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CORS WORKING PAPER 2015:1
CORS WORKING PAPER 2015:1
LOCATION-ALLOCATION OF PUBLIC SERVICES –
CITIZEN ACCESS, TRANSPARENCY AND MEASUREMENT
Anders Fredriksson
April 2015
Center for Organization Studies
Department of Business Administration
University of São Paulo, Brazil
LOCATION-ALLOCATION OF PUBLIC SERVICES –
CITIZEN ACCESS, TRANSPARENCY AND MEASUREMENT1
This version: APRIL 2015
ANDERS FREDRIKSSON
CORS — Center for Organization Studies, FEA-USP, Universidade de São Paulo, Av. Prof. Luciano Gualberto,
908, São Paulo CEP 05508-900, SP, Brazil
CRED — Centre for Research in Economic Development, Département de Economie, Université de Namur,
Rempart de la Vierge 8, Namur B5000, Belgium
IIES — Institute for International Economic Studies, Stockholm University, SE-106 91 Stockholm, Sweden
anders.fredriksson@unamur.be
Abstract
Access to public services is an important determinant of economic opportunities and well-being.
We discuss how location-allocation analysis can be used to both determine, and to evaluate, the
spatial allocation of public services, and discuss different distance-based performance metrics.
We illustrate the method by comparing the allocation of Citizen Service Centers (Servicekontor)
in Swedish counties, to a suggested (per county) optimal allocation of the same centers. We also
conduct a similar analysis for Poupatempo (“Savetime”) in the state of São Paulo, Brazil. The
analysis can be adapted and applied to other public services such as health clinics, schools and
civil registries. We suggest that advances in methods, computation and data availability will
make it possible and relatively straightforward to analyze allocation problems that were
previously unfeasible, thus enabling increased transparency in decisions of where to allocate
vital public services.
1
I thank Love Ekenberg, Wouter Gelade, Catherine Guirkinger, Thiago Paixão, Imran Rasul, Sylvia Saes and Rohini
Somanathan and participants at the CRED workshop (UNamur), as well as at the CSAE/Oxford 2014 development
economics workshop, for feedback on early ideas for this draft. I also thank Eric Thorén at the Swedish Tax Agency,
Ilídio Machado, Cristina Onaga and Carlos Torres at Poupatempo, and the Swedish Transport Administration for
road data. Any errors are the sole responsibility of the author.
1. Introduction
Access to public services is an important determinant of economic opportunities and well-being.
This may concern schooling, health clinics and hospitals, security, water and irrigation, but also
access to the public offices responsible for civil registration, ID-cards, payments of pensions and
unemployment benefits, polling places, etc. This paper looks at one specific aspect of access, i.e.
the spatial allocation of public services. We suggest an easy-to-implement method for how
location-allocation analysis can be used to plan such services. Importantly, the same method
would be available to citizens to evaluate the degree of optimality in spatial access. We use
population-, location- and distance data, largely publicly available, to illustrate our method.
Using an intuitive accessibility criterion, we evaluate the access to Citizen Service Centers in
Sweden. We also study the optimality of a 2008-2011 expansion of similar centers in the state of
São Paulo, Brazil. The method can be adapted to take into consideration other decision criteria
than the ones considered in this paper, and the examples given can be generalized to other
countries and public services.
The first contribution of the paper is to illustrate how location-allocation analysis can be applied
on a large scale to plan, and to evaluate, the spatial allocation of public services. The methods
have been used by Operations researchers for at least 40 years, ranging from theory development
to real world projects such as the planning of health clinics and ambulances. We argue that
improvements in computing capacity and spatial data availability, together with modern solution
methods, can enable a large-scale deployment of location-allocation analysis by government
officials (planners) and citizens (evaluators) alike. The method can thus provide, albeit with
certain restrictions in the problem size that can be studied, increased accuracy and transparency
in the provision of public services.
The second contribution is a spatial analysis of the location of Swedish and Brazilian Citizen
Service Centers. In Sweden, Servicekontor (“Service offices”) is a recently introduced “single
window” government office, physically co-locating three different authorities (Tax, Social
Insurance, Pensions). By analyzing, per county, the actual and suggested optimal locations of
such offices, we suggest several distance-related measures to evaluate the access to this specific
public service. In the state of São Paulo, Poupatempo (“Savetime”) is a government “one stop
shop” for many public services, and was introduced in 1997. We analyze the spatial optimality in
the 2008-2011 expansion into the interior of the state. The Brazilian analysis is more elaborate in
that it also takes into account pre-existing offices and is done for a larger geographical area and a
larger number of municipalities. It is still feasible to implement, however, thus further illustrating
the method suggested. Whereas the Swedish analysis compares access between counties and
proposes several measures for such comparisons/access quantifications, the Brazilian analysis is
kindred to a planner’s problem of expanding an existing public service into a larger geographical
area.
The paper studies an important aspect of public services, i.e. physical access. Corbacho and
coauthors (2012A, 2012B), and Kondylis and Manacorda (2012), are recent examples of papers
connecting distance to public services with socioeconomic outcomes.2 Fredriksson (2015)
instead conducts an impact evaluation of the above mentioned Poupatempo, estimating the time
saved when undertaking an errand at this one stop shop, rather than through traditional means,
explicitly considering the opportunity cost of travel time. Location-allocation methods fit well
into such economic analyses of the effects of distance on different outcomes. The paper provides
no panacea for the analysis of public goods and services provision, however. First, whereas we
discuss a method that can increase accuracy and transparency in decisions related to the access to
public services, the paper says nothing about quality. It is well established, especially in
developing countries, that the quality of public services, once accessed, is a fundamental
problem. Schools closed on school day, teacher absenteeism, reduced class hours, no
schoolbooks, bribes to be attended by a nurse or a doctor, or doctors attending only those that
accept being referred to a private clinic, are but a few examples of such problems (see e.g. World
Bank, 2004; Banerjee and Duflo, 2007; Banerjee et al., 2008). We instead focus on the spatial
allocation, an important aspect of citizen access to public services. Second, there are many
alternative (possibly multi-criteria) planner objectives / utility functions for the allocation of
public goods and services. We discuss our underlying assumptions and some alternative such
formulations in the paper.
The remainder of the paper proceeds as follows. In section 2, we discuss the location-allocation
method, and assumptions and other considerations that enable the analysis. Section 3 applies the
2
Corbacho and coauthors (2012A, 2012B) argue that distance to a birth registry not only affects whether a child is
registered or not (a pre-condition for other documents later in life), but also has an impact on schooling. Kondylis
and Manacorda (2012) argue that distance to school affects education outcomes, but not child labor.
method to the allocation of Citizen Service Centers in Sweden and Brazil and introduces
distance-related metrics to assess the spatial optimality of public services. Section 4 discusses the
results and the potential of citizen access to the methods applied.
2. Method
This section discusses several aspects of Location-allocation analysis, with the aim of reaching a
realistic, implementable and transparent analysis of the spatial allocation of public services.
2.1 Citizen accessed public services with predictable demand
We will consider public services where demand is relatively stable and where citizens visit
facilities. The analysis may apply to schools, primary health care clinics, pharmacies, civil
registries, Citizen Service Centers, etc. Typical services at Poupatempo in São Paulo are issuance
of identity cards (which teenagers get as they approach 18) and renewal of driver’s licenses
(compulsory for drivers every five years), both of which have a highly predictable demand.
Other examples of predictable demand are number of children of school age, number of
unemployed requesting job search assistance or benefits, number of retirees, number of voters,
etc. Although the access to ambulance, police and fire stations is similar in certain respects,
stochastic demand and design for “worst case” scenarios make these services different. They are
excluded from the paper. The analysis is also restricted to services provided at a level higher than
the individual municipality (e.g. federal, state, county), where administrative-, cost- or other
considerations make the number of offices less than the number of municipalities/population
centers. Thus a spatial allocation problem. As an example, there are 290 municipalities and 103
Servicekontor in Sweden.
2.2 Objectives of the planner
In Operations Research the accessibility problems to which this paper relates are classified as
Coverage problems, “p-center” problems or “p-median” problems (or variants thereof). The
Coverage problems aim at placing facilities such that the individual (customer, client, citizen)
living furthest away is within a certain distance (or travel time), thus asking how many facilities
are needed as a minimum (“Location Set Covering Model”). Alternatively, it is recognized that
full coverage is too expensive. The maximum amount of individuals covered given a fixed
number of units is instead sought, recognizing that those (potentially) beyond a threshold
distance will not use the service (“Maximal Covering Location Problem”). In the “p-center”
problem, a number p of facilities should be placed to minimize the distance for the individual
living furthest away.
The “p-median” class of problems instead allocates facilities such that the travel distance for the
average citizen is minimized. The “center” and “median” problems correspond to different utility
functions, where the former implicitly give more weight to some individuals (those far away)
and the latter give individuals equal weight, irrespective of location. Both problems can be
specified in the continuous two-dimensional plane, or over a network (e.g. cities and roads
between cities).3
We will consider the problem of allocating a fixed number of units/facilities/centers, choosing
between a number of candidate cities, in order to minimize the population-weighted travel
distance.4 We thus solve a discrete p-median problem. Other objectives can be specified, and are
discussed in the paper, but we consider minimization of average citizen distance a natural
starting point.5 We do not consider different queue lengths and congestion at units, but it can be
added to the analysis. Each potential allocation will be associated with a specific number of users
of each unit, which can be used to add a queue/congestion penalty. We also assume that each
individual visits a unit an equal amount of times. Note that this assumption implies that demand
does not depend on distance, but it could be modified, by e.g. assuming that the service is not
used beyond a certain distance threshold. As discussed in section 2.4, the assumption can also be
adjusted with usage fractions that are a function of age/gender etc., depending on the service
studied.
3
The papers by Marianov and Serra (2002), and Revelle and Eiselt (2005), provide overviews of the locationallocation theory development, as well as examples of private- and public sector applications. Rushton (1984) and
Oppong (1996) discuss applications to developing country problems.
4
In the applications in section 3, this also implies minimizing the travel time, given the road data that is used.
5
We were inspired by information from Poupatempo, in using this problem set-up. The specification of a “pmedian” problem for the analysis of emergency services would be less appropriate. For such problems the
Location Set Covering Model is instead typically used.
In order to be explicit about the assumptions, these are summarized here. We consider 1)
constant demand across citizens, 2) citizens visiting units, 3) fewer units than municipalities, 4)
the choice between placing no unit and placing one unit in a given municipality, and 5) no
queueing/congestion at units. We also assume 6) travel times/distances constant over the
day/year, thus leaving out traffic congestion and seasonal variations due to rainy seasons, winter
etc.6 The analysis is thus “rural” rather than “urban”, in that we think of trips between cities,
rather than within cities (this is why the Stockholm County is not analyzed below). 7) Citizens of
a municipality/urban agglomeration are assumed to live in the latitude/longitude point of the city
center, which is also the point considered for the placement of a potential unit. This assumption
is needed because a less aggregate population distribution (e.g. city districts or zip code areas)
would need to be accompanied by a finer road distance grid (all distances between all population
points). Also not part of the analysis is differential access to public transport for different routes.
It is instead assumed that 8) all citizens travel at the same speed and on the same route between
any pair of municipalities.7 Finally, it is assumed that 9) the cost of each unit is the same. A
modification of this criterion could be implemented in the analysis and is discussed in section 4.
2.3 Complexity of the problem
The generalized “p-center” and “p-median” problems are “NP-hard”.8 This statement effectively
implies that it is currently not known if these problems can be solved in “polynomial time”,
although special cases may be. The number of computations and the solution time instead
increase exponentially with the problem size. In practice, for a discrete problem (choosing where
to place p units in a choice between n candidate cities), there is a maximum number of units
and/or candidate locations above which the problem becomes unfeasible, if seeking the optimum.
6
See Oppong (1996) for a discussion.
As the location-allocation analysis is based on population density and distances, the algorithm will typically select
“central” and populous locations. It is unlikely that such selected locations, in general, would be less covered by
public transport than other municipalities, although exceptions may exist. Another possible argument is that we
want to avoid reverse causality in the sense of unit placement being guided by considerations that lead to
“spatially inferior” locations, instead of unit placement in central locations leading to those places getting better
public transport.
8
Nondeterministic Polynomial Time Hard. See Kariv and Hakimi (1979), and Megiddo and Supowit (1984), for a
discussion of problem complexity.
7
For some of the problems there are methods that reduce the computational complexity and still
deliver the optimal results. Smith et al. (2015) report that the largest p-median problems for
which exact solutions are found, using commercially available software that deploy Lagrangian
relaxation techniques developed by Beasley (1985), are those of selecting 50 locations from 500
candidate cities. Many real-world applications will be smaller, as there are often legislative or
administrative divisions that limit the problem size. Although these methods use heuristics
(“educated guesses”) as part of the solution procedure, an iterative lower/upper bound procedure
assures that the optimum is found, for small enough problems.9 Sometimes we do not know,
however, how “good” the solution delivered by the heuristic is, as we do not know the optimum.
Athreya and Somanathan (2007) adapt a heuristic for facility location problems to consider also
pre-existing units, and apply it to analyze the spatial allocation of post offices in India. The
method delivers an average distance that is, at worst, 61% larger than the minimum distance.
The method we apply in this paper is exhaustive iteration of all combinations, thus always
finding the optimum. Marianov and Serra (2002) stated that “complete enumeration can be used
in a network with up to 50 nodes and 5 facilities in reasonable computer time” (p. 134). We
instead find that, as of 2015, problems with 6000 times as many iterations (the below solved
Poupatempo problem) are feasible to perform on a standard computer. One can thus solve small
problems using exhaustive iteration (select 10 locations from 30 candidate cities), and use
commercially available software for larger problems (select 50 locations from 500 candidates),
depending on the needs.
2.4 Data
The data needed for the type of analysis we conduct is population and a road distance/travel time
matrix with fastest or closest distances between all population points.10 Less aggregate data gives
more accuracy.
9
An example of a heuristic is: “start with an educated guess on a set of cities, then study all combinations of cities
that lie in the vicinity of this initial guess, update the allocation, and repeat the procedure until no further
improvement can be found”.
10
Oppong (1996) discusses earlier arguments about geospatial data limitations in developing countries. Such
concerns should be much less of an issue today, although they may still be relevant in some regions.
For Sweden, we use the 2010 population data from SCB (Statistics Sweden). The road distance
data, from the Transport Administration, is a manually compiled 2002 (fastest) road distance
database comprising 481 locations, including the main urban agglomeration for (almost all) 290
municipalities, as well as other locations.11 For São Paulo, we use the 2007 municipality
population data from SEADE (the São Paulo state data entity). The analysis was done for the
interior of the state, with 606 municipalities. We consider 37 of these municipalities as having
been candidates for getting one of the 16 new Poupatempo units, implemented 2008-2011. We
first used “as the crow flies” distances (similar results as below, not reported). We then repeated
the analysis with real distance (fastest) road data from Open Street Maps (i.e. all distances
between the 606 municipalities and the candidate cities + the pre-existing units).
In both countries, less aggregate population data exists, geographically as well as along certain
socioeconomic characteristics. One would need a more elaborate road distance matrix to take
advantage of the former, whereas demand characteristics related to age and gender can be
incorporated by using different weights on different subgroups of the population.
One advantage of using “real” distances or travel times, instead of “as the crow flies”, is that
geographical conditions other than distance are implicitly considered. That is, if a certain city is
easier to reach, it will be reflected in the distances/travel times, and hence impacting the
calculations undertaken.12
With population and road data, and with the restrictions discussed above, it is straightforward to
solve (discrete) allocation problems of the type “choose 10 cities where to implement health care
centers, from a list of 30 candidates, to minimize average citizen travel distance”. The analysis
can be done with or without the consideration of pre-existing units (as is done in this paper). A
modern computer can undertake four parallel such calculations in less than an hour, if using
exhaustive iteration, and much faster if using methods implemented in commercial software.
This opens up for implementing a “citizen portal” where such calculations can be made and
visualized, which is discussed in section 4.
11
There are 2000 locations in the Swedish population data, thus averaging around seven locations per
municipality. All individuals living outside the points available in the road distance matrix were assigned to a
municipality’s main town (“centralort”). Marianov and Serra (2002) discuss errors introduced by such population
aggregation.
12
In our specific analysis we used the distances of the fastest routes, but travel times can be used instead.
3. Analyzing Citizen Service Centers in Sweden and Brazil
Swedish Servicekontor (“Service offices”) are single-window Citizen Service Centers that
handle errands related to the Tax-, Social Insurance- and Pensions Agencies. The offices were
implemented following a reorganization of the Tax Agency, starting in 2007, and the Social
Insurance Agency has since closed down its separate offices. Offices were placed where there
were previously a tax office, but new offices opened as well. The Pensions Agency has never had
separate offices. Related developments are a general move towards e-government, and cost
reductions from co-location. A citizen can visit any office, and personnel are trained to handle
errands related to all three authorities. The area of Sweden is 450.000 km2, there are 103
Servicekontor offices and around 3.5 million yearly visits, out of a population of 9.5 million.
Poupatempo (“Savetime”) in São Paulo is a government service “one stop shop” that co-locates
many different state authorities. It was first established in 1997 in order to address several
concerns with a malfunctioning government bureaucracy, citizens’ dependence on bureaucracy
intermediaries, etc. Examples of agencies located at Poupatempo are DETRAN (the Department
of Transit), IIRGD (the Institute for civic identification), SERT (the Secretary of Labor and
Labor Relations), public utility companies, the consumer complaints bureau, post office, a public
bank, etc. The Poupatempo offices are much bigger and encompass more errands than their
Swedish “counterparts”. A São Paulo state citizen can visit any office. The area of São Paulo is
250.000 km2, with a population of 44 million and 38 million yearly Poupatempo visits (in 2015).
In this paper we analyze the 2008-2011 expansion into the interior of the state, which increased
the number of units from 5 to 21. A new build-out was then undertaken in 2014.
We conduct two types of analysis. For Sweden, we compare allocations and citizen access to
Servicekontor between counties, and calculate a suggested (per county) optimum. We discuss
three different distance-based accessibility measures. For São Paulo, we analyze the spatial
optimality of the 2008-2011 Poupatempo expansion, explicitly considering the pre-existing units.
3.1 Servicekontor in Sweden
The analysis of the Servicekontor is presented in table 1, for all but three Swedish counties. The
table listing is in north-south order, where the county code is displayed in figure 1A. Figures 1B
and 1C show the population density and the location of the service centers. Columns 5-7 in table
1 list the actual allocation of the service centers and the average citizen distance. Column 7
largely reflects that northwest Sweden is scarcely populated with long travel distances to urban
centers, although at least one county in the south (Kalmar, code H) shows similar characteristics.
Figure 1A. Counties (red=excluded). 1B. Population density.
1C. Servicekontor.
Columns 8-10 show the results of the location-allocation analysis. Taking Norrbotten as the
example, we iterate all combinations of placing 6 units in 14 municipalities, thus yielding
14!/(8!×6!)=3003 possible allocations. For each iteration, the population-weighted average
distance to the closest unit is calculated, and the optimum is found as the allocation with the
smallest average distance. The results are quite remarkable, in that the minimum distance
allocation is indeed implemented in all but three counties, and when not, only one unit differs
between the allocations. In some counties, it is intuitive and straightforward where units should
be placed, with the choice corresponding to the most populous municipalities.
1
County information
County
2
3
4
5
6
Access to Servicekontor: Actual allocation
Area
# municicode km2 Population palities # offices
Municipalities with offices
7
8
9
Location-allocation optimum
10
Average citizen
Average citizen
%
distance (km) Change from actual distance (km) reduction
11
12
13
Changes to actual allocation
14
+1
-1
Average citizen
distances (km)
+1
-1
Total distance
changes (Mkm)
Norrbotten
BD 97257
248609
14
6
Arvidsjaur Gällivare
Haparanda Kiruna Luleå Piteå
19,2
Haparanda → Kalix
17,4
9,4
15,0
24,1
-2,10
2,42
Västerbotten
AC 54672
259286
15
4
Lycksele Skellefteå Umeå
Vilhelmina
14,7
no change
14,7
-
12,4
20,0
-1,20
2,72
Jämtland
Z
48945
126691
8
3
Strömsund Sveg Östersund
23,3
no change
23,3
-
17,3
32,5
-1,52
2,33
Västernorrland
Y
21552
242625
7
4
Härnösand Sollefteå Sundsvall
Örnsköldsvik
9,8
no change
9,8
-
5,8
15,1
-1,93
2,55
Gävleborg
X
18119
276508
8
6
Bollnäs Gävle Hudiksvall
Ljusdal Sandviken Söderhamn
5,4
no change
5,4
-
4,2
8,8
-0,65
1,90
Dalarna
W 28030
277047
14
5
Avesta Borlänge Falun Ludvika
Mora
14,2
no change
14,2
-
10,8
18,3
-1,92
2,24
Uppsala län
C
8192
335882
10
3
Enköping Tierp Uppsala
9,2
no change
9,2
-
5,5
14,5
-2,49
3,55
Värmland
S
17517
273265
16
4
Arvika Hagfors Karlstad
Kristinehamn
18,5
Hagfors → Sunne
17,7
4,3
14,6
23,2
-2,11
2,59
Västmanland
U
5118
252756
10
4
Fagersta Köping Sala Västerås
5,3
no change
5,3
-
3,4
8,7
-0,97
1,72
Örebro län
T
8504
280230
12
3
Karlskoga Lindesberg Örebro
11,1
no change
11,1
-
7,4
14,8
-2,07
2,11
Södermanland
D
6076
270738
9
4
Eskilstuna Katrineholm
Nyköping Strängnäs
7,1
no change
7,1
-
4,6
11,1
-1,35
2,14
Östergötland
E
10545
429642
13
3
Linköping Motala Norrköping
9,3
no change
9,3
-
7,2
15,2
-1,82
5,09
Jönköpings län
F
10438
336866
13
6
Gislaved Jönköping Nässjö
Tranås Vetlanda Värnamo
7,1
no change
7,1
-
6,0
10,1
-0,78
1,99
Kronoberg
G
8425
183940
8
3
Ljungby Växjö Älmhult
11,5
no change
11,5
-
8,8
15,4
-0,99
1,45
Kalmar län
H
11166
233538
12
3
Kalmar Oskarshamn Västervik
20,5
no change
20,5
-
14,5
31,1
-2,80
4,93
Halland
N
5427
299484
6
4
Falkenberg Halmstad
Kungsbacka Varberg
4,0
no change
4,0
-
1,9
8,2
-1,27
2,51
Blekinge
K
2931
153227
5
2
Karlshamn Karlskrona
11,4
no change
11,4
-
6,5
33,0
-1,49
6,62
6,0
Klippan → Åstorp
5,9
1,0
5,5
6,5
-1,23
1,19
7
8
9
10
11
12
13
14
Skåne
M 10969
1
2
1243329
33
12
Eslöv Helsingborg Hässleholm
Klippan Kristianstad
Landskrona Lund Malmö
Simrishamn Trelleborg Ystad
Ängelholm
3
4
5
6
Table 1. Actual and optimal allocations. See main text for a discussion of columns 5-14. Note that for some counties (län) the county name is equivalent to that of the main city.
Whereas the optimal-actual differences in Värmland and Skåne each represents one different
inland municipality allocation, it cannot be ruled out that concerns other than Swedish population
density may have guided the allocation in Haparanda, at the Finland border.13 Columns 11-14 are
analyzed below. One aspect of the analysis so far is that most counties are small, with few
municipalities and few units, thus making the location-allocation analysis less complex than if
undertaken for larger entities. It also puts limits on how optimal an allocation that can be
achieved and runs the risk of placing units close to each other, on different sides of a county
border. In addition, the service centers were not planned according to county divisions, and
citizens can visit any center. We therefore conducted an alternative and aggregate analysis for
one Swedish province, Småland, comprising the Jönköping, Kronoberg and Kalmar counties.14
Whereas the counties individually have the optimum implemented, this is not the case when
considering the province as a whole, and the average citizen could be better off in terms of travel
distance. The results are in table 2, and the top three allocations, all excluding the Älmhult unit
and instead having an additional unit in the Kalmar County, are shown in figure 2.
Access to Servicekontor: Actual allocation
Location-allocation optimum
# municiAverage citizen
Average citizen
%
palities # offices
Municipalities with offices
distance (km) Change from actual distance (km) reduction
Småland province:
Gislaved Jönköping Nässjö Tranås
Jönköping, Kronoberg
33
12
Vetlanda Värnamo Ljungby Växjö
12,33
Älmhult → Vimmerby
11,28
8,5
and Kalmar counties
Älmhult Kalmar Oskarshamn Västervik
Table 2. Location-allocation solution for the Småland province.
The Småland analysis thus suggests four units in the Kalmar County and only two in Kronoberg,
whereas the actual allocation has three units in each (table 1). The allocation of a unit in
Vimmerby instead of Älmhult would result in an average increase in travel distance of 27 km for
those that would have used the Älmhult unit, but a reduction in travel distance by 49 km for
those using the Vimmerby unit. The affected population groups (as predicted by the model) are
of almost equal size (numbers not shown in the table). The allocation difference therefore results
13
It also cannot be ruled out that for some counties, the results would change slightly with a finer road distance
grid. The current database contains 481×481 distances, which means that most municipalities have one or two
urban agglomerations for which distances to all other points are available. These points are typically the principal
town (“centralort”) in the municipality, and one additional location, which sometimes corresponds to the second
largest agglomeration. We assigned all municipality population living outside the locations available in the distance
database to the principal town, thus slightly overweighting its importance in the location-allocation analysis.
14
The Småland “landscape” has slightly different borders than the three county-region, but differences are minor.
in a substantial net gain. This is true irrespective of the fact that the Vimmerby unit would have
little usage (only 3.5% of Småland users). The allocation internalizes citizens’ travel time.
Figure 2. Actual Småland allocation (left). Optimal allocation (right). The top three allocations are shown, all
excluding the Älmhult unit (but confirming the other 11 units), and including instead a unit in Vimmerby (top
allocation, #1), Hultsfred (second best, #2) and Nybro (#3). The result is intuitive in that the “empty” area between
the coast and the inland is better covered, with a unit allocated to this region for each of the top three allocations.
For a constant number of units, there is a tradeoff between population and distance. If a unit
placed in a densely populated county reduces the average distance by 0.5km, and by 5km if
instead allocated to a sparsely populated county, the latter case contributes more to an aggregate
distance reduction as long as the population ratio is less than ten.
In the final four columns of table 1, the per county gains/losses when adding/removing one unit
are analyzed. This analysis takes as a starting point the actual allocation in column 6. Adding
means placing a new unit in the municipality that would contribute the most to reducing the
average distance (with the new distance in column 11), whereas the removal would be done from
the municipality that would result in the smallest increase in the average distance (column 12).
To know the aggregate impacts of these changes, we must multiply with the county population,
which is done in columns 13 and 14. Taking the unit addition in Norrbotten as the example,
column 13 shows the product of the population (column 3) and the distance difference between
columns 11 and 7, times two (for return trip), and correspondingly for the reduction in column
14. By comparing columns 13 and 14, one can identify pairs of changes that, if undertaken,
would reduce the average (Swedish) citizen travel distance. There are five such pairs in the table.
In order of overall reduction, it would amount to allocating an additional unit in Kalmar and
removing one in Skåne (largest reduction in column 13, smallest increase in column 14), adding
a unit in Uppsala and reducing in Kronoberg (second largest difference), Värmland instead of
Västmanland, Norrbotten instead of Gävleborg, and Örebro instead of Jönköping.15
The analysis of distances can be summarized as follows: Column 7 reflects that in some counties,
public services are far, but we cannot make immediate welfare statements based on this column.
For three counties we identify a sub-optimal allocation (columns 8-10), based on the assumptions
and the location-allocation analysis. The actual and optimal allocations have the same number of
units, but the latter one is associated with higher citizen welfare (as measured by travel distance).
An average citizen in Jämtland has almost six times the distance of that of Halland. Such uneven
access is well documented, from a Swedish/European regional perspective (Dahlgren, 2008). To
judge whether the allocations are fair, in terms of the objective chosen (i.e. minimizing average
citizen travel distance), counties must be compared with each other. One exercise is therefore to
study if there are between-county re-allocations of the (current number of) service centers that
would allow for a reduction of average travel distance. This is similar to asking “how can units
be optimally placed, given the current budget, in order to reduce average citizen travel distances,
and what are the most significant improvements that can be made?” This question was addressed
in columns 13 and 14, which, rather than column 7, constitute a ranking of counties in terms of
how advantaged/disadvantaged they are with respect to the access to Servicekontor. According
to this criterion, the most disadvantaged counties are Kalmar, Uppsala, Värmland, Norrbotten
and Örebro, and the most advantaged Skåne, Kronoberg, Västmanland, Gävleborg and
Jönköping. It is important to note that another utility function, such as that implied by solving the
above discussed “Location Set Covering problem”, could lead to a different conclusion.16
15
What matters for the comparison of columns 13-14 is that the percentage of the population that uses the
service centers does not differ between counties (essentially the above assumption that demand is constant across
citizens). With a current usage ratio of around 40% of the population per year, columns 13-14 then represent the
hypothetical total change in distance traveled over a 2.5-year period, due to the additions/reductions of units.
16
Several other caveats apply to the analysis. First, we started with the actual rather than the optimal allocation,
and the addition/reduction analysis could be repeated by instead starting at the optimum. Importantly, neither of
these two analyses is the same as conducting the analysis without restrictions. We would then instead ask, “what
is the optimal allocation of five units in Norrbotten” and “what is the optimal allocation of seven units in
Norrbotten”, which in general does not guarantee the same result as starting with the optimal or actual allocation
of six units and then add/subtract one. Second, and as illustrated by the Småland analysis, the fact that counties
are small with few municipalities may lead in itself to suboptimal allocations. With larger (and fewer) entities to
analyze, both the location-allocation optima and the units suggested by the addition/reduction analysis may
change. Third, it may be that the addition/reduction analysis merits a county not only one but two (or more) new
units, and an analysis such as columns 11-14 should be undertaken also considering such possibilities.
3.2 Poupatempo in São Paulo, Brazil
The location-allocation analysis of Poupatempo – i.e. selecting 16 locations out of 37 in order to
minimize the average citizen travel distance for the 2008-2011 expansion - is presented in table 3
and in figure 3. Our selection of the 37 candidate cities was based on criteria, obtained from
Poupatempo in 2012, that were relevant for the 2007 expansion decision. The most important
criteria were municipality population and spatial dispersion, i.e. to underweight municipalities in
the densely populated Bandeirantes/Anhangüera highway region (running in a north-northwest
direction from the metropolitan area), to avoid concentrating Poupatempo units in this area.
There are some differences with the above analysis, the most important being that we actually
solve a “global” problem, without any division of the area studied. Poupatempo is a São Paulo
state authority, and we analyze the entire state at the same time. We also take into account the
location of the five pre-existing units, which are shown in the upper panel of figure 3.17 Whereas
we did the Swedish analysis with a county accessibility comparison in mind, in São Paulo we
rather analyze an expansion decision of where to place 16 new units, based on how access to
Poupatempo looked in 2007. The size of the São Paulo computation problem is much bigger and
the decision is more complex. There are 606 municipalities (of which we consider 37 as having
been candidates to get a Poupatempo unit in the expansion). More relevant for computation
times, the number of combinations is much larger than the most complex allocation problems
considered above (with 37!/(21!×16!)=12.9 billion possible allocations).18
With the objective of minimizing average citizen distance, the units in São Paulo are,
notwithstanding the above, somewhat too concentrated along the Bandeirantes/Anhangüera
highways (see figure 3). The optimal allocation reflects a larger dispersion of units, although the
reduction in average travel distance is modest (6.2%, as compared to e.g. 8.5% in the Småland
analysis). It should be noted however that São Paulo has almost five times the population of
Sweden, and more visits per inhabitant, i.e. the allocation choices have a larger overall impact.
17
We also considered the pre-existing units in the metropolitan area, although these are not shown in figure 3.
Another difference is that the degree of urbanization is higher in São Paulo (96%) than in Sweden (88%), and
there are twice as many population points per area unit, which probably makes the analysis more accurate. Fewer
individuals will be assigned to urban locations that only approximate where they live. We also conducted an
analysis of which municipalities are “twin cities” rather than two independent geographical units, and (in a few
cases) adjusted latitude/longitude and population data accordingly.
18
Figure 3. Upper panel: Pre-existing units (blue) and new units (black) in the Poupatempo 2008-2011 expansion. Lower panel: result
from the location-allocation analysis, i.e. the optimal allocation, with 11 of 16 actual units confirmed by the analysis (black), and five
units suggested (green), instead of the actual, but not confirmed, units (red). The actual average travel distance is 40.21 km, the
optimum 37.71 km. The table in the lower panel is a robustness analysis, in that each candidate municipality’s frequency in the top 0.5
km allocations (allocations between 37.71 and 38.2 km) is shown. This criterion selects the same allocation, with the exception of
Piracicaba, that replaces Caraguatatuba, which is ranked 17 th in frequency of appearance in the top locations. The numbers on the map
correspond to the ranking in the top 0.5km table. The robustness criterion is suggestive only however, as the implementation of that
specific allocation (i.e. the table top 16 rather than the one allocation with smallest distance) does not guarantee an allocation close to
the optimum.
Access to Poupatempo: Actual 2011 allocation
Location-allocation optimum
# candidate
Average citizen
Average citizen
%
Change from actual
locations # units
New municipalities with Poupatempo
distance (km)
distance (km) reduction
São_José_do_Rio_Preto Sorocaba Franca Marília
Piracicaba
Itapetininga
Presidente_Prudente Araçatuba Santos Araraquara
Taubaté
Mogiana Ourinhos
State of São Paulo
37
16
40,21
→
37,71
6,2
Piracicaba Jundiaí Botucatu Caraguatatuba Taubaté
São_Carlos
Pindamonhangaba
São_Carlos Rio_Claro Tatuí
Rio_Claro Tatuí
Limeira
Table 3. Location-allocation solution for the Poupatempo 2008-2011 expansion.
4. Discussion
In the paper we suggest an intuitive and easy-to-implement location-allocation analysis for the
planning and evaluation of spatial access to public services. We apply it to Citizen Service
Centers in Sweden and Brazil. The Swedish analysis presents different distance related measures
that can be used to compare counties (columns 7, 9/10 and 13/14 in table 1). These measures
constitute a type of index of accessibility to public services, with the advantage that they have a
very precise underlying interpretation and quantification. Indeed, “metric” is more correct, as the
measure is quantitative rather than ordinal/categorical. This is different from e.g. the
Transparency International Corruption Perceptions Index and allows for its use in regression
analysis, etc.
The metric can be used to not only assess the degree of misallocation but also be correlated with
socioeconomic outcomes, or used to study political “manipulation” in the spatial distribution of
services.19 In line with this reasoning, Banerjee et al. (2008) argue that previous studies provide
no analysis of the reasons for misallocation.
In addition, the analysis of columns 11-14 in table 1 constitutes a “county-based” heuristic that
takes the individual county optima as a starting point, then looks for deviations that reduce the
nation-wide average distance. Cotteels et al. (2012) conduct a kindred analysis of the allocation
of radiotherapy centers, in Belgium, then in Flanders and Wallonia separately. Their aggregate
solution differs from the disaggregate, which hints at sub-optimality in the latter.20
Both types of analysis here presented can be repeated for other countries, regional divisions and
types of public services. The Brazilian location-allocation expansion analysis is “robust”, in the
19
20
I thank Rohini Somanathan for discussions regarding these points.
The authors stress that the study is exploratory and based on limited information.
sense that it is performed on the administrative level for which the state program Poupatempo is
implemented, and thus constitutes the “global” solution. This is a desirable feature, i.e. that the
analysis should, if possible, correspond to the administrative level for which allocation decisions
are taken (a similar discussion appears in Rushton, 1984). In addition, we show that it is possible
to obtain, using exhaustive iteration on a standard computer, the optimum for quite a large and
complex allocation problem. More complex problems can be analyzed using commercially
available software.
In both the Swedish and Brazilian cases, we find small to moderate differences between the
actual allocations and the suggested optima. Replications of the method for other services would
show if this is a typical result. Notwithstanding, the analysis identifies regions which are
underserved by the actual allocations, such as the Kalmar county in Sweden and the Itapetininga
(southwest) region in São Paulo (“actual” here refers to the years 2011-2013). It also precisely
quantifies the changes that would come about by implementing the optimum.
The analysis in the paper builds on population figures, distances and assumptions about usage. It
should be studied how actual usage figures can be integrated into the analysis, and such figures
could also validate the predictions given by the location-allocation analysis.
Many alternative planner objectives can be specified. Consider that of adding a fixed + variable
cost of unit operation, where the latter would depend on usage, instead of the current assumption
with a predetermined amount of units and equal cost per unit. This incorporates the government
budget more realistically into the analysis, whereas we have focused on citizens’ travel
(distance/time) costs, and would be a natural extension of the analysis presented. The
administrative costs could then be compared to a (monetization of) citizens’ opportunity cost of
time. Whereas such an inclusion of establishment and operational costs would add realism to the
model, an important argument runs also in the other direction: The exclusion of citizen travel
time would imply that the full social cost is not considered. A unit with little usage may still be
socially beneficial, if it is the closest one in a sparsely populated (but large) area. The placement
internalizes citizens’ opportunity cost of time.
One source of data that is useful in such an analysis, and for which a tool was developed at
Poupatempo, is to collect data on where users live. In Sweden, with unified personal numbers,
such identification should also be possible.
Another consideration to further investigate is the combination of efficiency and equity
objectives, such as to avoid solutions where scarcely populated areas may get very long
distances. A further extension is to conduct a cross-region or cross-country comparison using a
uniform standard, for a certain type of service (e.g. “everybody getting an ID should have such a
center within 2h travel”), and compare actual-optimal differences between regions or countries.
4.1 Citizen monitoring of public services
We are not the first to evaluate the spatial optimality in access to public services. Rushton (1984)
and Oddong (1996) cite several early studies from developing countries, e.g. the health sector in
Honduras, Nigeria and Sierra Leone. More recently, Atheya and Somanathan (2007) studied the
location of post offices in South India, Dahlgren (2008) schools in a Swedish county, and the
above discussed study by Cotteels et al. (2012) assesses the spatial optimality of radiotherapy
centers in Belgium. We argue, however, that the method here applied, once refined, can be
applied on a large scale. There are Citizen Service Centers in many countries, and county/state
comparisons can be done, similar to the above. Such calculations can be presented as an
accessibility index, which can be correlated with socioeconomic outcomes, or used to study
reasons for misallocation.
With increased availability of road distance data (probably the main limitation for the type of “pmedian” analysis we conduct), together with computing capacity, it should become increasingly
possible to provide a web-based citizen monitoring platform of public services allocation. This
could involve both the presentation of indices themselves, as well as a simple (limited-options)
user application (i.e. “analyze the location of health care facilities in your region”). The
latitude/longitude of most public services are readily available. Examples of applications are
schools, birth registries (the access to which is analyzed in Corbacho and Rivas, 2012A),
pharmacies, etc. The method which should be applied is ultimately a trade-off between realistic
allocation criteria, the possibility to scale up the analysis for replication in different
regions/countries, and data availability that allows for citizen transparency. One advantage of
relying on a simple location-allocation formulation is that data requirements are lower, hence
allowing a transparent analysis to be conducted with publicly available data.
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