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Urbani izziv, volume 22, no. 2, 2011
122
is paper examines Ildefons Cerdà’s 1860 Plan for the
Urban Expansion of Barcelona; specically, how and why
it was conceived in a unique way, in which the provision
of services to the population was an important part. Cerdà
based his expansion proposal on an in‑depth socio‑stati‑
stical study of old Barcelona’s population conditions. e
high mortality rates of the working‑class population and
poor health and education conditions pushed Cerdà to
design a new type of urban planning, which he dened as
“urbanism”. In his proposal for the new city, he planned
the location of services such as marketplaces, schools and
hospitals. e rst part of this paper introduces the urban
and political preconditions of Barcelona and the statisti‑
cs on which Cerdà based his contribution. e second
part uses location theory and a geographic information
system(GIS) to analyse the pattern of location and the
population served by markets and hospitals. In addition,
topographic maps from 1926 and 1975 are used to study
the development of the expansion up to when it was fully
developed. e evolution of the city diered from Cerdà’s
proposal, partly due to unexpected increases in popula‑
tion density, the built environment, and higher amounts
of building occupation. Nevertheless, Cerdà’s layout of
streets and avenues has prevailed.
Keywords: urban planning, location theory, optimisati‑
on, wellbeing, GIS, spatial decision support system
UDC: 911.375.1(460)
DOI: 10.5379/urbani-izziv-en-2011-22-02-005
Montserrat PALLARES-BARBERA
Anna BADIA
Jordi DUCH
Cerdà and Barcelona: The need for a new city and
service provision
Urbani izziv, volume 22, no. 2, 2011
123
Cerdà and Barcelona: The need for a new city and service provision
1 Introduction
is paper examines Ildefons Cerdà’s 1860 Plan for the Ur‑
ban Expansion of Barcelona; specically, how and why it was
conceived in a unique way, in which the provision of services
to the population was an important part. Cerdà based his ex‑
pansion proposal on an in‑depth socio‑statistical study of old
Barcelona’s population conditions. e high mortality rates
of the working‑class population and poor health and educa‑
tion conditions pushed Cerdà to design a new type of urban
planning, which he dened as “urbanism”, in which his main
objectives were to obtain a high degree of wellbeing for the
population through rational housing conditions and provision
of services. In his proposal for the new city, he planned the
location of services such as marketplaces, schools and hospitals.
e rst part of this paper introduces the urban and political
preconditions of Barcelona and the statistics on which Cerdà
based his contribution. e second part uses location theory
and a geographic information system(GIS) to analyse the pat‑
tern of location and the population served by markets and
hospitals. In addition, topographic maps from 1926 and 1975
are used to study the development of the expansion up to when
it was fully developed. e evolution of Barcelona through his‑
tory diered from Cerdà’s proposal, partly due to unexpected
increases in population density, larger percentages of land use
and higher amounts of building occupation. Nevertheless,
Cerdà’s layout of streets and avenues has prevailed. Moreover,
more recent plans for urban expansion and restructuring of the
city have been in line with Cerdà’s ideas. is paper postulates
that urban planning is an important factor for quality of life
and wellbeing. e city proposed by Cerdà was a response
to the needs of Barcelona’s population living inside the city
walls. Aer the plan was approved, the evolution of the city
was modied and adjusted to full specic economic prots
more than to respond to social needs.
An appropriate urban fabric can transform the liveability of
a place. e population’s level of wellbeing depends on the
capacity of service provision, which is uneven across space.
Education and health provision are related to population in‑
come dierences. Urban planning can provide mechanisms
of resource distribution and increased spatial justice(Smith,
1977; Soja, 2010). In line with these ideas, the issue at the heart
of this paper is how urban planning containing the necessary
services for the population can be used as a tool to redistrib‑
ute wellbeing among the population. is paper endeavours to
answer this question by studying, rst of all, the preconditions
of old Barcelona at the end of the nineteenth century with
very little service provision and inadequate housing conditions
for its population needs; and, in contrast, the proposed city
planning, which had a group of services‑to‑population embed‑
ded in its layout. e optimality and rationality underlining
the location of urban services in Cerdà’s proposal has yet to
be analysed; this is carried out in the second part of this pa‑
per, in which we ascertain some determining factors involved
in locating facilities in order to balance social wellbeing and
quality of life.
In 2010, the motto for the Shanghai World Expo was “Better
City, Better Life”. Policymakers and institutions focused their
concerns on the urban population because more people live in
cities than in any other type of location in the world. In2050
the population in cities will have grown to about 70% of the
total world population(United Nations, 2010). e challenge
for current cities tests their capacity to provide a good quality
of life for their population. Cities have two sides. Urban ag‑
glomerations are important in that they create economic spaces
where knowledge and wealth are generated and businesses are
attracted and kept(De Blij, 2009; Glaeser, 2011). Otherwise,
in order to create good city elements, disagglomeration econo‑
mies must be resolved.
Cities and the form that settlements take are important within
many disciplines. Cities are potential alternatives for social
organisation and institutionalisation (Le Galès, 2002). In a
shrinking political landscape, cities are potential alternative
structures to states and regions, where groups and institutions
can be organised. Cities are changing rapidly, and a good way
to make progress is to understand their past in order to con‑
struct their future. In this regard, evaluating the normative
urban actions that have changed people’s way of life can con‑
tribute to building better urban environments.
A broad variety of models have been generated for urban en‑
vironments and quality of life. ese range from highly theo‑
retical models to empirical‑explorative models stemming from
dierent disciplines(Kamp etal., 2003). Urban policies devel‑
oping quality of life focus on the relationship between people
and their everyday urban environments(Pacione, 2003). Ur‑
ban environment problems are multidimensional, stemming
from private and public agents, economic circumstances and
environmental conditions. Attempts to address these problems
are also multifaceted, operating at a variety of urban scales
and across all dimensions of life quality. Various disciplines
approach urban problem‑solving by exploring various compo‑
nents of quality of life, and identify strategies to solve specic
problems in socio‑spatial contexts.
Spatial disciplines specialise in how land‑use patterns, den‑
sity, property values and political fragmentation aect the
cost of services (Carruthers & Ulfarsson, 2003). Increasing
social wellbeing in cities might commence with a social and
territorial diagnosis, followed by adjusting urban policies to
the population’s needs. Wellbeing varies with location, and
Urbani izziv, volume 22, no. 2, 2011
124
maps indicate which part of the population enjoys this, and
where(Smith, 1973; Coates etal., 1977). For instance, if clean
air is considered important for health, a map showing exposure
to air pollution would be decisive in deciding where to live.
Exposure to air pollution decreases as the distance from the
city centre increases. Residential quality is directly related to
the way people live. Geographies of income per capita, trac
congestion, crime, access to public parks or public spending on
education are useful elements for analysing the dimensions of
wellbeing. erefore, decision‑making processes about where
to locate services are crucial in any society.
Wellbeing is not a simple concept. Many factors aect it and
where it occurs. Geographically, welfare dierences oen
exhibit considerable order and regularities. Wellbeing varies
between neighbourhoods, usually related to income levels,
and between developed and developing nations. Individual
location decisions depend on wellbeing factors such as type
of neighbourhood, safety, friendliness and sociability of neigh‑
bours and whether an individual’s children have good friends
living nearby. Individual welfare is therefore also aected by
decisions made by other residents(Cox, 1979) and by other
factors, such as what type of housing has been built and the
characteristics of services located in that neighbourhood.
Location theory(Lloyd& Dicken, 1972; Conkling& Yeates,
1976; Dicken, 1976; Osleeb& Ratick, 1990; Moreno, 1995)
also provides explanations of industrial, migration, retail and
residential location(Tiebout, 1956; Krugman, 1998; Davis&
Weinstein, 2002; Levy, 2004). Advantages and disadvantages,
eciency, type of activity and characteristics of the population
are included in the decision process about location. Planning
an ecient service distribution that facilitates access to jobs,
education and health services would be factors to increase “spa‑
tial justice”(Soja, 2010). An ecient policy‑planning strategy
for services would provide equity in accessibility and reduce
overcrowding, contributing to increased spatial justice.
Specically, this paper uses a p‑median model(Hakimi, 1964)
to analyse how service areas are formed around a group of
facilities. e p‑median model seeks to locate a xed number
of facilities minimising the aggregate distance‑time of the pop‑
ulation receiving the service. ese problems are considered
“travel to get a good”. We assume that these types of services
are public goods. e factor space gives a public good a dif‑
ference in availability; that is, individual service consumption
will decrease as distance to the facility increases. Assuming all
consumers have an equal utility function, their level of con‑
sumption of the good is directly proportional to the distance
they have to travel to obtain the good.
2 A case study: The Cerdà plan for the
urban expansion of Barcelona and
its evolution
e Cerdà plan for the expansion of Barcelona has captured
the interest of architects, urban planners, geographers and his‑
torians for decades. Nevertheless, little research has been car‑
ried out on studying the optimality and rationality underlin‑
ing the location decisions regarding urban services within the
Cerdà plan(Pallares‑Barbera, 1986, 2005). Cerdà’s diagnosis
began by studying the living conditions of the population in
the social structure of old Barcelona. His proposal for urban
expansion was based on improving the population’s living
conditions. erefore, he planned a rational distribution of
basic services to the population. Schools, markets and hospitals
were proposed in order to meet the educational, shopping and
health needs of this population.
Barcelona’s urban landscape has been shaped by political strug‑
gles, civil society and its geographic location. Situated in a
valley on the Mediterranean coast, and surrounded by two
hills, Montjuïc and Tibidabo, and two rivers, the Besòs and
the Llobregat, Barcelona evolved into its full structure from
the end of the nineteenth century through mainly the rst half
of the twentieth century. In the twenty‑rst century, the city
is made up of four main parts, one being the medieval Ciutat
Vella ‘Old City’. Another section is the Eixample ‘Expansion’, a
residential and service area designed by Cerdà. e third part
consists of the old villages scattered across the valley, which
became part of the city in the twentieth century and largely
developed during the 1960s and 1970s. Finally, the fourth part
is new neighbourhoods redeveloped for major events, such as
the Olympics in 1992 and the Forum de les Cultures in 2004,
from the mid‑1980s to the present.
Nineteenth‑century Barcelona was an industrial society and
was active in trade through the port, historically connected to
all other Mediterranean ports with goods and passenger traf‑
c. e industrial revolution involved a huge densication of
the urban fabric in which the bourgeois society, working class
and factories were brought together in a walled medieval city.
en the quality of living conditions in the city decreased,
with a high population density (856 inhabitants per hectare,
when Paris had fewer than 400 in comparison), high‑density
housing for the working class(10square metres per person),
a poor drinking‑water supply and a poor sewerage system. In
1834, 1854, 1864 and 1870 epidemics broke out, and 3% of
the population died each time. e average life expectancy
was 38.83 and 19.68years for the wealthier and poorer class‑
M. PALLARES-BARBERA, A. BADIA, J. DUCH
Urbani izziv, volume 22, no. 2, 2011
125
es, respectively (males’ average from 1837 and 1847; Cerdà,
1867). In 1854, the Old City had the same dimensions as in
the fourteenth century, and contained 200 streets less than
3metres wide and 400 less than 6metres wide. Urban expan‑
sion was prevented by the medieval wall, which was built and
maintained for political reasons. e walls of Barcelona sur‑
rounded the entire city and were a sort of stone border between
Barcelona and the rest of the world(Aibar& Bijker, 1997).
Between 1854 and 1868 the contested walls were demolished;
which opened up the possibility of urban expansion toward
the surrounding countryside. To plan the urban growth, in
1859 the council held a contest for an urban project to link
the city’s medieval core to the surrounding villages. Aer con‑
sidering various projects, the council chose the plan by Antoni
Rovira, the council’s chief architect. However, in a surprising
intervention by the Spanish government, the recently created
Ministry of Public Works in Madrid ordered the municipality
to implement Ildefons Cerdà’s plan.[1]
Ildefons Cerdà i Sunyer (1815–1876), the son of wealthy
rural parents from a tiny town north of Barcelona, studied
engineering in Madrid(Estapé, 1968–1971).[2] He travelled
widely around Europe and discovered technological innova‑
tions applied to industry and to means of communication.
ese ideas inuenced his urban‑planning concepts. Upon his
return to Barcelona, his general beliefs were to understand how
“social order” had to be embedded in an urban development,
where movement, communication and technology had to be
the basis for a new city(Figure1). Cerdà’s exhaustive diagnosis
of urban dynamics and the statistics of the living conditions
of the working class[3](Cerdà, 1867) were the pillars for his
Barcelona expansion proposal.
His detailed description of the population’s professions(tai‑
lors, shoemakers, cooks and merchants) and building func‑
tions(convents, palaces, warehouses, mills and charitable in‑
stitutions [Span. casas de beneciencia]; Cerdà, 1867) does not
include schools, teachers, physicians or hospitals. e lack of
such services, or at least their very low inuence on society,
resulted in a scenario in which high mortality rates and chil‑
dren employed in factories, instead of attending school, were
common in general daily life.
2.1 Cerdà’s “foundation” for a new city
Cerdà’s “social philosophy”(Cerdà, 1844, 1867) focused on
his “urbanisation idea”. In order to conceptualise urbanism,
he studied the origins of urban forms and wrote up his nd‑
ings in two volumes(Cerdà, 1849). He developed a theory
about the scientic and modern organisation of urban form.
His model included the eects of the epoch’s new technology
on urban forms: the railroad, streetlights, the telegraph, and
sewers. In 1854, he did not use the word “expansion” for his
plan; he talked instead of the “foundation” for a new city.
Regularity was a main feature, with an unlimited geometrical
grid of perpendicular intersections in the streets. His main
objective in implementing the grid form was to avoid privi‑
leged zones for social classes and to achieve “optimal hygienic
density”(Solà‑Morales, 1991). His leitmotif was to achieve op‑
timal living standards of 6cubic metres per person and room,
and 40square metres per person in housing(or, as he wrote,
40square metres per person within towns): “Nowadays, one
would need 6cubic metres of atmospheric air per person and
per hour in order to breathe correctly. ... Scientic studies
establish a minimum of 40square metres per person within
towns”(Cerdà, 1859: 64).
He produced various documents on “scientic” urbanisation,
which included statistics about the working class, his 1861
map and the First‑Dra Document for Barcelona’s Expan‑
sion(Span. Memoria del Ante‑Proyecto del Ensanche de Barce‑
lona). For Cerdà, the possibility of a substantial improvement
of the conditions of urban life would involve solving two ques‑
tions: rst, how building new roads, sanitary infrastructure
and municipal equipment could be nanced and, second, how
housing prices could be adjusted to dierent wages (Soria y
Puig, 1991). ree of his main concepts were used to deter‑
mine the side length of the blocks(113.3metres): the number
of square metres per person, the number of inhabitants per
house and the width of streets(Cerdà, 1861).
Where
x is the length of the side of the block;
p is the number of square metres per person;
v is the number of inhabitants per house;
b is the width of the street;
d is the height of the facade; and
f is the depth of the building site.
Figure 1: Cerdà’s 1861 Map for the Urban Expansion of Barcelo-
na(source: Cerdà, 1861).
Cerdà and Barcelona: The need for a new city and service provision
Urbani izziv, volume 22, no. 2, 2011
126
Without an explanatory interpretation, Cerdà took the val‑
ues of the variables to be 2b= 20 metres, f= 20 metres, d=
20 metres, v= 43 and p= 40, obtaining 113.3 metres, the
current side length of the block.
e plan proposed incorporating an additional 1,969hectares
to a medieval core of only 192hectares by implementing a grid
of streets between the Old City and the peripheral villages. e
grid consisted of 1,000 blocks, 113.3metres by 113.3metres
in length and width, with streets measuring 20 to 30metres
wide. Like a compact garden‑city model, the grid had two
parallel buildings on each block, from 10metres to 20metres
deep(building occupation: 40% of total block), with yards and
green spaces in between each block, intertwined with pedes‑
trian paths in the middle that linked the inner open spaces
together independent of the street network. Furthermore, the
corners of each block were cut at 45° angles, 20metres long, to
create small squares between the octagonal blocks(Figure2).
e map’s legend contained 33 schools, three hospitals located
on the edge of the city for hygienic conditions, eight parks, 10
markets and 12 administrative buildings. Adopting and imple‑
menting his plan, with amendments and modications, Barce‑
lona became a modern city and a model for other cities(Cerdà,
1861). Inspired by the diagnosis of the territory, Cerdà rede‑
ned urban strategies and adjusted them to the scale of the
metropolis. His timeless idea was the foundation for many
projects that followed in twentieth‑ and twenty‑rst‑century
Barcelona.[4]
2.2 Implementation of Cerdà’s plan
Aer the plan was approved, council ordinances immediately
modied the plan. Real‑estate investment became attractive
to developers, who, with land speculation and the freedom
to introduce modications, could triple their investments in a
4‑year period. e rst modication allowed a 100% increase
in the construction area, converting the parallel‑building de‑
sign into a fully built block with open space in the inside. e
council’s policy allowed automatic rezoning of rural land into
urban land. In the rst 20years aer the approval of the plan,
only 100hectares were built. It took a quarter of a century for
this area to double. By 1872, 90% of the newly constructed
housing did not comply with Cerdà’s guidelines (Casellas,
2009). Over time, new council ordinances would further
modify the plan and increase construction densities:
e average width of the streets was reduced from 35metres to 20
to 30 metres; the explicit concern with special housing facilities for
workers, as a means of achieving a more egalitarian city, was com‑
pletely abandoned; the depth of buildings was extended to 20metres
in all cases; and the former regular distribution of parks(82.35hec‑
tares) and public facilities was not made obligatory.(Busquets Grau
etal., 1992)
As early as 1890, buildings occupied 70% of the block area on aver‑
age, instead of the original 50%. e situation was exacerbated by suc‑
cessive building bylaws, and in 1958 the building volume of the block,
which according to Cerdà’s bylaws should not exceed 67,200 cubic
metres, reached 294,771.63cubic metres.(Aibar& Bijker, 1997)
e evolution of the plan was dierent from what Cerdà had
anticipated. Cerdà calculated how manyhectares the popula‑
tion living within the city walls needed to settle in the new
premises of the expansion. Seven municipalities[5] surrounded
the Barcelona Valley. e expansion had to take place in the
plain between the Old City and these municipalities (Fig‑
ure3). Between 1855 and 1860, the total population of these
eight urban concentrations was 249,209(Statistical Institute
of Catalonia, 2011), among which the highest‑percentage ag‑
glomerates were within the Old City. Apart from tiny urban
concentrations,[6] the Barcelona Valley was an agricultural
space lled with orchards and vineyards connected by ru‑
ral routes to the Old City, where the marketplace and the
ab
Figure2: a) Block with housing built on two of the sides; b)Corners,
squares and octagonal forms (source: a: Cerdà, 1861, b: Barcelona
City Council, 2011).
Figure 3: The Old City of Barcelona, neighbouring towns and the
1860 expansion proposal(source: Cerdà, 1860).
M. PALLARES-BARBERA, A. BADIA, J. DUCH
500 1,000 2,000
Metres
Cerdà´s project boundary
Built space in 1860
Urbani izziv, volume 22, no. 2, 2011
127
port were located. By 1926, the national topographic map of
Spain (Span. Mapa Topográco Nacional de España) showed
the urban space scattered across the plain and some of Cerdà’s
block morphology built and streets delineated(Figure4).
Urban development grew rapidly during the rst quarter of the
twentieth century. Within the projected expansion, 910 blocks
were already fully or partially built(628.2hectares). Outside
the expansion, the neighbouring municipalities[7] expanded
greatly, with 2,070 urban blocks built in 722.2 hectares. e
dierences between both developments are evident in the
dierent land area occupied by the blocks. ese two urban
processes have interesting implications related to which social
classes occupied each type of building and what the housing
prices were, which are beyond the scope of this paper. e
population grew during the rst decades of the twentieth
century, with 721,869 inhabitants in 1920 and 1,005,565 in
1930(Statistical Institute of Catalonia, 2011). e early build‑
ings in the expansion were concentrated in the most emblem‑
atic newly‑built streets such as Passeig de Gràcia, Passeig de
Sant Joan and Urgell, where the bourgeoisie hired prestigious
architects(Gaudí, Domènec& Montaner, and Puig& Cada‑
falch) to build their elegant homes.
By 1951, 1,201 blocks in 814.4hectares of Cerdà’s expansion
had already been developed, and Barcelona as a whole had
a population of 1,280,179 (National Geographic Institute,
1951; Statistical Institute of Catalonia, 2011). From 1950 to
1960, the Expansion section suered a drastic deterioration.
e council did not have a maintenance or restoration policy,
and many Modernist structures were demolished. Further‑
more, new additional oors built with cheap materials were
added on top of nineteenth‑century buildings, with absolute
disregard for the structural design of the buildings. e inner
courtyards that Cerdà designed as open spaces were further
converted into storage rooms and garages. Over time, the total
built area of a block changed from the 13,520square metres
allowed under the rst ordinances, approved in the 1880s,
to the 101,497square metres allowed by Mayor Josep Maria
de Porcioles in the 1960s (Casellas, 2009). In 1977, 1,464
Figure4: Barcelona’s built environment in 1926(source: National Geographic Institute, 1926).
Cerdà and Barcelona: The need for a new city and service provision
Streets designed by Cerdà
Barcelona city limits
Orthogonal blocks fully built
Orthogonal blocks partially built
Urban areas outside Cerdà´s expansion
Non-orthogonal blocks within Cerdà´s expansion
0 1,000 2,000 Metres
Urbani izziv, volume 22, no. 2, 2011
128
blocks in 932 hectares of Cerdà’s expansion[8] had already
been developed, and Barcelona as a whole had a population of
1,754,714(Statistical Institute of Catalonia, 2011; Figure5).
Economic development attracted people from other parts of
Spain and Barcelona’s metropolitan area was developed.
3 Methodology
is methodology focuses on determining the optimality and
sense of eciency that the location of facilities in the Expan‑
sion section had, but that Cerdà never explained. At the same
time, as his background suggested and as described above, his
sense of eciency was intended to improve the social wellbeing
of the population, which was scant within the Old City. Cerdà
attributed the causes of mortality and poor urban conditions
to greed and ignorance: “e errors in the lack of hygienic
means in founding a city are a consequence of ignorance and
greed and prevent the development of robust, wise and in‑
dustrious generations. ese errors increase mortality, decrease
the average life expectancy and primarily contribute to epi‑
demic attacks every twentyyears”(Cerdà, 1860: 55). Under
these beliefs, his plan had to be built using new standards of
the(new) culture of the(new) century “[t]o attain the good
conditions that the culture of our time demands for the entire
population”(Cerdà, 1860: 56).
To carefully capture the meanings of Cerdà’s service locations
and why he decided to plan them in a regular pattern, scat‑
tered across Barcelona, this section of the article analyses the
main variables of his implicit model. Although the need for
services for the population was explicitly stated in the plan’s
proposal, the methodology behind the service pattern was not
explained. In the map, the distribution of markets and health,
education and social services can give a sense of Cerdà’s idea
of social equality. For him, urbanism was a tool to diminish
the dierences in the living conditions of the various social
classes, particularly in Old Barcelona. e population’s health
and education achieved through service provision throughout
Figure5: Barcelona’s built environment in 1977(source: National Geographic Institute, 1977).
M. PALLARES-BARBERA, A. BADIA, J. DUCH
Streets designed by Cerdà
Barcelona city limits
Orthogonal blocks
Urban areas outside Cerdà´s expansion
Non-orthogonal blocks within Cerdà´s expansion
0 1,000 2,000 Metres
Urbani izziv, volume 22, no. 2, 2011
129
the urban network introduced a perception of a modern way
of living. en, his proposal implied regularly distributing
basic services throughout the Expansion section. Of all these
services, two services– markets and hospitals– are analysed
in this paper, and the mathematical model and its implementa‑
tion is suggested.
Optimality and location have primarily been studied in loca‑
tion theory as a means of making decisions and obtaining e‑
cient urban planning. In addition, spatial optimisation models
that use GIS as a tool to solve location problems (Church,
1999, 2002; Cromley & Hanink, 1999; Malczewski, 1999)
make it possible to eciently distribute urban space, study
the compatibility of adjacent uses, and plan the location of
dierent but complementary urban land uses adjacent to one
another (Ligmann‑Zielinska & Jankowski, 2007; Church&
Jankowski, 2008). One of the functions is to locate comple‑
mentary and compatible functions together such as schools
and housing, or shops and banks; however, in contrast, pol‑
luting industry and housing would be considered incompatible
uses, and their adjacent location would therefore be restricted.
“Unwanted activities”(Bosque & Moreno, 2004) such as in‑
cinerators or nuclear waste dumps have very strict restrictions
for adjacent use compatibility and distance in location models.
Optimisation modelling is a generative technique that allows
multiple scenario analysis, in which the outcomes obtained are
non‑inferior(Pareto‑optimal) to the objectives contained in
the model. It involves testing and analysing the optimal and
suboptimal objectives and generating a number of compro‑
mised spatial solutions that can be both feasible and dierent
from one another. e optimal solution will be that which
minimises the aggregate distance.
Within the theory of location of public facilities, the p‑median
model (Hakimi, 1964) aims to locate a xed number of fa‑
cilities, so that the average distance or time that users take to
reach them is minimised. e basic constraint is that there is
a xed budget for the system of facilities and that all facilities
have the same “investment”(per facility) and “expansion”(per
user) cost. Following this background, the methodology in this
paper consists of two separate parts: rst, the spatial optimisa‑
tion model itself is proposed and explained and, second, the
implementation used to test this model in Cerdà’s plan is ex‑
plained, analysed and evaluated, and the results are discussed.
3.1 The optimisation model
e p‑median model is a two‑objective model; one of the
objectives is to minimise aggregate travel time between a
population node and a group of facilities(p), and the other
is to nd the distance that separates users from their nearest
facility(Narula etal., 1977). In these consumer‑oriented loca‑
tion problems, consumers must travel to obtain the good– as
opposed to, for instance, re engines and ambulances, in which
the service is “delivered” to consumers(Park, 1983).
In the objective function, we want to minimise the distance
the population has to travel to obtain the service, subject to
constraints that ensure that all users receive the service, that
the service is provided by only one facility, that the service is
provided by facilities that are open and that the total number
of facilities is not exceeded. In order to attain this result, the
decision variable of this model is xij.
General model:
Given
Choose
Where
In order to minimize Z equal to
Subject to
Where:
ai = the quantity of the population in node i;
i= the origin of the population;
j= the destination of the population;
n= the number of nodes;
dij= the shortest distance berween node i and node j;
yj= the possible location of services;
p= the number of services;
xij= 1, if the population of node i is assigned to j, 0
otherwise;
yj= 1, if the service is located to j, 0 otherwise.
We impose some assumptions that can be relaxed in future
analysis:
Cerdà and Barcelona: The need for a new city and service provision
Urbani izziv, volume 22, no. 2, 2011
130
1. ere is no heterogeneity regarding income levels; we have
a utilitarian social welfare function, in which the objective
function places the same weight on all individuals. Hence,
income dierences are ignored.
2. ere is no congestion in service capacity.
3. ere is homogeneity in product and quality.
In this paper, the implementation of this model is carried out
assuming a set of known locations. e population in each
node j, where the facility is located, is null. e results obtained
can be suboptimal locations because the general model is not
solved; that is, in the general model the specic location of
services would be unknown(not given). However, the spe‑
cic location nodes would be the result of solving the general
location‑allocation model. e optimal location would be that
which has the minimum aggregate distance to services.
3.2 Implementation of the model in GIS
Part of the use of GIS is the spatial and alphanumerical infor‑
mation with which we implement the model. In this particular
case, the main diculty lies in the fact that we are working
from an image that is a proposal for the organisation of Bar‑
celona’s structure. It is a drawing of the expansion made by
Cerdà, which must be geo‑referenced so that it can be incor‑
porated into the GIS. Because it is a proposal, current coor‑
dinates must be identied on Cerdà’s map in order to be able
to geo‑reference it. Cerdà identied a reference coordinate,
the Clock Tower (Cat. Torre del Rellotge). With this point,
and the two central axes of Barcelona, Meridian Avenue(Cat.
Avinguda Meridiana) and Avenue of the Parallel (Cat. Avin‑
guda del Parallel), a total of 25 points could be identied. e
sequence that evolved in the georeferencing process using the
GIS ArcMap was the following:
1. To move and rotate Cerdà’s map so it can be placed on the
axes of the current streets;
2. To place the central point of the Clock Tower of Cerdà’s
map on the same geo‑referenced point of the axes of the
current streets;
3. To identify up to 25 control points to carry out the geo‑re‑
ferencing process;
4. To carry out the geo‑referencing process. e nal root
mean square(RMS) error was 1.79.
4 Spatial analysis of Cerdà’s location
pattern: Hospitals and markets
e substantial idea at the root of Cerdà’s proposal for design‑
ing a city for the new industrial era contained many elements
of present‑day cities; and in proposing this he was implicitly
“scientically” rejecting the old pattern implied by the city of
Figure6: Cerdà’s facility location pattern(source: Cerdà, 1861).
M. PALLARES-BARBERA, A. BADIA, J. DUCH
Hospital
Park
Equipment (state, industry)
Market
Social Facility
Railroad
Road axis
Facilities and infrastructure
0 500 1,000 2,000 Metres
S
Urbani izziv, volume 22, no. 2, 2011
131
the industrial revolution. Improving urban living conditions
by creating a plan of almost 2,000hectares of square grids and
available housing, and inserting elements of sanitary, educa‑
tional and social amenities between housing and streets would
at least partially satisfy his egalitarian goal. Almost 250,000
inhabitants(Statistical Institute of Catalonia, 2011) of the old
Barcelona had to be evenly distributed in the new Barcelona
and services had to be provided by 33 schools, three hospi‑
tals located on the edge of the city for hygienic conditions,
eight parks, 10 markets and 12 administrative buildings. e
regularity in the location distribution of facilities in the plan
suggested the existence of some optimising criterion, in which
the p‑median model would provide answers by minimising the
weighted distances to the facility located.
4.1 Data
We based our analysis on the data found in Cerdà’s urban plan
documents, in which he proposed a density of 250 inhabitants
per hectare and 40square metres per person. e number of
facilities and their locations is taken from the set that Cerdà
planned in his map. e number of demand points is 926 cen‑
troids. For the analysis, we considered the population centroid
to be located in the centre of each block. e population in
each demand point or centroid is calculated taking into ac‑
count the parameters given by Cerdà, in relation to types of
housing for dierent classes of the population; and assuming
social classes are mixed in each block. Percentages of popu‑
lation per income level are calculated based on the propor‑
tion that the Barcelona census of 1856 gave regarding various
professions and considering the percentage of construction
Interval time in minutes Population % Cumulative %
1–9 16,251 11.0 11.0
10–19 52,500 34.0 45.0
20–30 50,500 33.0 78.0
>30 33,224 22.0 100.0
Total 152,475 100.0
Table1: Population within each hospital service area.
Figure7: Spatial analysis: Hospital service areas(source: Cerdà, 1861; Cartographic Institute of Catalonia, 2006).
Cerdà and Barcelona: The need for a new city and service provision
Up to 10
Up to 20
Up to 30
Over 30
Hospital access time (in minutes)
0 500 1,000 2,000 Metres
N
Hospital
Urbani izziv, volume 22, no. 2, 2011
132
allowed for each block taken from the 1860 map. e Old City
is not included. ere is no population in the facility points.
A large group of Cerdà’s blocks in the grid have 12,370square
metres, but sometimes a block is twice as big or divided in half
or in quarters, depending on the pattern of streets and avenues.
Each person’s travel time would be calculated from the cen‑
tre of each block to its closest market or hospital. Distance is
considered to be “Manhattan or L1 rectilinear”[9] distance; that
is, a person cannot travel diagonally between blocks, but must
follow the assigned orthogonal pattern of streets. Streets are
113metres long and 20 or 30metres wide. Travel time for the
population to obtain a service is assumed to be walking time,
whereby a person is considered to walk 4kilometres per hour.
4.2 Analysis and discussion
e group of facilities proposed in the map is parks, hospi‑
tals, schools, state facilities, markets and “social facilities”(Fig‑
ure6). In this paper we analyse the service areas of markets and
hospitals using ArcGIS Spatial Analyst. Two variables enter‑
ing into the analysis are facilities’ location and population in
demand points. e expected results would give the service
area within a distance time away from the location facility and
the population covered within this area. Introducing dierent
intervals of time around the point where the facility is located
into the analysis would give dierent scenarios in which a dif‑
ferent proportion of population is served by a facility, and
the maximum time this population must travel to reach the
service. Further research, which is beyond the scope of this
Interval time in minutes Population % Cumulative %
1–5 19,444 13.0 13.0
6–11 54,268 36.0 49.0
12–24 70,691 46.0 95.0
>24 8,072 5.0 100.0
Total 152,475 100.0
Table2: Population within each market service area.
Figure8: Spatial analysis: Marketplace service areas(source: Cerda, 1861; Cartographic Institute of Catalonia, 2006).
M. PALLARES-BARBERA, A. BADIA, J. DUCH
Up to 6
Up to 12
Up to 24
Time of access to markets
(in minutes)
0 500 1,000 2,000 Metres
N
Market
Urbani izziv, volume 22, no. 2, 2011
133
paper, could be carried out in order to analyse the optimal
location of schools and other services.
e implementation of the general p‑median model is restrict‑
ed in this analysis. Service area analysis diers from the general
p‑median model in that in the former the facility location is
given, whereas in the latter the location allocation is a solu‑
tion to the problem; that is, given a xed number of facilities
and given a set of points of demand, the optimal location of
facilities would be the result of the problem‑solving procedure.
As regards hospitals, we consider a given set of three hospital
locations– as in Cerdà’s proposal(Figure7). Service areas are
constructed around each of the hospitals with the following
travel distance intervals: 1 to 9 minutes, 10 to 19 minutes,
20 to 30minutes and more than 30minutes. In this scenar‑
io, for the four service areas displayed, 45% of the expansion
proposal’s population is covered within a 19‑minute distance;
and 78% within a scope of 30minutes to a hospital(Table1).
Implicit assumptions are imposed, such as no trac conges‑
tion, all people can walk and the capacity of each hospital is
not saturated.
Comparing the average life expectancy inside the city walls of
Barcelona between richer and poorer classes, which was 38.83
and 19.68 years, respectively (males, average from 1837 to
1847; Cerdà, 1867); with 10 midwives and 69 surgeons(Cer‑
dà, 1867), and considering the direct relationship between
the number of hospital beds and life expectancy, the proposed
location of three hospitals near the population would increase
their life expectancy enormously. Anachronistically, but for
means of comparison, in 2009 the global low‑income group
life expectancy was 57years, whereas the world high‑income
life expectancy was 80, and the life expectancy in Spain(2009)
is 82 for both sexes in all income groups(World Health Or‑
ganization, 2011).
With the objective of minimising the distance travelled to
the nearest market, market service area analysis has similar
restrictions as hospital service area analysis. erefore, the
walking population is assumed to move at 4kilometres per
hour and markets are assumed to not have the capacity for
congestion. Market location and number are given according
to Cerdà’s map. e service areas constructed around each of
the hospitals have the following travel distance intervals: 1 to
5minutes, 6 to 11minutes, 12 to 24minutes and more than
24minutes(Table2). Within 24minutes 94% of population
is covered by a market(Figure8). With three markets in the
Old City, two of them sh markets(Pescadería del Mercado
del Borne, 425square metres, and Pescadería del Mercado de
Isabel II, 900square metres) and one of them for general gro‑
ceries(Mercado de la Plaza de Isabel II, 3,525square metres;
Cerdà, 1867), the proposed increase to 10 markets would pro‑
vide better provision and diversity of goods to the population.
e structural question of this paper postulates that urbanism
can be used as a tool for improving wellbeing. ese nd‑
ings reveal that, by imposing a regular pattern of markets and
hospitals, the population is within walking distance from a
service that can prevent illness and improve their health, or
30minutes’ walking distance from their basic needs for eve‑
ryday nutrition. Other analysis could be done by increasing
the population demand or the number of facilities, or by im‑
proving the capacity, which would have dierent results in
service areas.
5 Conclusion
Today’s Barcelona is the result of historical institutional poli‑
cy‑making, social movements and cultural phenomena; in ad‑
dition, its twenty‑rst century morphology is a result of the
massive urban‑planning intervention that enlarged the city in
the 1860s(Figure9). Cerdà constructed a theory of how peo‑
ple should live, based on his social statistics for the working
class, and on evaluating the needs of the entire population
and the need to implement economic activity in a modern
“futuristic” city. is paper evaluated the foundations of his
“science”; however, much more remains to be done. His pro‑
posal changed the way in which people thought about urban
space, and introduced the idea of changing people’s behav‑
iour by modifying public space. Part of his work was utopian,
referring to a theoretical city, where it would be dicult to
implement all the new and revolutionary elements that he
thought had to be in a city. We worked under the hypothesis
that “utopia” goes beyond reality but could contain the optimal
objectives that must be attained in order to increase the popu‑
lation’s wellbeing. Optimal objectives are like a framework;
they contain standards and goals, reality escapes the optimal
and usually suboptimal aims are not even achieved; however,
the utopian standards are sown and the plant can grow inwards
or outwards, and very tall. is is not the only one; other uto‑
pian urban models, such as Oscar Niemeyer’s Brasilia, oered
alternative solutions and a structure with which cities can be
compared and with which they can experiment.
Cerdà’s most important innovation was to create a new urban
culture and to build a bridge between the urban roles and
functions of a metropolis and a healthy population. Cerdà es‑
tablished the links of the city, which connect humanity and its
structures. He put forward normative policy mechanisms for
the urban era and inspired the city with embedded urban tech‑
nologies and mechanisms of self‑defence and self‑protection.
His model of innovations and new functions was a framework
for the city’s ability to generate the information needed to
solve inner‑city problems.
Cerdà and Barcelona: The need for a new city and service provision
Urbani izziv, volume 22, no. 2, 2011
134
e structural question of this paper was to examine how good
urban planning can be used to improve wellbeing. Assump‑
tions have been made associating good health and good quality
of life with service provision to improve wellbeing. We tested
what level of the population was served by the location of
hospitals and markets proposed by Cerdà, as opposed to the
null provision in the Old City. Cerdà’s idea of service eciency
was in part a solution stemming from common sense and from
the progressive goal that the poor conditions of the working
population could be improved through good urban planning.
In this paper we worked with modern location theory models
and GIS to analyse his results; in fact, service‑area analysis
of hospitals and markets has been useful for nding primary
solutions to this problem. Specically, and with restrictions
to be relaxed in a future analysis, we have shown that 78% of
Barcelona’s Expansion section population has a hospital within
30 minutes’ walking distance and 95% of the population is
within a maximum of a 24‑minute walk to a market. Many
things can be achieved in future research. Most of these fall
under the following proposals: considering facility location as
an endogenous variable of the model, taking into account the
capacity of services, introducing dierent population densities,
introducing a dierent typology of services, individual deci‑
sions aecting wellbeing, a heterogeneous population, various
levels of income, eciency (minimising aggregate demand)
and further discussing the spatial eciency and wellbeing as‑
sociated with service distribution.
Since the 1960s, Barcelona has expanded to become a metro‑
politan continuum where the transport infrastructure has con‑
tributed to its metropolitan area growth. Aer 152years, Bar‑
celona’s services and population are very dierent from Cerdà’s
proposal. e idea evolved and today complexity makes any
comparison very dicult. e population inside the Expan‑
sion section and in the old (and then incorporated) neigh‑
bouring towns makes up a large city where the urban planning
provided by the original model has contained many complex
processes that have resulted in contemporary Barcelona.
Montserrat Pallares-Barbera
Harvard University, Institute for Quantitative Social Sciences, Center
for Geographic Analysis, Cambridge, Massachusetts, USA
Autonomous University of Barcelona, Geography Department,
Barcelona, Spain
E-mail: mpallares@cga.harvard.edu
Anna Badia
Autonomous University of Barcelona, Geography Department,
Barcelona, Spain
E-mail: anna.badia@uab.cat
Figure9: Orthophoto map of Barcelona(source: Cartographic Institute of Catalonia, 2010).
M. PALLARES-BARBERA, A. BADIA, J. DUCH
Urbani izziv, volume 22, no. 2, 2011
135
Jordi Duch
Autonomous University of Barcelona, Geography Department,
Barcelona, Spain
E-mail: jordi.duch@uab.cat
Notes
[1] Between 1857 and 1860 three urban-planning projects to en-
large Barcelona were presented by Ildefons Cerdà i Sunyer in 1860,
Miquel Garriga Roca between 1857 and 1858, and Antoni Rovira i
Trias in 1859. The proposal presented by Rovira i Trias was chosen
by the Barcelona City Government, whereas the proposal pre-
sented by Cerdà i Sunyer was chosen by the government of Ma-
drid and signed by Queen Isabel II in 1860. Much controversy and
opposition surrounded the approval and development of Cerdà’s
proposal. Political and social claims comprising low sustainable
argumentation contradicted the plan. Changes in city hall, from a
progressive to a conservative government, defended Rovira’s Plan.
Economic agents, mainly landowners, added their voice, being
afraid of the eects of the plan’s proclaimed low density. Cerdà’s
proposal went forward with some changes(García Melero, 1998).
[2] In addition to engineering, he developed military and political
careers, both in Madrid and Barcelona. In 1851, he was elected
progressive deputy for Barcelona’s San Pedro district. In 1954 he
was appointed síndico by the progressive city hall; and the region-
al deputy chief(Span. governador civil) appointed Ildefonso Cerdà
as a municipal architect to start thinking about how to develop
Barcelona.
[3] It is an accurate database of health, salary, family members,
conditions and living standards of the working class.
[4] In 1933 the Catalan Architects and Technicians for the Im-
plementation of Contemporary Architecture group(Cat. Grup
d’Arquitectes i Tècnics Catalans per al Progrés de l’Arquitectura Con‑
temporània) designed a plan that would later be known as El Pla
Macià, referring to the rst president of the Catalan government
during that period. The plan revived Cerdà’s design, adapting it to
the new economic and demographic situation(Casellas, 2009). The
1992 Vila Olímpica Project followed Cerdà’s grid.
[5] Sants, Sarrià, Sant Gervasi, Gràcia, Horta, Sant Andreu del Palo-
mar and Sant Martí de Provençals.
[6] The neighbouring towns have been part of Barcelona since
1897.
[7] Camp de l’Arpa, Clot, La Llacuna and Icària.
[8] This area corresponds to the built-up area, which diers from
the total 1,969hectares projected by Cerdà, which included streets
and parks.
[9] “Manhattan or L1 rectilinear”: given a set of origin-destination
points in the plane and a set of polygonal barriers to travel, the
problem is to nd the minimum rectilinear distance paths be-
tween given origin-destination points in the presence of polygonal
barriers to travel(Larson& Li, 1981).
Acknowledgements
This research was funded by the Spanish Ministry of Education,
Science and Technology, and the Spanish Ministry of Science and
Innovation, Spain (project numbers: CSO2010-17178; B.O.E. Núm.
80, Jueves 2 de abril de 2009, Sec. III. Pág. 31721, Resolución 5562);
and the Catalan Government, Quality Groups (project number
2009SGR0106). The authors are grateful to Wendy Guan of Harvard
University, Institute of Quantitative Social Sciences, Center for Geo-
graphic Analysis(CGA), for her support and to Giovanni Zambotti,
also from the CGA, for providing us technical support.
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