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Control
Problems
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May
11-13, 2015.
Ottawa,
Canada
Information
Control
Problems
in Manufacturing
May 11-13,
11-13, 2015.
2015.
Ottawa,
Canada
May
Ottawa,
Canada
May 11-13, 2015. Ottawa, Canada
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IFAC-PapersOnLine 48-3 (2015) 2362–2367
Optimal
Optimal Allocation
Allocation of
of Public
Public Service
Service Centres
Centres in
in the
the Central
Central Places
Places of
of Functional
Functional
Optimal
Allocation
of
Public
Service
Centres
in
the
Central
Places
of
Regions
Optimal Allocation of Public ServiceRegions
Centres in the Central Places of Functional
Functional
Regions
Regions
Samo Drobne*. Marija Bogataj**
Samo Drobne*. Marija Bogataj**
Samo Drobne*.
Drobne*. Marija
Marija
Bogataj**

Samo
Bogataj**

Bogataj**
Samo Drobne*. Marija

*
Jamova

* University
University of
of Ljubljana,
Ljubljana, Faculty
Faculty of
of Civil
Civil and
and Geodetic
Geodetic Engineering,
Engineering,
Jamova cesta
cesta 2,
2, SI-1000
SI-1000 Ljubljana,
Ljubljana, Slovenia
Slovenia
*
of
and
Geodetic
Engineering,
Jamova
cesta
(Tel:
+386
11 4768
e-mail:
samo.drobne@
fgg.uni-lj.si).
* University
University of
of Ljubljana,
Ljubljana, Faculty
Faculty
of Civil
Civil
and649;
Geodetic
Engineering,
Jamova
cesta 2,
2, SI-1000
SI-1000 Ljubljana,
Ljubljana, Slovenia
Slovenia
(Tel:
+386
4768
649;
e-mail:
samo.drobne@
fgg.uni-lj.si).
*
University
of
Ljubljana,
Faculty
of
Civil
and
Geodetic
Engineering,
Jamova
cesta
2,
SI-1000
Ljubljana,
Slovenia
(Tel:
+386 11Studies,
4768 649;
649;
e-mail:
samo.drobne@
fgg.uni-lj.si).
**
Advanced
Vrtojba,
Mednarodni
prehod
6,
SI-5290
Sempeter
pri
Gorici,
Slovenia
+386
4768
e-mail:
samo.drobne@
fgg.uni-lj.si).
** Mediterranean
Mediterranean Institute
Institute for
for(Tel:
Advanced
Studies,
Vrtojba,
Mednarodni
prehod
6,
SI-5290
Sempeter
pri
Gorici,
Slovenia
(Tel:
+386
1
4768
649;
e-mail:
samo.drobne@
fgg.uni-lj.si).
** Mediterranean
Mediterranean Institute
Institute for
for Advanced
Advanced
Studies,[email protected]).
Vrtojba, Mednarodni
Mednarodni prehod
prehod 6,
6, SI-5290
SI-5290 Sempeter
Sempeter pri
pri Gorici,
Gorici, Slovenia
Slovenia
(e-mail:
**
Studies,
Vrtojba,
(e-mail:
[email protected]).
** Mediterranean Institute for Advanced
Studies,[email protected]).
Vrtojba, Mednarodni prehod 6, SI-5290 Sempeter pri Gorici, Slovenia
(e-mail:
(e-mail:
[email protected]).
(e-mail: [email protected]).
Abstract:
Abstract: In
In the
the European
European Union,
Union, Member
Member States
States and
and their
their regions
regions are
are responsible
responsible for
for planning,
planning, funding
funding
Abstract:
In the
the European
European
Union,
Member
States
and
their
regions
are
responsible
forHow
planning,
funding
and
administration
of
public
services,
which
should
be
based
also
on
smart
city
tools.
smart
is
aa city
Abstract:
In
Union,
Member
States
and
their
regions
are
responsible
for
planning,
funding
and
administration
of
public
services,
which
should
be
based
also
on
smart
city
tools.
How
smart
is
city
Abstract:
In the European
Union,
Member
States
responsible
forHow
planning,
funding
and
administration
ofalso
public
services,
which
shouldand
be their
basedregions
also
onare
smart
city
tools.
How
smart actively
is
a city
city
could
be
evaluated
by
its
ability
to
produce
favorable
conditions
to
get
urban
operators
and
administration
of
public
services,
which
should
be
based
also
on
smart
city
tools.
smart
is
a
could
be
evaluated
also
by
its
ability
to
produce
favorable
conditions
to
get
urban
operators
actively
and
administration
ofalso
public
services,
which
shoulddevelop
be based also
on smarttopublic
city
tools.
How
smart actively
is a The
city
could
be
evaluated
by
to
favorable
conditions
get
operators
involved
spatial
innovation
dynamics,
also
innovative
logistics
networks.
could
be into
evaluated
by its
its ability
ability
to produce
produce
favorablethe
get urban
urban
operators
actively
involved
into
spatialalso
innovation
dynamics,
also to
to develop
theconditions
innovativeto
public
logistics
networks.
The
could
be
evaluated
also
by
its
ability
to
produce
favorable
conditions
to
get
urban
operators
actively
involved
into
spatial
innovation
dynamics,
also
to
develop
the
innovative
public
logistics
networks.
The
method
supports
local
authorities
and
state
government’s
decision
optimal
allocation
of
involved
into spatial
innovation
develop
the innovative
publicon
method presented
presented
supports
localdynamics,
authoritiesalso
andto
state
government’s
decision
onlogistics
optimalnetworks.
allocationThe
of
involved
into
spatial
innovation
dynamics,
also
to state
develop
the method
innovative
public
logistics
networks.
The
method
presented
supports
local
authorities
and
government’s
decision
on
optimal
allocation
of
regionally
based
public
services.
The
article
is
presenting
the
for
optimal
coverage
of
the
state
method
presented
supports
local
authorities
and
state
government’s
decision
on
optimal
allocation
of
regionally
based public
services.
The
article is
presenting
the methoddecision
for optimal
coverageallocation
of the state
method
presented
supports
local
authorities
and
state
government’s
on
optimal
of
regionally
based
public
The
is presenting
the
method
for
coverage
of
territory
functional
regions,
smart
is
the
and
optimal
of
regionally
based
public services.
services.
The article
article
presenting
theof
method
for optimal
optimal
of the
the state
state
territory with
with
functional
regions, where
where
smartiscity
city
is aa center
center
of
the activities,
activities,
and coverage
optimal allocation
allocation
of
regionally
based
public
services.
The
article
presenting
theof
method
forusing
optimal
coverage
of the state
territory
with
functional
regions,
where
smartiscity
city
is aa center
center
the activities,
activities,
and
optimal allocation
allocation
of
services
influence
city
growth.
Sets
of
functional
regions
were
modelled
the
Intramax
method.
An
territory
with
functional
regions,
where
smart
is
of
the
and
optimal
of
services
influence
city
growth.
Sets
of
functional
regions
were
modelled
using
the
Intramax
method.
An
territory
with functional
regions,
where
smart city
is a center
ofmodelled
the where
activities,
and
optimal
allocation
of
services regionalization
influence
city growth.
growth.
Sets
offunctional
functional
regions
were
using
the Intramax
Intramax
method.
An
optimal
on
of
regions
is
presented
the
number
is
services
influence
city
Sets
functional
regions
modelled
using
the
method.
An
optimal
regionalization
on number
number
ofof
functional
regions
iswere
presented
where
the optimal
optimal
number
is chosen
chosen
services
influence
city
growth.
Sets
of
functional
regions
were
modelled
using
the
Intramax
method.
An
optimal
regionalization
on
number
of case
functional
regions
is presented
presented
where the
thefor
optimal
number
is chosen
chosen
according
to
services.
The
study
Slovenian
regionalization
eldercare
is
optimal
regionalization
number
of
functional
regions
is
where
optimal
number
is
according
to the
the cost
cost of
of on
services.
The
case
study for
for
Slovenian
regionalization
for
eldercare
is presented.
presented.
optimal
regionalization
number
of case
functional
regions
is presented
where thefor
optimal
number
is chosen
according
to the
the cost
cost of
of on
services.
The
study for
for
Slovenian
regionalization
eldercare
is presented.
presented.
according
to
services.
The
case
study
Slovenian
regionalization
for
eldercare
is
Keywords:
region,
functional
region,
central
place,
optimal
allocation,
service,
eldercare.
© 2015, IFAC
(International
Federation
of Automatic
Control)
Hosting
byservice,
Elsevierfor
Ltd.
All rights
according
toregion,
the
cost
of services.
The central
case
study
foroptimal
Slovenian
regionalization
eldercare
is reserved.
presented.
Keywords:
functional
region,
place,
allocation,
eldercare.
Keywords:
Keywords: region,
region, functional
functional region,
region, central
central place,
place, optimal
optimal allocation,
allocation, service,
service, eldercare.
eldercare.
Keywords: region, functional region, central place, optimal allocation, service, eldercare.

Many
Many researchers
researchers (e.g.
(e.g. Ball,
Ball, 1980;
1980; Casado-Diaz,
Casado-Diaz, 2000;
2000;
1.

Many researchers
researchers
(e.g.
Ball,
1980;
Casado-Diaz,
2000;
1. INTRODUCTION
INTRODUCTION
Tomaney
and
Ward,
2000;
Laan
and
Schalke,
2001;
Andersen,
Many
(e.g.
Ball,
1980;
Casado-Diaz,
2000;
Tomaney
and
Ward,
2000;
Laan
and
Schalke,
2001;
Andersen,
1.
INTRODUCTION
1. INTRODUCTION
Many
researchers
(e.g.
Ball,
1980;
Casado-Diaz,
2000;
Tomaney
and Ward,
Ward,
2000;
Laan
and
Schalke,
2001; Andersen,
Andersen,
2002)
showed
already
that
the
standard
administrative
regions
Tomaney
and
2000;
Laan
and
Schalke,
2001;
1.
INTRODUCTION
2002)
showed
already
that Laan
the standard
administrative
regions
1.1
Tomaney
and
Ward,
2000;
and
Schalke,
2001;
Andersen,
1.1 Formal
Formal political
political region
region and
and functional
functional region
region
2002) showed
showed
already
that the
the standard
standard
administrative
regions
covering
territory
of
Member
States
basic
2002)
already
that
regions
1.1 Formal
Formal political
political region
region and
and functional
functional region
region
covering
territory
of European
European
Memberadministrative
States used
used as
as
basic
1.1
2002)
showed
already
that resource
the standard
administrative
regions
covering
territory
of
European
Member
States
used
as
basic
1.1
Formal
political
region
and
functional
region
entities
for
policy
making,
allocation,
and
research
do
covering
territory
of
European
Member
States
used
as
basic
How
smart
is
a
city
could
be
evaluated
also
by
its
ability
to
entities
for
policy
making,
resource
allocation,
and
research
do
covering
territory
of
European
Member
States
used
as
basic
How smart is a city could be evaluated also by its ability to not
entities
for
policy
making,
resource
allocation,
and
research
do
provide
meaningful
information
on
actual
conditions
of
entities
for
policy
making,
resource
allocation,
and
research
doaa
How
smart
is
a
city
could
be
evaluated
also
by
its
ability
to
produce
favourable
conditions
to
get
urban
operators
actively
How
smart
is
a
city
could
be
evaluated
also
by
its
ability
to
not
provide
meaningful
information
on
actual
conditions
of
entities
for
policy
making,
resource
allocation,
and
research
doa
produce
favourable
conditions
to get urban
operators
actively
How
smart
is
a
city
could
be
evaluated
also
by
its
ability
to
not
provide
meaningful
information
on
actual
conditions
of
particular
areas.
As
such,
there
has
been
a
move
towards
provide
meaningful
information
on
actual
conditions
of
a
produce favourable
favourable
conditions
to get
get
urban operators
operators
actively not
involved
into
spatial
innovation
dynamics,
also
to
evaluate
produce
conditions
to
urban
actively
particular
areas.
As such,
there hasonbeen
a conditions
move towards
not
provide
meaningful
information
actual
of
a
involved
into
spatial
innovation
dynamics,
also
to
evaluate
particular
areas.
As
such,
there
has
been
aa move
towards
produce
favourable
tobeget
urbaninoperators
actively
functional
regions.
A
functional
region
is
defined
as
a
region
particular
areas.
As
such,
there
has
been
move
towards
involved
intoservices
spatialconditions
innovation
dynamics,
alsocity
to and
evaluate
which
public
are
best
to
located
the
what
involved
into
spatial
innovation
dynamics,
also
to
evaluate
functional areas.
regions.AsA such,
functional
region
is defined
as atowards
region
particular
there
has
been
a
move
which
public
services
are
best
to
be
located
in
the
city
and
what
involved
intoservices
spatial are
innovation
alsocity
to and
evaluate
functional
regions.
A
is
as
aa region
by
of
and
intrafunctional
regions.
A functional
functional region
region
is defined
defined
as its
region
which
public
best to
towhich
bedynamics,
located
in the
the
what characterised
is
the
functional
will
covered
by
which
public
services
areregion
best
be
located
in
city and
what
characterised
by its
its agglomeration
agglomeration
of activities
activities
and by
by
intrafunctional
regions.
A functional
region
is defined
as its
a region
is
the optimal
optimal
functional
region
which
will be
be
covered
by these
these
which
public
services
are
best
to
be
located
in
the
city
and
what
characterised
by
its
agglomeration
of
activities
and
by
its
intraregional
transport,
information
and
communication
characterised
by
its
agglomeration
of
activities
and
by
its
intrais the
the optimal
optimal
functional
region
which
will
becentral
covered
by these
these
services.
Different
services
in
a
city
as
a
place
of
a
is
functional
region
which
will
be
covered
by
regional
transport,
information
and
communication
services.
Different
services
in which
a city will
as abecentral
place
of a characterised
by
its agglomeration
of activities
and by
its intra-a
is
the
optimal
functional
region
covered
by
these
regional
transport,
information
and
communication
infrastructure,
facilitating
production
and
services,
therefore
regional
transport,
information
and
communication
services.
Different
services
in
a
city
as
a
central
place
of
a
region
have
different
optimal
size
of
services.
Different
services
a city
as aterritory
central covered
place ofby
a infrastructure,
facilitatinginformation
production and
therefore a
regional
transport,
andservices,
communication
region
have
different
optimalin
of the
the
covered
services.
Different
services
inissize
aunderstand
city
as aterritory
central
place
ofby
a large
infrastructure,
facilitating
production
and
services,
therefore
a
mobility
of
people,
items
in
production
processes
and
infrastructure,
facilitating
production
and
services,
therefore
region
have
different
optimal
size
of
the
territory
covered
by
them.
While
a
formal
region
as
an
area
having
region
have
different
optimal
size
of
the
territory
covered
by
large
mobility
of
people,
items
in
production
processes
andaa
them. While
a formal optimal
region issize
understand
as an area
having
infrastructure,
facilitating
production
and within
services,
therefore
region
have
different
of
the
territory
covered
by
large
mobility
of
people,
items
in
production
processes
and
final
products,
but
also
enabling
services
its
interaction
large
mobility
of
people,
items
in
production
processes
and
them.
While
a
formal
region
is
understand
as
an
area
having
the
characteristics
(at
one)
also
them.
While
a formal region
is understand
anwell-defined
area having final
products,
but
also enabling
services
within processes
its interaction
large
mobility
of
people,
items
in production
and
the same
same
characteristics
(at least
least
one) and
and as
also
them.
While
a formalregion
region
isbased
understand
as
anwell-defined
area having
final
products,
but
also
services
borders,
which
is
rarely
well
defined.
final
products,
but
also enabling
enabling
services within
within its
its interaction
interaction
the
same
characteristics
(at
least
one)
and
also
well-defined
border,
a
functional
is
around
something
(local
the
same
characteristics
(at
least
one)
and
also
well-defined
borders,
which
is
rarely
well
defined.
final
products,
but
also
enabling
services
within
its interaction
border,
a functional
region
isleast
based
around
something
(local borders,
the
same
characteristics
(at
one)
and
also
well-defined
which
is
rarely
well
defined.
which is rarely well defined.
border, market
functional
region
is based
based
around
something
(local borders,
labour
(LLM)
areas,
around
their
central
border,
aa functional
region
is
around
(local
In
society,
the
basic
characteristic
borders,
which
is rarely
defined.
labour
market
(LLM)
areas,
around
theirsomething
central places,
places,
border,
aaround
functional
region
is destination
based
around
something
(local
In industrial
industrial
society,
thewell
basic
characteristic of
of aa functional
functional
labour market
market
(LLM)
areas,
around
their
central
places,
utilities
sources
or
point,
even
pizza
labour
(LLM)
areas,
around
their
central
places,
In
industrial
society, the
the
basicmarket,
characteristic
ofintra-regional
functional
region
is
the
integrated
labour
in
which
In
industrial
society,
basic
characteristic
of
aa functional
utilities
around
sources
or
destination
point,
even
pizza
labour
market
(LLM)
areas,
around
their
central
places,
region
is
the
integrated
labour
market,
in
which
intra-regional
utilities area
around
sources
or destination
destination
point, area)
evenand
pizza
In
industrial
society,
the
basicmarket,
characteristic
ofand
a functional
delivery
can
be
understood
as
aa functional
its
utilities
around
sources
or
point,
even
pizza
region
is
the
integrated
labour
in
which
intra-regional
commuting
as
well
as
intra-regional
job
search
search
region
is
the
integrated
labour
market,
in
which
intra-regional
delivery
area
can
be
understood
as
functional
area)
and
its
well as intra-regional
jobinsearch
and
search for
for
utilities
around
sources
or destination
point,
even
pizza
delivery could
area
can
befuzzy
understood
as aa functional
functional
area)
and
its commuting
region
is theas
integrated
labour
market,
which
intra-regional
borders
be
and
changing
in
aa time
horizon.
delivery
area
can
be
understood
as
area)
and
its
commuting
as
well
as
intra-regional
job
search
and
search
labour
demand
is
much
more
intensive
than
the
inter-regional
commuting
as
well
as
intra-regional
job
search
and
search for
for
borders
could
be
fuzzy
and
changing
in
time
horizon.
delivery
area
can
be
understood
as
a
functional
area)
and
its
labour
demand
is
much
more
intensive
than
the
inter-regional
borders
could
be
fuzzy
and
changing
in
a
time
horizon.
commuting
as
well
as
intra-regional
job
search
and
search
for
Therefore,
functional
region
an
area
that
made
up
of
borders
could
be fuzzy
and is
changing
in a is
time
horizon.
labour
demand
is
much
more
intensive
than
the
inter-regional
counterparts.
Consequently,
the
identification
and
delineation
labour
demand
is
much
more
intensive
than
the
inter-regional
Therefore,
functional
region
is
an
area
that
is
made
up
of
counterparts.
Consequently,
the
identification
and
delineation
borders
could
be
fuzzy
and
changing
in
a
time
horizon.
Therefore,
functional
region
is
an
area
that
is
made
up
of
labour
demand
is
much
more
intensive
than
the
inter-regional
different
e.g.
communities,
Therefore,
functional spatial
region units
is an(ESUs,
area that
made up of counterparts.
Consequently,
the
and
delineation
of
are
based
of
Consequently,
the identification
identification
andconditions
delineation
different elementary
elementary
spatial
units
e.g.is
communities,
Therefore,
functional
region
is and
an(ESUs,
area
that
is
made
upThe
of counterparts.
of functional
functional regions
regions
are commonly
commonly
based on
on the
the
conditions
of
different
elementary
spatial
units
(ESUs,
e.g.
communities,
counterparts.
Consequently,
thethis
identification
and
delineation
municipalities)
that
are
linked
function
as
a
unit.
different
elementary
spatial
units
(ESUs,
e.g.
communities,
of
functional
regions
are
commonly
based
on
the
conditions
of
local
labour
market.
Based
on
perception,
Smart
(1974)
functional
regions are
commonly
based
on theSmart
conditions
of
municipalities)
that are
linked
and(ESUs,
function
ascommunities,
a unit. The of
different
elementary
spatial
units
e.g.
local
labour
market.
Based
on
this
perception,
(1974)
municipalities)
that
are
linked
and
function
as
a
unit.
The
of
functional
regions
are
commonly
based
on
the
conditions
of
participating
ESUs
could
change
in
a
time
horizon.
Functional
municipalities)
that
are
linked
and
function
as
a
unit.
The
local
labour
market.
Based
on
this
perception,
Smart
(1974)
delineated
functional
regions
and
this
“industrial”
approach
is
local
labour
market.
Based
on
this
perception,
Smart
(1974)
participating ESUs
could
changeand
in a function
time horizon.
Functional
municipalities)
that
are
linked
as
a
unit.
The
delineated
functional
regions
and
this
“industrial”
approach
is
participating
ESUs could
could
changeone
in aa or
timefew
horizon.
Functional
local
labour
market.
Based
on
this
perception,
Smart
(1974)
region
is
organized
around
central
places.
participating
ESUs
change
in
time
horizon.
Functional
delineatedinfunctional
functional
regions
and(OECD,
this “industrial”
“industrial”
approach
is
accepted
the
recent
literature
2002;
Cörvers
et
al.,
delineated
regions
and
this
approach
is
region
is
organized
around
one
or
few
central
places.
participating
ESUs
could
change
in
a
time
horizon.
Functional
accepted
in
the
recent
literature
(OECD,
2002;
Cörvers
et
al.,
region is
is on
organized
around
one which
or few
few
central
places.
delineated
regions
and(OECD,
this
“industrial”
approach
is
Dependent
number
of
functions,
are
concentrated
in
region
organized
around
one
or
central
places.
accepted
infunctional
the recent
recent
literature
2002;
Cörvers
et al.,
al.,
2009;
Casado-Diaz
and
Coombes,
2011),
while
the
economic
accepted
in
the
literature
(OECD,
2002;
Cörvers
et
Dependent
on
number
of
functions,
which
are
concentrated
in
region
is on
organized
around
one which
or few
central
places.
Casado-Diaz
andliterature
Coombes,
2011),2002;
whileCörvers
the economic
Dependent
number
of
functions,
are
concentrated
in 2009;
accepted
in
the
recent
(OECD,
et
al.,
central
places,
such
central
places
create
a
highly
stratified
Dependent
on
number
of
functions,
which
are
concentrated
in
2009;
Casado-Diaz
and
Coombes,
2011),
while
the
economic
shocks
like
economic
crises
require
Casado-Diaz
and Coombes,
2011),
thereconsider
economic
central
places,
such central
places which
create are
a highly
stratified
Dependent
on
number
of functions,
concentrated
in 2009;
shocks
like the
the nowadays’
nowadays’
economic
criseswhile
require
central places,
places,
such
central
places
create
highly
stratified
2009;
Casado-Diaz
and Coombes,
2011),
while
thereconsider
economic
network
of
cities.
Regarding
economic
and
cohesion
of
central
such
central
places
create
aasocial
highly
stratified
shocks
like
the
nowadays’
economic
crises
require
reconsider
the
labour
market
perception.
In
the
post-industrial
society,
shocks
like
the
nowadays’
economic
crises
require
reconsider
network
of
cities.
Regarding
economic
and
social
cohesion
of
the labour
market
perception.
In thecrises
post-industrial
society,
central
places,
such
central
places
create
asocial
highly
stratified
network
of
cities.
Regarding
economic
and
cohesion
of
shocks
like
the
nowadays’
economic
require
reconsider
European
Union
(EU)
regions,
which
are
the
main
goal
network
of
cities.
Regarding
economic
and
social
cohesion
of
the
labour
market
perception.
In
the
post-industrial
society,
intensity
of
flows
of
workers
and
flows
of
items
decline
and
the
labour
market
perception.
In
the
post-industrial
society,
European
Union
(EU)
regions,
which
are
the
main
goal
of
network
ofSpatial
cities. Development
Regarding
economic
and
social
cohesion
of
intensity
of
flows
of
workers
and
flows
of
items
decline
and
European
Union
(EU)
regions,
which
are
the
main
goal
of
the
labour
market
perception.
In
the
post-industrial
society,
Perspective
(ESDP
1999),
the
European
Union
(EU)
regions,
which
are
the
main
goal
of
intensity
of
flows
of
workers
and
flows
of
items
decline
and
services
in
a
functional
region
is
progressing.
intensity
of
flows
of
workers
and
flows
of
items
decline
and
European Spatial
Development
Perspective
(ESDP
1999),
the
European
Union
(EU)
regions,
which
are
the
main
goal
of
intensity
of
services
in
a
functional
region
is
progressing.
European
Spatial
Development
Perspective
(ESDP
1999),
the
intensity
of
flows
of
workers
and
flows
of
items
decline
and
regional
state-of-art
and
especially
future
development,
must
European
Spatial
Development
Perspective
(ESDP
1999),
the
intensity
of
services
in
a
functional
region
is
progressing.
intensity of services in a functional region is progressing.
regional state-of-art
and especially
future development,
must
European
Spatial
Development
Perspective
(ESDP
1999),
the
A
number
of
regionalisation
procedures
for
delineation
regional
state-of-art
and
especially
future
development,
must
intensity
of
services
in
a
functional
region
is
progressing.
be
studied
as
the
base
for
further
economic
and
political
regional
state-of-art
and especially
development,
must A number of regionalisation procedures for delineation of
of
be studied
as the base
for furtherfuture
economic
and political
regional
state-of-art
and
especially
future
development,
must A
number
of
procedures
forthedelineation
of
functional
have
suggested
literature.
A
A
number regions
of regionalisation
regionalisation
be studied
studied
as the
thethebase
base
for further
further
economic
and
political
decisions.
Here,
regions
became
a
subject
of
complex,
be
as
for
economic
and
political
functional
regions
have been
been procedures
suggested in
infor
thedelineation
literature. of
A
decisions.
Here,
the
regions
became
a
subject
of
complex,
A
number
of
regionalisation
procedures
for
delineation
of
be
studied
as
the
base
for
further
economic
and
political
functional
regions
have
been
suggested
in
the
literature.
A
recent
review
of
different
approaches
and
methods
is
in
regions
have
been
suggested
in
the
literature.
A
decisions.
Here, nonlinear
the regions
regions
became
atransparent
subject of
of functional
complex, functional
open,
dynamic
system
of
decisions.
Here,
the
became
a
subject
complex,
recent review
of different
approaches
and
methods
is in
open,
dynamic
nonlinear
system
of
transparent
functional
functional
regions
have
been
suggested
in
the
literature.
A
decisions.
Here,
the
regions
became
a
subject
of
complex,
recent
review
of
different
approaches
and
methods
is
in
Casado-Diaz
and
Coombes
(2011).
Methods
for
delineation
of
review
of
different
approaches
and
methods
is
in
open, dynamic
dynamic
nonlinear
system
of transparent
transparent
functional recent
connections
between
smaller
and
larger
territorial
areas.
open,
nonlinear
system
of
functional
Casado-Diaz
and
Coombes
(2011).
Methods
formethods
delineation
of
connections
between
smaller
and
larger
territorial
areas.
recent
review
of
different
approaches
and
is
in
Casado-Diaz
and
(2011).
Methods
for
of
open,
dynamic
nonlinear
of transparent
functional functional
regions
can
rule-based
(Coombes
et
Casado-Diaz
and Coombes
Coombes
(2011).into
Methods
for delineation
delineation
connections
between
smallersystem
and larger
larger
territorial areas.
areas.
connections
between
smaller
and
territorial
functional
regions
can be
be divided
divided
rule-based
(Coombes of
et
Casado-Diaz
and Coombes
(2011).into
Methods
for delineation
connections between smaller and larger territorial areas.
functional regions
regions
can be
be divided
divided
into
rule-based
(Coombes of
et
functional
can
into
rule-based
(Coombes
et
functional regions can be divided into rule-based (Coombes et
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10.1016/j.ifacol.2015.06.441
INCOM 2015
Samo Drobne et al. / IFAC-PapersOnLine 48-3 (2015) 2362–2367
May 11-13, 2015. Ottawa, Canada
al., 1986; Coombes and Bond, 2008) and hierarchical methods
(Smart, 1974; Masser and Brown, 1975, 1977; Masser and
Scheurwater, 1980; Slater and Winchester 1978; Slater, 1981).
There were developed several methods to determine
functional areas/regions, that can be used for statistical
purposes to analyse different aspects of labour market
performance (Smart, 1974; Combes et al. 1986; Casado-Diaz,
2000; Van der Lann and Schalke, 2001; Newell and Papps,
2001; Karlsson and Olsson, 2006; Mitchell and Stimson, 2010;
Landréa and Håkansson, 2013) and other socio-economic
aspects (Green et al., 1986; Tomaney and Ward, 2000; Baum
et al., 2008; Karlsson et al., 2008), to evaluate the
administrative regions (Slater, 1976; Anderseen, 2002; Nel et
al., 2008; Cörves et al., 2009), to analyse functional urban
regions (Shimizu, 1975; Sykora and Muliček, 2009; Drobne et
al., 2010; Manley, 2014), for analyses and applications of
transport policy (Krygsman et al., 2009), to analyse housing
market areas for housing policy (Goetgeluk and de Jong, 2007;
Brown and Hincks, 2007), to analyse commodity market areas
(Brown and Pitfield, 1990), to analyse telephone
communication patterns (Fischer et al., 1993), to enhance
economic development (Freshwater et al., 2013) – but only
some of them have been developed for study the location
problems and opportunities of services (Shortt et al., 2005;
Drobne and Bogataj, 2014). The optimal delineation of
functional regions for individual services or group of services
has not been subject of scientific investigation.
The location-allocation models which try to answer the
question where optimally locating a set of facilities and how to
allocate resources are part of colourful and ever growing body
of literature also given in the review papers of Rahman and
Smith (2000), Plastria (2001), Klose and Drexl (2005), Revelle
and Eiselt (2005), Sahin and Süral (2007), Revelle et al.
(2008), and Farahani et al. (2010). About optima location and
allocation of services have wrote Harper et al. (2005), Mestre
et al. (2015) and many other researchers. Specific problems of
servicing elderly has been considered in Cromley and Shannon
(1986), Johnson et al. (2005) and in others. However, as far as
the authors know it, there is no literature that couples both
problems: location-allocation problem of facility location and
the problem of optimal delineation of the functional regions.
In this paper a method for delineation of functional regions
servicing elderly like developed by Drobne and Bogataj (2014)
is coupled by a general location-allocation model for servicing
in the functional regions on the special way using Intramax
method. Here we are looking for such allocation of activities
in the potential centres of functional regions, and delineation
of these functional regions, that the costs of communication
between city as a central place and other areas in the functional
region, and other costs of services (including investments)
would be minimal, when the functional regions are covering
the area of a state as tessellations.
1.2 From the classical tradition of location theory to the
post-industrial smart city
Higher fix costs of public service activity A in a central place
influence lower number of central places k an a broader
territory of a country where A would be placed. Therefore,
some “expensive” activities will find optimal location in less
2363
central places and some “cheaper” in more. Therefore, the
tendencies of growth in modern city decline from the pure
Tinbergen’s description of spatial allocation of production
activities. Tinbergen (1968) explained how the smallest towns
and villages produce certain goods, let us say type TYA
goods. The next largest towns produce type TYA and TYB
goods. They satisfy the demands of their own population and
they export goods of TYB to smaller central places and
villages. Larger towns manufacture three kinds of goods,
TYA , TYB and T Y C for their own population, exporting
T Y C and so on. The market area as a functional region of the
goods is a result of the competition of spatial oligopoly of
central places at different levels of centrality. If some central
places of a certain level are stronger than others, their market
area grows and attracts customers from other central places.
Models of spatial games can describe this process, like
presented by Bogataj and Usenik (2005). The authors also
presented that the same competition appears in the strategic
logistics of supply chains. Activity cells need to find an
optimal level of central place to benefit the appropriate
structure of human resources, subventions and other fiscal
policies, and lower production or distribution costs.
In post-industrial age among the factors influencing urban and
regional growth, importance of services is growing and
influence of production is declining. The answer to the
question where to locate services, especially public services
like schools, hospitals and eldercare is given in the next
chapter, where  and  are subject of negotiation.
2. THE DELINEATION OF 21ST CENTURY
LOCAL LABOUR MARKET AREAS
AND FUNCTIONAL REGIONS
2.1 Intramax procedure
To follow the ideas of functional regions as a local labour
market areas (Casado-Diaz and Coombes, 2011), delineation
could be made as described in the first part of this chapter. Let
us consider the labour commuter as a person in employment
whose territorial unit (ESU, e.g. community, municipality) of
workplace is not the same as territorial unit of residence. To
analyse functionally delineated regions as LLM areas, the
groupings have been arranged using the Intramax method,
which belongs to the methods of hierarchical clustering.
Regionalisation procedures based on hierarchical clustering
were initially developed in the 1970s and 1980s, and were
introduced as alternatives to the more ad hoc methods. The
methods include Markov chain techniques of Brown and
Holmes (1971), as well as the strategy of Masser and Brown
(1975, 1977) and Masser and Schuerwater (1980), which is
based on refinements to Ward’s (1963) hierarchical
aggregation procedures.
The objective of the Intramax procedure is to maximise the
proportion within the group interaction at each stage of the
grouping process, while taking account of the variations in the
row and column totals of the matrix. In the grouping process,
two ESUs are grouped together, for which the objective
function is maximised (Breukelman et al., 2009):
2437