Scholarly article on topic 'The Performance of an Urban Road System: An Innovative Approach Using D.E.A. (Data Envelopment Analysis)'

The Performance of an Urban Road System: An Innovative Approach Using D.E.A. (Data Envelopment Analysis) Academic research paper on "Civil engineering"

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Abstract of research paper on Civil engineering, author of scientific article — Gianfranco Fancello, Barbara Uccheddu, Paolo Fadda

Abstract Improving the efficiency of transport networks by enhancing road system performance, lays the foundations for the positive change process within a city, achieving good accessibility to the area and optimizing vehicle flows, both in terms of cost management and attenuation of environmental impacts. The performance of an urban road system can be defined according to different thematic areas such as traffic flow, accessibility, maintenance and safety, for which the scientific literature proposes different measurement indicators. However variations in performance are influenced by interventions which differ from one another, such as infrastructure, management, regulation or legislation, etc. Therefore sometimes it is not easy to understand which areas to act on and what type of action to pursue to improve road network performance. Of particular interest are the tools based on the use of synthetic macro-indicators that represent the individual thematic areas and are able to describe the behavior of the entire network as a function of its characteristic elements. These instruments are of major significance when they assess performance not so much in absolute terms but in relative terms, i.e. in relation to other comparable urban areas. Therefore the objective of the proposed paper is to compare performances of different urban networks, using a non-parametric linear programming technique such as Data Envelopment Analysis (DEA), Farrel (1957), in order to provide technical support to the policy maker in the choice of actions to be implemented to make urban road systems efficient. This work forms part of a research project supported by grant, PRIN-2009 prot. 2009EP3S42_003, in which the University di Cagliari is a partner with a research team comprising the authors of this paper, and which concerns performance assessment of road networks (2013a, 2013b).

Academic research paper on topic "The Performance of an Urban Road System: An Innovative Approach Using D.E.A. (Data Envelopment Analysis)"

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ScienceDirect

Procedia - Social and Behavioral Sciences 87 (2013) 163 - 176

SIDT Scientific Seminar 2012

The performance of an urban road system: an innovative approach using D.E.A. (Data Envelopment Analysis)

Gianfranco Fancelloa*, Barbara Uccheddua, Paolo Faddaa

aDipartimento Ingegneria Civile Ambientale ed Architettura, Universita degli studi di Cagliari, Piazza d'Armi, 09123 Cagliari, Italy Abstract

Improving the efficiency of transport networks by enhancing road system performance, lays the foundations for the positive change process within a city, achieving good accessibility to the area and optimizing vehicle flows, both in terms of cost management and attenuation of environmental impacts. The performance of an urban road system can be defined according to different thematic areas such as traffic flow, accessibility, maintenance and safety, for which the scientific literature proposes different measurement indicators. However variations in performance are influenced by interventions which differ from one another, such as infrastructure, management, regulation or legislation, etc. Therefore sometimes it is not easy to understand which areas to act on and what type of action to pursue to improve road network performance. Of particular interest are the tools based on the use of synthetic macro-indicators that represent the individual thematic areas and are able to describe the behavior of the entire network as a function of its characteristic elements. These instruments are of major significance when they assess performance not so much in absolute terms but in relative terms, i.e. in relation to other comparable urban areas. Therefore the objective of the proposed paper is to compare performances of different urban networks, using a non-parametric linear programming technique such as Data Envelopment Analysis (DEA), Farrel (1957), in order to provide technical support to the policy maker in the choice of actions to be implemented to make urban road systems efficient. This work forms part of a research project supported by grant, PRIN-2009 prot. 2009EP3S42_003, in which the University di Cagliari is a partner with a research team comprising the authors of this paper, and which concerns performance assessment of road networks (2013a, 2013b).

© 2013TheAuthors. PublishedbyElsevier Ltd.

Selectionandpeer-reviewunder responsibilityofSIDT2012ScientificCommittee. Keywords: road networks, efficiency, DEA

* Corresponding authors. Tel.: +39 070 675 5274; fax: +39 070 675 3209. E-mail address: fancello@unica.it

1877-0428 © 2013 The Authors. Published by Elsevier Ltd.

Selection and peer-review under responsibility of SIDT2012 Scientific Committee.

doi: 10.1016/j.sbspro.2013.10.601

1. Introduction

DEA is a typical benchmarking analysis, commonly used in econometrics to estimate the efficiency of production units and has been widely adopted over the years in areas such as health, education, finance, local public transport, ICT and macroeconomics of sector studies.

The applications of DEA to transportation issues concern all principal modes of transport. The efficiency of container port terminal operators has been studied by Marchese et al, (2000), different terminals have been compared by Cullinane, Song, Teng-Fei Wang (2004), Rolle and Hayuth (1993) defined a theoretical ratio of the port efficiency, Budria-Martinez (1999) analyzed the efficiency of ports in relation to the evolution of the efficiency of a single port, Tongzon (2001) studied the factors affecting efficiency performance of a port, with particular attention to the number of cranes and berths for container ships and waiting times. The DEA has also been used for airport analysis: for example, Curi, Gitto, Mancuso (2008) measured the efficiency of Italian airports after the privatization of the sector and the study by Adler, Berechman. (2001), measured airport quality from the airlines viewpoint using DEA. In the 1990s the first works appeared using DEA in combination with other analytical techniques (Stochastic Frontier Analysis or Free Disposal Hull), to study local public transport in order to study compare results. DEA is often used not only to assess the efficiency of companies but also the regulatory impact on the local public transport sector Piacenza, (2006) or for other specific evaluations of particular policies Gagnepain and Ivaldi, (2002). Levaggi (1994) adopted parametric and non-parametric approaches for analyzing the efficiency of urban transport in Italy, and Buzzo, Erbetta, Petraglia and Piacenza (2007), analyzed the regulatory and environmental effects on public transit efficiency using a mixed DEA-SFA approach. Hermans , Brijs, Wets, Vanhoof (2009) propose a computational model based on DEA, created on the model output, for identifying the positive and negative aspects of road safety in each country analyzed, Shen, Hermans, Brijs, Wets, Vanhoof (2012) use DEA as a performance measurement technique that provides an overall perspective on a country's road safety, and further assess whether the road safety outcomes determined in a country correspond to the numbers that can be expected based on the level of exposure. In doing so, three model extensions are considered; the DEA based road safety model (DEA-RS), the cross-efficiency method, and the categorical DEA model. Lastly, regarding the application to urban transport management, Fancello, Uccheddu and Fadda (2013c) adopted DEA for comparing urban road systems in different cities, assessing network performance using a number of indicators.

The aim of DEA is to calculate an efficiency frontier measured as relative performance of different units called DMU (Decision Making Unit) in terms of distance per unit to the ideal frontier, constructed using observed input and output data. The efficiency frontier is a set of points that shows the efficient combination of input and output that can be obtained in the systems examined, Cooper, Lewin and Seiford (1994). Fig. 1 shows a graphical representation of DEA in which three DMU (A, B and C), are compared, each using a single input x to produce the output y. The line denotes the efficiency frontier: point A on the frontier, represents an efficient DMU and the points B and C, outside the frontier, the inefficient DMUs, Charnes, Cooper and Rhodes (1978).

In their original study, Charnes, Cooper, and Rhodes (1978) described DEA as a "mathematical programming model applied to observational data that provides a new way of obtaining empirical estimates of relations, such as

Fig. 1. Representation of DEA

the production functions and/or efficient production possibility surfaces, that are cornerstones of modern economics".

The efficiency score in the presence of multiple input and output factors is defined as: Efficiency = weighted sum of outputs/weighted sum of inputs.

Assuming that there are n DMUs, each with m inputs and s outputs, the relative efficiency score (1), (2) of a test DMUp is obtained by solving the following model proposed by Charnes et al. (1978):

Max g^ZM. (1)

Y™ u-x- y '

Subject to fr ^ (2)

vk, uj > 0 Vk, j

Where k = 1 to s; j = 1 to m; i = 1 to n;

yki = amount of output k produced by DMU i; Xji = amount of output j produced by DMU i; vk = weight given to output k; Uj = weight given to output j.

Each DMU selects input and output weights that maximize its efficiency score. In general, a DMU is considered to be efficient if it obtains a score of 1 while a score of less than 1 implies that it is inefficient. Relative efficiency in DEA has the advantage of avoiding the need for assigning a priori measures of relative importance to any input or output, Cooper, Seiford and Zhu, (2004). This approach is called CCR model: it calculates the efficiency ratio for the DMUs based on their inputs and outputs and, after comparison of the results, determines the DMU's efficiency. Using linear programming, we determine the optimal weights, which maximize the efficiency ratio for each DMU: the optimal weights usually vary from one DMU to another.

The CCR model is built on the assumption of constant returns to scale: this means, that inputs and output are linked in a strictly proportional ratio (if all inputs are doubled, outputs are expected to double, too). The Banker-Charnes-Cooper (BCC) model (1984) is an extension of the CCR model and allows for the fact that productivity at the most productive scale size may not be attainable for other scale sizes at which a given DMU is operating. Therefore, the BCC model estimates the pure technical efficiency of a DMU at a given scale of operation. The only difference between the CCR and BCC models is the convexity condition of the BCC model, which means that the frontiers of the BCC model have piecewise linear and concave characteristics, which lead to variable returns-to-scale.

Charnes, Cooper, Lewin, Seiford (1994) describe several advantages of the DEA approach:

• it uses individual observations and not not their average;

• it produces an aggregate measure of efficiency for each DMU, using known variables as inputs and outputs;

• it uses a multiplicity of input and output, whereas the units of measurement can different from one another;

• it evaluates the efficiency of homogeneous DMUs;

• it calculates which inputs and outputs of inefficient DMU need to be changed to attain efficiency;

• it yields Pareto efficient solutions.

DEA does however also present some drawbacks:

• the efficiency of each DMU depends on the efficiency of the other DMUs;

• it is impossible to prove that all DMU are inefficient;

• to consider only one value for each input and output, produces measurement errors or approximations;

• If a DMU has a slightly higher production than the another it is considered efficient and therefore able to

change the production frontier.

The objective of this paper is to compare performances of different urban networks, using a non-parametric linear programming technique such as Data Envelopment Analysis (DEA), Farrel (1957), in order to provide technical support to the policy maker in the choice of actions to be implemented to make urban road systems efficient. In this investigation, concerning the use of DEA to study the efficiency of roads systems, the DMUs are the road networks in different urban contexts. Inputs and outputs are selected from among the main characteristics of road system indicators: traffic flow, accessibility and safety. For comparing the performance of different road networks, by means of linear programming, the following requirements need to be met:

• Homogeneity: the road network must use the same type of inputs to produce the same types of results;

• Independence: the flows relating to different networks should be completely independent;

• Autonomy: each network has the ability to decide how to use their inputs to produce their results.

The analysis will have an input-oriented approach where, starting from fixed outputs, the optimal value will be defined, in percentage terms, as the amount of input that the road system can cope with to become efficient. The concept of "performance" of an urban transport network will be explored, highlighting what has emerged from analysis of the state-of-the-art literature, with specific reference to synthetic indicators calculation representing different issues. The inputs will be identified by examining the needs that emerged from the analysis of population mobility and accessibility, while the outputs will be defined according to traffic flow, environmental quality and safety. The application, simply illustrative, concerned the urban road networks in eight different cities (Benevento, Caltanissetta, Crotone, Matera, Savona, Viareggio, Vigevano and Viterbo) selected according to the following criteria: population between 60,000 and 65,000 and perimeter of the urban area between 15 km and 20 km. DEA analysis allowed to calculate, for each urban system, a value of relative efficiency on the basis of which the eight networks have been ranked, distinguishing efficient from inefficient ones. The efficiency of each network is only meaningful within the context examined, in relation to the model chosen and to the sample units considered. One only needs to introduce a new network or to change the model characteristics, from input to output oriented for example, to obtain different efficient networks or different efficiency values, Zhao, Triantis, Murray-Tuite and Edera (2011). With the DEA analysis, a value of relative efficiency is calculated for each urban system that makes it possible to rank the networks examined, discriminating between efficient and inefficient

1.1. Definition of DEA parameters

Two analyses have been conducted in parallel: the first assuming constant returns to scale using the CRS method Charnes, Cooper and Rhodes, (1978), the second assuming variable returns to scale using the VRS method, Banker, Charnes and Cooper (1984). Both analyses are input-oriented: the level of relative efficiency is therefore the maximum proportion of the inputs that the network must guarantee, if efficient, to have at least the current output level. This means that required the movement to attain the output level is attributed to the input. We also evaluated some cases in which cities with efficient networks are adopted as peers for some of the inefficient ones (ie, efficient and dominant cities evaluated as best practice, and whose input values can be used as reference by the inefficient cities and dominated by them).The inputs and outputs chosen to measure the level of performance of road systems are given in Table 1 and are grouped according to the four macro-areas of investigation: traffic flow, accessibility, safety, public transport. Since the DEA shows, within the inefficient networks, the input values that should be adopted in order to achieve efficiency, the inputs are represented by values that need to be minimized (by contrast the output values should be maximized). Therefore, for this kind of analysis, referring to some of the indicators chosen, the required reciprocal value is calculated, so as to maintain

consistency among the values of the calculated production functions. The indicators are evaluated according to the their ease of retrieval. Preferably simple and generic indicators are used that are easy to acquire, rather than high performance and characteristic indicators that are difficult to obtain.

Table 1. Macro-areas, Input and Output

Macro-areas/Input-Output Input Output

Circulation (number of vehicles registered in the metropolitan area)/(length metropolitan area network - m.a.n.) Level Of Service

Accessibility number of major attractors within 300 m from the town hall (Rate of average time needed to reach the town hall)/(number of main accesses)

Safety (€ spent by the Administration)/(length m.a.n.) (number of fatal accidents)/(length m.a.n.)

Local Public Transport (number of public buses)/(length ma.n.) (number of passengers transported in a year from bus system)/(length m.a.n.)

The inputs and outputs shown in Table 1, each assigned an identification code, are described in detail below:

• I_1 (number of vehicles registered in the metropolitan area)/(length metropolitan area network):

although generic, this indicator is able to show the occupation level of the road network. Flow density indicators are easy to retrieve from website databases, that are updated annually by Italian town councils or the Public Car Registry;

• O_1 Level Of Service, LOS: it is an indicator of quality level and network congestion. For the purposes of the present analysis we used the standard value V/C specified in H.C.M. (Highway Capacity Manual); its value increases with increasing congestion and diminishing network quality. As it was not possible to calculate the average value of the LOS for all networks it was decided to use an identical value of 0.55 (which indicates an LOS of between B and C, representative of the different traffic conditions in medium-sized cities such as those studied) for all the networks examined. This indicator has been used in the analysis by calculating the reciprocal value (1/LOS), so as to minimize the effect;

• I_2 number of major attractors within 300 m from the town hall: this is an indicator of the degree of accessibility of schools, public offices, places of entertainment and culture from a given point, symbolically identified as the town hall. The larger the number of attractors, the greater the degree of network accessibility, with a consequent increase in the level of user satisfaction. The data have been calculated with GIS and used in the analysis by calculating the reciprocal value (1/number attractors);

• O_2 Average time needed to reach the town hall: this indicator of the degree of network accessibility is calculated using GIS with which the main accesses of the urban road network have been identified. We calculated the journey time along the shortest path from every access point to the town hall. These were then added together and divided by the number of accesses obtained in the network. The lower the value obtained, the greater the level of network user satisfaction. This indicator was therefore used in the analysis by calculating the reciprocal value (1 / (Stimes / ^accesses));

• I_3 (€ spent by the Administration)/(length metropolitan area network): this is an indicator of road safety; the higher its value, supposedly better the safety through road maintenance and upgrading. Missing data from the on-line survey have been recovered through direct calls to the competent authorities. This indicator was used to calculate the reciprocal value (1 / (€ spent / km network));

• O_3 (Number of fatal accidents)/(length metropolitan area network): this is an indicator of road safety; the higher its value, supposedly greater the inefficiencies and the more dangerous the road system; consequently this indicator was used to calculate the reciprocal value (1 / (number of fatalities / km network));

• I_4 (Number of public buses)/(length metropolitan area network): this is an indicator of the degree of efficiency of local public transport services; an indicator of the flow density of local public transport. The higher its value, supposedly greater is the degree of satisfaction of the users who benefit from a fast and capillary service;

• O_4 (Number of bus passengers transported per year)/(length metropolitan area network): this is an indicator of the degree of satisfaction of public transport users. Although it was easy to retrieve for the provincial capitals, for others it was necessary to contact the bus company.

The application of DEA, moreover, requires a minimum number of networks to be able to properly discriminate between the efficiency results. It is necessary to carefully evaluate the trade-off between the DMU and inputs/outputs sets. In fact, a large amount of input and output data allows one to better characterize the production process, but, increasing the variables data requires more observation data. Too many input/output data, for a small DMU's set, can generate a great deal of DMU efficiency data, often unusable for benchmarking analysis. A practical rule suggests that a good level of usability of results can be obtained when DMUs are at least equal to twice the product of output and input: 2*(I*O).

Tables 2 and 3 show the elementary data and the values of the calculated inputs and outputs

Table 2. Elementary Data

Cities Metropolitan area Vehicles registered Major attractors. Average time Main

[Km] [n.] [n.] [t] [n.]

Benevento 180 48.569 9 33.70 5

Caltanissetta 140 51.211 5 21.40 6

Crotone 280 43.032 11 54.10 5

Matera 185 47.585 10 34.00 5

Savona 165 52.981 13 31.70 4

Viareggio 225 54.634 7 27.10 4

Vigevano 175 47.525 10 41.40 6

Viterbo 195 62.049 6 34.40 6

Cities Euro spent [€] Fatal accidents [n.] Public buses [n.] Pax per 1000 inhab. [n.] LOS

Benevento 3,085,000 2.70 154 37.80 0.55

Caltanissetta 500,000 9.70 74 9.70 0.55

Crotone 3,450,000 9.00 207 11.40 0.55

Matera 1,250,000 2.70 211 24.40 0.55

Savona 1,300,000 5.30 221 72.20 0.55

Viareggio 1,983,000 8.70 16 19.02 0.55

Vigevano 670,000 5.00 9 5.07 0.55

Viterbo 2,159,000 7.30 135 42.20 0.55

Table 3. Original Input and output values

Cities I_1 I_2 I_3 I_4 O_1 O_2 O_3 O_4

Benevento 269.83 0.11 0.00006 1.17 1.82 0.15 66.67 13.027.35

Caltanissetta 365.79 0.20 0.00028 1.89 1.82 0.28 14.43 4.175.64

Crotone 153.69 0.09 0.00008 1.35 1.82 0.09 31.11 2.516.06

Matera 257.22 0.10 0.00015 0.88 1.82 0.15 68.52 8.021.40

Savona 321.10 0.08 0.00013 0.75 1.82 0.13 31.13 27.371.68

Viareggio 242.82 0.14 0.00011 14.06 1.82 0.15 25.86 5.452.65

Vigevano 271.57 0.10 0.00026 19.44 1.82 0.14 35.00 1.845.48

Viterbo 318.20 0.17 0.00009 1.44 1.82 0.17 26.71 13.763.04

To observe the responses of different urban networks 8 tests have been performed divided into two groups, as shown in Table 4:

• 4 Input = 1 Output: for a total of four tests, one for each of the four outputs with the aim of understanding which output is sensitive to which inputs;

• 1 Input = 4 Output: for a total of four tests, one for each of the four inputs with the aim of determining which input generates the best effects in the network.

The data rule has been observed in all the tests conducted: 2*(4*1)=8 and 2*(1*4)= 8, 8 is the maximum number of DMU we can use.

Table 4. Test

Group TEST I_1 I_2 I_3 I_4 O_1 O_2 O_3 O_4

1 01 X X X X X

1 02 X X X X X

1 03 X X X X X

1 04 X X X X X

2 05 X X X X X

2 06 X X X X X

2 07 X X X X X

2 08 X X X X X

The 8 tests have been conducted using both the CCR (constant returns to scale, hereinafter defined as CRS) and the BCC (returns to scale variables, hereinafter referred to as VRS) methods. The test results were analyzed in two different ways: comparing the efficiency scores of the two test groups and in terms of macro-areas.

1.2. Results

1.2.1. Comparisons of efficiency sores for the four test groups

Tables 5 shows the results obtained for the CRS and VRS tests respectively for the first group, in which the four available inputs were used to obtain one output at a time.

Table 5. Results CRS/VRS - Group 1

TEST 01_CRS 02_CRS 03_CRS 04_CRS 01_VRS 02_VRS 03_VRS 04_VRS

Benevento 1 1 1 1 1 1 1 1

Caltanissetta 0.57 1 0.14 0.13 0.57 1 0.57 0.57

Crotone 1 0.89 0.76 0.19 1 1 1 1

Matera 1 1 1 0.36 1 1 1 1

Savona 1 1 0.59 1 1 1 1 1

Viareggio 0.69 0.93 0.40 0.26 0.69 0.96 0.69 0.73

Vigevano 0.84 0.97 0.51 0.07 0.84 0.97 0.86 0.84

Viterbo 0.79 0.95 0.33 0.69 0.79 1 0.79 0.81

Table 5 shows that Benevento is efficient in all four CRS and VRS tests, whereas Crotone, Matera and Savona are efficient in all the VRS tests (less restrictive). In 3_CRS only Benevento and Matera attain efficiency: the values of the data have for these two cities are lower the others (they both have 2.7 fatalities versus a minimum value of 5.00 and 9.70 in the other cities). Comparing the results, we observe that CRS is more restrictive than VRS: this means that in test 3_CRS the best DMU's are really the most efficient cities. In the VRS test 3_ the other cities attain efficiency, notwithstanding the worst output. This depends on the relative equilibrium between input and output. Can a city with a number of fatalities per year of 9 be considered to perform better than another with half that number, but with less competitive input data? Consequently it may be necessary to reduce the number of inputs, or increase conversely, the number of outputs.

Table 6. Results CRS/VRS - Group 2

05_CRS 06_CRS 07_CRS 08_CRS 05_VRS 06_VRS 07_VRS 08_VRS

Benevento 1 0.93 1 0.79 1 1 1 1

Caltanissetta 1 0.85 0.39 0.87 1 1 1 1

Crotone 1 0.84 0.71 0.55 1 0.84 0.71 0.55

Matera 1 1 0.40 1 1 1 1 1

Savona 1 1 0.96 1 1 1 1 1

Viareggio 0.94 0.62 0.51 0.06 0.94 0.65 0.51 0.06

Vigevano 0.81 0.88 0.22 0.04 0.81 0.92 0.22 0.04

Viterbo 0.94 0.63 0.75 0.71 1 1 1 1

Table 6 show the results obtained in the CRS and VRS tests respectively for the second group (all outputs and one input rotation). Here again (except for test 5 where the CRS and VRS models yield the same results), the CRS model always produces a smaller number of efficient cities. Note that in test 7 Benevento is the only city with an efficient network. The input value (€ 3,085,000) is the second highest, while Crotone (with a higher input value € 3,450,000) fails to achieve efficiency, as its input fails to attain adequate output values. Savona has an efficiency score of 0.96, higher than Crotone (0.71), while it has a lower input (€ 1,300,000). In this case too we

have to consider whether the city is really efficient, as determined by the test (compared with a lower investment there is indeed a higher level of performance), or whether the value is debatable and not really reliable. Overall Benevento is not only more efficient in the test, but also dominant.

1.2.2. Cities

Figures 2, 3,4 and 5, indicate for each city and for all the tests, the results of the two CRS and VRS analyses. The X axis shows the individual tests, while the Y axis shows the efficiency scores.

Fig. 2. CRS/VRS tests: Benevento - Caltanissetta

The results for Benevento and Caltanissetta, shown in Figure 2, have shown that the former city is among the most efficient, while the latter is efficient in fewer test. The CRS test shows a slight decrease in efficiency for test 6 (0. 94) for Benevento; compared to the other cities it has fewer attractors (9, while, Savona, Matera and Crotone have 13, 10 and 11 respectively).

Fig. 3. CRS/VRS Crotone - Matera

The CRS and VRS tests results (shown in Figure 3) for Crotone and Matera (the latter among the top performing cities), showed that in test 3 (group 1), Matera has an efficiency score of 1, along with Benevento, while the inefficient networks had very low values, ranging from 0.76 (Crotone) to 0.14 (Caltanissetta). Examining the input and output data we observe that the value of Output 3 is, for the two cities, much higher than the others; both cities have a very low input 1 value.

Fig. 4. CRS/VRS Savona - Viareggio

The CRS and VRS test results depicted in Figure 4, for Savona and Viareggio, respectively the most efficient city and one of the three cities with the worst results (Viterbo, Viareggio and Vigevano) show that Viareggio, never attains an efficiency score of 1. This means that it is never on the efficiency frontier. Observing the test results, we notice that only in tests 2 (group 1) and 5 (group 2) does Viareggio reach a value close to 1 (0.94), while in test 2 Benevento, Caltanissetta, Matera and Savona are efficient. In test 5 Crotone is efficient as well as the previous four cities. In test 2, despite the fact that Viareggio has a few good inputs and outputs, the equilibrium of the whole input and output set never attains the efficiency level.

Fig. 5. CRS/VRS Vigevano - Viterbo

The results of the two most inefficient cities, Vigevano and Viterbo, shown in Figure 5, showed that in the CRS tests, neither of these two cities attains efficiency, and in only three of the VRS tests, does the Viterbo network achieve efficiency: in test 2 (group 1), where six out of eight networks are found to be efficient (except for Vigevano and Viareggio) and in test 7 (group 2), where five out of eight are found to be efficient. In test 2 Viterbo has a good average value (output 2), only outperformed by Caltanissetta; Viterbo has also invested substantially in road upgrading and maintenance works, the third highest value after Benevento and Crotone. Test 5 shows that the output 4 of Viterbo is one of the highest of the eight cities examined, which means that a large number of people use public transport.

1.3. Conclusions of D.E.A.

The cities with the most efficient road networks are Savona, Matera and Benevento. Table 7 shows the ranking of each city at two different tests, this position has been determined by counting the number of times each city was efficient (with efficiency score of 1). Note, however, that:

• in the CRS tests, Viareggio Viterbo and Vigevano never attain efficiency;

• in the VRS tests, Savona, Matera and Benevento both came first with the same score, followed by Crotone and Caltanissetta, while Viareggio and Vigevano never attained efficiency.

Table 7. Ranking and Efficiency score

Ranking Efficiency score of 1

CRS VRS CRS VRS

Savona 1 1 6 8

Matera 2 2 6 8

Benevento 3 3 6 8

Crotone 4 4 2 5

Caltanisetta 5 5 2 5

Viareggio 6 7 0 0

Vigevano 7 8 0 0

Viterbo 8 6 0 2

The CRS tests are more detailed than the VRS tests. The three top performing cities maintained primacy in both the CRS and VRS tests. The degree of efficiency achieved by each network is meaningful only in the context in which it has been measured, and then only in relation to the specific model and sample units considered. Simply introducing a new road network or changing the model characteristics (from input to output-oriented) or inputs, will produce different efficient networks or different efficiency scores, Banker, Charnes and Cooper (1984). The results show that the DEA technique is well suited for analyzing and comparing road networks. The main issue is not so much the technique but the calculation of the indicators, which should be chosen according to their utility and on the basis of their ability to retrieve the data necessary for processing them. In fact in the present study some indicators have been omitted as, even if they were significant for the analysis, they would have been impossible to develop because of the lack of primary data.

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