mality
gap
is
calculated
by
subtracting
the
lower
bound
form
the
upper
bound.
The
confidence
interval
for
the
optimality
gap
gets
tighter
as
we
enlarge
the
number
of
replications
and
the
sam-
ple
sizes
of
SAA
problems.
This
mostly
occurs
due
to
a
smaller
variance
of
the
lower
bound.
Therefore,
increasing
the
number
of
replications
but
mostly
the
sample
size,
gives
us
a
better
guarantee
regarding
how
close
we
are
to
the
optimal
solution
of
the
original
problem.
Based
on
the
results,
the
optimality
gap
indicated
that
the
solutions
found
by
the
SAA
procedure
are
sufficient
to
be
used
in
a
real
life
appliance.
We
note
that
the
average
CPU-time
for
small
size,
i.e.
N
=
20,
40
SAA
problems
are
less
than
45
seconds,
while
CPU-time
for
medium
sample
size,
i.e.
N
=
60,
varied
between
2
and
3
min
and
for
bigger
sample
size,
i.e.
N
=
100,
varies
between
7
and
8
min.
It
is
clear
that
CPU
time
increased
exponentially
as
we
increased
the
sample
size.
Calculating
the
performance
of
a
given
first
stage
solution
in
the
reference
sample
required
approximately
2
min
of
CPU
time.
One
of
the
goals
of
solving
numerous
replications
and
sample
sizes
by
SAA
method
is
to
find
good
candidates
for
the
first
stage
solutions
to
be
evaluated
in
the
reference
sample.
The
solution(s)
with
the
best
performance
in
the
reference
sample
is
reported
and
this
solution
can
be
considered
in
designing
the
RLND
of
the
com-
pany.
The
upper
bound
from
these
solutions
do
not
vary
a
lot,
but
the
best
upper
bounds
are
obtained
from
the
cases
which
used
100
scenarios
in
the
SAA
samples,
regardless
from
the
number
of
replications.
Furthermore,
uncertainty
is
one
of
another
challenge
that
is
faced
in
real
world
applications.
The
approaches
that
handle
uncer-
tainty
help
researchers
to
get
accurate
results
with
the
real
world
applications.
In
real
world,
parameters
are
not
always
known;
although,
in
deterministic
optimization
programming,
parameters
are
assumed
certain.
On
the
other
hand,
stochastic
programming
methodologies
deal
with
uncertain
parameter
by
incorporating
dif-
ferent
possible
scenarios
in
the
model
infrastructure.
The
model
developed
in
this
study
considered
three
types
uncertainties
while
determining
the
optimal
solution
and
these
uncertainties
are:
amount
of
WEEE
in
system,
the
quality
of
collected
WEEE
and
the
transportation
costs
between
nodes.
The
results
show
that
our
solution
approach
produces
good
first
stage
solutions
as
candidate
solutions
to
be
tested
in
reference
sample.
We
noted
that
our
solution
scheme
was
capable
of
find-
ing
good
solutions
even
with
small
sized
SAA
problems.
Increasing
the
sample
size
develops
the
lower
bound
on
the
optimal
func-
tion
value;
consequently
the
quality
guarantee
on
the
optimality
is
improved.
Higher
sample
size
guarantee
the
quality
of
the
solu-
tions,
whilst
multiple
replications
help
the
solution
approach
to
find
more
candidate
first
stage
solutions
to
be
tested
in
the
refer-
ence
sample.
Fig.
5(a)
and
(b)
present
the
average
objective
function
value
and
standard
deviation
on
upper
bound,
respectively.
As
seen
in
Fig.
5,
usually
higher
average
objective
function
values
(a)
and
tighter
standard
deviations
(b)
are
obtained
with
higher
sample
sizes.
Another
observation
could
be
that
higher
number
of
(a)
(b)
1.423
1.424
1.425
1.425
1.426
1.427
1.428
1.428
N=20
N=40
N=60
N=100
Ave. UB_Objecve(1000)
Sample
Size
M=5
M=10
M=20
0
1
2
3
4
5
6
7
8
N=20
N=4
0
N=60
N=100
σ_UB(1000)
Sample
Size
M=5
M=10
M=20
Fig.
5.
Average
objective
function
values
and
standard
deviations
on
upper
bound.
B.
Ayvaz
et
al.
/
Resources,
Conservation
and
Recycling
104
(2015)
391–404
401
(a) (b)
1.426
1.427
1.428
1.429
1.430
1.431
1.432
1.433
N=20
N=40
N=60
N=100
Best Objecve(1000)
Sample
Size
M=5
M=10
M=20
10
15
20
25
30
35
40
45
N=2
0
N=40
N=6
0
N=100
σ_gap (1000)
SampleSi
ze
M=5
M=10
M=20
Fig.
6.
Best
objective
function
values
and
standard
deviation
on
the
optimality
gap.
Fig.
7.
Opened
facilities.
Fig.
8.
WEEE
amount—Turkey
(2011).
402
B.
Ayvaz
et
al.
/
Resources,
Conservation
and
Recycling
104
(2015)
391–404
replications
did
not
guarantee
better
average
objective
function
values
but
the
narrower
standard
deviations.
As
seen
in
Fig.
6(a),
although,
increasing
the
number
of
replica-
tions
mostly
do
not
help
in
finding
better
solution,
it
helped
when
N
=
100.
However,
we
can
conclude
that
increasing
the
number
of
replications
reduces
the
gap
on
optimality
by
a
lot,
as
seen
in
Fig.
6(b).
Lastly,
based
on
the
results
in
Fig.
6,
we
note
that
increas-
ing
sample
sizes
improves
the
solution
found
and
the
optimality
gap
especially
when
fewer
replications
are
considered.
Working
with
higher
sample
sizes
provides
better
solutions
with
less
opti-
mality
gap
but
CPU-time
increases.
Therefore
a
tradeoff
between
gathering
better
solutions
and
CPU
times
occurs
for
the
managers
and
researchers.
According
to
the
analysis
the
best
solution
is
to
open
collecting
centers
2,
3,
8,
9,
10
sorting
centers
1,
5,
6,
7
and
recycling
centers
2,
3,
4
as
shown
in
Fig.
7.
Comparing
to
the
Regulatory
Impact
Assessment
of
EU
Waste
Electrical
and
Electronic
Equipment
(REC
Turkey,
2011)
report,
the
results
are
relevant,
as
presented
in
Fig.
8.
WEEE
production
in
Turkey
(Fig.
8)
supports
the
optimal
solution
presented
in
Fig.
7.
Consequently,
the
results
show
that
the
proposed
method
pro-
vides
reliable
solutions
with
a
90%
confidence
interval
under
uncertainties
in
RLND
network
design
for
decision
makers.
4.
Conclusions
In
recent
years,
RL
has
received
more
attentions
from
companies
in
order
to
have
sustainable
process
due
to
the
economic,
politi-
cal,
and
environmental
reasons.
Today’s
WEEE
generation
increases
each
day
and
this
causes
air
and
environment
pollution.
Fortun-
ately,
the
number
of
companies
which
realize
the
importance
of
recycling
increases
as
well.
Thus,
modeling
reverse
supply-chain
networks
is
required
more
than
ever.
Above
all,
developing
sus-
tainable
networks
in
reverse
logistics
has
become
a
fundamental
concern
due
to
the
environmental
issues.
For
the
reason
that
companies
face
pressures
from
stakehol-
ders
and
governmental
regulations,
they
need
to
recycle
as
much
as
a
specific
percentage
of
their
annual
production.
Therefore,
in
practice,
creating
a
sustainable
RL
network
becomes
a
mandatory,
especially
when
there
are
many
uncertainties,
i.e.,
quality
of
WEEE,
costs
etc.,
in
the
system.
To
conserve
resources,
reusing,
remanufacturing
and
recycling
are
the
three
of
the
most
important
processes,
and
reverse
sup-
ply
chain
starts
with
these
activities.
However,
all
companies
do
not
have
chance
to
develop
a
RL
network
due
to
budged
and
opera-
tional
capability
constraints.
Thus,
a
need
of
third
party
RL
network
occurs.
This
paper
mainly
focuses
on
developing
a
generic
reverse
logistics
network
for
a
third
party
recycling
company.
In
this
study,
a
two-stage
stochastic
profit
maximization
RLND
problem,
which
is
a
quite
new
technique
for
reverse
supply
network,
with
a
real
case
study
in
WEEE
recycling
industry
is
presented.
The
mathematical
formulation
of
the
problem
can
be
employed
to
any
supply
chain
network
design
that
comprises
of
multi
echelons.
It
is
also
probable
to
adapt
the
model
to
a
single
echelon
networks.
The
specific
goal
is
to
determine
optimal
loca-
tions
for
collecting,
sorting
and
recycling
centers
and
to
determine
the
transportation
of
waste
amounts
between
nodes
in
a
RLND
problem.
The
contributions
of
this
paper
are
as
follows:
First,
this
study
is
the
first
appliance,
in
WEEE
literature
for
RLND
network
design
under
uncertain
parameters,
such
as,
amount
of
WEEE,
quality
of
collected
WEEE
and
transportation
costs.
Second,
the
RLND
net-
work
is
modeled
as
a
SP
model
and
it
is
solved
by
SAA.
Third,
the
proposed
model
is
a
generic
RLND
for
third
party
reverse
logis-
tic
companies.
Lastly,
the
proposed
model
is
easy
and
effective
to
support
establishing
RLND
decisions
for
managers
and
decision
makers.
Acknowledgement
The
authors
would
like
to
thank
the
editor
and
the
three
anonymous
referees
for
their
helpful
comments
and
suggested
improvements.
Appendix
A.
Distances
between
regions
and
collecting
centers
(km).
Adana
Ankara
Antalya
Bursa
Eskis¸
ehir
Istanbul
Izmir
Izmit
Sakarya
Tekirda˘
g
City
Region
1
2
3
4
5
6
7
8
9
10
Adana
1
5
490
558
837
686
939
900
828
791
1071
Afyon
2
573
256
292
273
144
454
327
343
306
586
Ankara
3
490
5
544
384
233
453
579
342
305
585
Antalya
4
558
544
5
537
424
718
444
607
570
850
Aydın
5
883
598
342
445
478
684
126
573
604
630
Balıkesir
6
897
533
505
151
300
390
176
279
310
380
Bursa
7
837
384
537
5
151
243
325
132
159
375
C¸
anakkale
8
1097
655
705
271
422
320
326
399
430
188
Diyarbakır
9
522
910
1080
1283
1132
1363
1422
1252
1215
1495
Edirne
10
1169
683
913
419
554
230
534
341
378
140
Erzurum
11
808
874
1251
1239
1107
1228
1453
1117
1080
1360
Eskis¸
ehir
12
686
233
424
151
5
324
411
213
176
456
˙
Istanbul
13
939
453
718
243
324
5
564
111
148
132
˙
Izmir 14
900
579
444
325
411
564
5
453
484
506
˙
Izmit
15
828
342
607
132
213
111
453
5
37
243
Kırıkkale
16
475
75
567
459
308
528
654
417
380
660
Konya
17
356
258
322
487
336
660
550
549
512
792
Kütahya
18
673
311
364
173
78
354
333
243
206
486
Manisa
19
884
563
428
290
395
529
35
418
449
511
Mersin
20
69
483
489
829
678
932
892
821
784
1064
Mu˘
gla
21
869
620
311
544
500
783
225
672
636
729
Ni˘
gde
22
205
348
544
717
566
797
786
686
649
929
Sakarya
23
791
305
570
159
176
148
484
37
5
280
Samsun
24
729
414
906
745
647
734
993
623
586
866
Tekirda˘
g25
1071
585
850
375
456
132
506
243
280
5
Trabzon
26
852
747
1236
1078
980
1067
1326
956
919
1199
Yalova
27
893
407
605
69
211
176
390
65
102
308
Zonguldak
28
754
268
753
342
359
331
667
220
183
463
B.
Ayvaz
et
al.
/
Resources,
Conservation
and
Recycling
104
(2015)
391–404
403
Appendix
B.
Distances
between
collecting
centers
and
sorting
centers
(km).
Antalya
Erzurum
Gaziantep
Kayseri
Kocaeli
Tekirda˘
g
Zonguldak
City
Collecting
center
1
2
3
4
5
6
7
Adana
1
558
808
209
333
828
1071
754
Ankara
2
544
874
671
318
342
585
268
Antalya
3
5
1251
767
618
607
850
753
Bursa
4
537
1239
1044
691
132
375
342
Eskis¸
ehir
5
424
1107
893
540
213
456
359
Istanbul
6
718
1228
1124
771
111
132
331
Izmir
7
444
1453
1109
848
453
506
667
Izmit
8
607
1117
1013
660
5
243
220
Sakarya
9
570
1080
976
623
37
280
183
Tekirda˘
g10
850
1360
1256
903
243
5
463
Appendix
C.
Distance
between
sorting
centers
and
recycling
and
disposing
center
(s)
(km).
Adana
Ankara
Izmir
Kocaeli
Samsun
Gebze
City
Sorting
center
1
2
3
4
5
1
Antalya
1
558
544
444
607
906
619
Erzurum
2
808
874
1453
1117
562
1.129
Gaziantep
3
209
671
1109
1013
725
1.025
Kayseri
4
333
318
848
660
453
672
Kocaeli
5
828
342
453
5
623
17
Tekirda˘
g
6
1071
585
506
243
866
255
Zonguldak
7
754
268
667
220
549
232
Appendix
D.
Distance
between
recycling
centers
and
market,
disposing
center
and
refinery
(km).
City
Recycling
center
Bursa
Gebze
Belgium
Adana
1
837
840
2125
Ankara
2
384
354
2125
Izmir
3
325
465
2125
Kocaeli
4
132
12
2125
Samsun
5
745
635
2125
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