An integrated group best-worst method – Data envelopment analysis approach for evaluating road safety: A case of Iran

Journal Pre-proofs An Integrated Group Best-Worst Method - Data Envelopment Analysis Approach for Evaluating Road Safety: A Case of Iran Hashem Omrani, Mohaddeseh Amini, Arash Alizadeh PII: DOI: Reference:

S0263-2241(19)31194-7 https://doi.org/10.1016/j.measurement.2019.107330 MEASUR 107330

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Measurement

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7 June 2019 18 October 2019 26 November 2019

Please cite this article as: H. Omrani, M. Amini, A. Alizadeh, An Integrated Group Best-Worst Method - Data Envelopment Analysis Approach for Evaluating Road Safety: A Case of Iran, Measurement (2019), doi: https:// doi.org/10.1016/j.measurement.2019.107330

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An Integrated Group Best-Worst Method - Data Envelopment Analysis Approach for Evaluating Road Safety: A Case of Iran

Hashem Omrani1, Mohaddeseh Amini and Arash Alizadeh Faculty of Industrial Engineering, Urmia University of Technology, Urmia, Iran

Abstract Evaluating road safety is an important issue for policy makers. One of the most important model for evaluation of road safety is data envelopment analysis-based road safety (DEA-RS). Conventional DEA-RS model is unable to consider decision makers’ (DMs) judgements in the evaluations and also suffers from weight flexibility of input and output variables. In this paper, to incorporate DMs’ preferences into decision making process and overcome the weight flexibility shortcoming of DEA-RS model, DEA-RS is combined with group best-worst method (BWM). For considering the preferences, a group BWM is proposed. The proposed model is applied to estimate the road safety efficiency in provinces of Iran. The results show that developed provinces such as Tehran has the safest roads in Iran. In contrast, provinces with poor road facilities are unsafe provinces in roads. At last, to improve the road safety performances, managerial implications and recommendations have been made for policy makers. Keywords: Data envelopment analysis-based road safety, Best-Worst Method, Group Decision-Making, Road safety

1. Introduction In recent decades, with rapid growth of economy and population, the motorization of transportation sector has been rapidly grown. It is expected that transportation sector continues fast expansion in the next decades. This accelerated expansion in transportation sector has led to new challenges such as road traffic and accidents. Road accidents became as a global problem to societies due to imposing irreparable financial and human life losses. In fact, the issue of road traffic fatalities and injuries has known as public health and socioeconomic challenge in almost all societies (Bao et al., 2011). According to the world health organization (WHO, 2018) report, about 1.35 million

1

Corresponding Author, Tel: +98-4433554180, Fax: +98-4413554181, Email address: [email protected]

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people around the world dies and in addition to this deaths, between 20 and 50 million people incur non-fatal injuries each year because of road traffic accidents. Also road traffic injuries are now the leading cause of death for children and young adults aged 5–29 years and the 8th leading cause of death for people of all ages (WHO, 2018). Most percent of these deaths and injuries occur in developing countries such as Libya and Iran. Since according to the WHO (2018) there is a strong association between the income level of countries and the risk of road traffic deaths. For example, the average rate of road traffic deaths in developing countries is 27.5 per 100,000 populations while the average rate of road traffic deaths is 8.5 per 100,000 populations in developed countries. If no intervention programs and no preventative actions are taken, road accidents will become among major causes of human death by 2030. Also, road traffic accidents cause heavy financial losses up to 3% of gross domestic product (GDP) which has destructive effects on the development of countries (WHO, 2018). Therefore, it is necessary an appropriate planning to reduce the effects of this socio economic phenomenon for each country. In other words, ensuring road safety for all road users is a safety challenge for all countries. Road safety researchers believed that road accident are not consequences of only human errors (Shen et al., 2014). Therefore, they use term “crash” instead of “accident”. By this consideration, a major part of these crashes are both preventable and predictable. Hence, policy makers try to incorporate intervention programs in road safety policies. For instance, United Nations General Assembly enacted a resolution in 2010 which calls on member states to take steps to make roads safer (www.who.int/roadsafety/decade of action/plan). In addition, some national, regional and international parts are working with non-government organizations (NGO), WHO and global road safety partners to implement road safety interventions in their area. For example, Bloomberg Philanthropies to reduce deaths and serious injuries on the roads of ten low- and middle-income countries funded a five-years Global Road Safety Program (2011-2014) (Gupta et al. 2017). According to the WHO (2018) report, intervention programs have improved the safety of roads and have reduced the rate of crashes deaths. Statistically, by implementing intervention programs, mortality rate has remained almost constant around 18 deaths per 100,000 over the last 15 years; However, insufficient progress is being made and the world is far from achieving target, which calls for a reduction in the number of deaths by a half by 2020 (WHO, 2018). Without monitoring the effectiveness of designed policies, identifying safety challenges and evaluating performances of road safety programs for sustainable improvement of road safety is not possible. Road safety performance evaluation as a management tool plays an important role in identifying the weakness and strength

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points of under-evaluation units, optimal assigning of limited budget, target setting and eventually finding the ranking of different units to compare with each other (Chen et al. 2016). National and sub-national comparison and monitoring road safety performances over time provides meaningful developments in safety of roads. In fact, evaluation and benchmarking of road safety performance occur to understand one’s own situation in road safety and to learn from good practices ones (Shen et al., 2012). In this study, the road safety performances in provinces of Iran are evaluated. According to the WHO (2018) report, Iran with 27.4 fatalities rate per 100,000 and approximately around 6% GDP lost due to road accidents in each year is among countries with poor performance in this field. Policy makers are trying to execute and monitor domestic road safety programs to improve safety of roads. Also, due to the importance of the issue, increasing amount of papers have been devoted to investigate road safety in Iran and around the world. In this study, a main question is: which provinces of Iran have the best performers in road safety? To answer this question, we incorporate common evaluating indicators in previous literature in a data envelopment analysis – road safety- assurance region (DEA-RSAR) model to assess road safety performance in Iranian provinces. The DEA- RS- AR is an appropriate approach to incorporate value judgment such as prior information and decision makers’ preferences into analysis (Liu, 2014). The Best-Worst Method (BWM) and DEA are combined to impose expert opinions in evaluation of road safety performance. In summary, the privileges of this paper are as followings: 

Preferences of a group of DMs are incorporated into DEA-RS evaluations



Flexibility of input and output weights are reduced



Distinguish power of conventional DEA-RS has been improved



Results are validated by applying principle component analysis (PCA) and numerical taxonomy methods



Road safety of a developing country has been investigated and results are analyzed

In this paper, the road safety performance of Iranian provinces has been evaluated since most countries face with their specific road safety problems. In fact, socioeconomic, population, motorization level and road safety experiences varies from region to region (Aron et al., 2013). In this regard, DMs’ judgments have been incorporated into DEA-RS model in order to decrease weight flexibility. Although a huge number of DEA models have been applied for evaluating road safety, however, a gap of considering a groups of DMs’ preferences into DEA models was tangible. The proposed approach, has addressed the weight flexibility weakness of conventional DEA-RS model. Besides, the distinguish power of conventional DEA-RS model has been improved using the proposed 3

model. Furthermore, since the proposed model considers both data and subjectivity in evaluations, leads to the more reliable and real results. The rest of paper is as follows: In section 2 literature on road safety and the applied models has been reviewed. In section 3, the proposed models used in this paper are described. In section 4, a numerical example is presented and solved. In section 5, data of Iranian provinces road safety performance has been investigated. Results are analyzed in section 6. Validation of the proposed model has been performed in section 7. In section 8 suggestion for policy makers are recommended. Finally, conclusion of the paper is summarized in section 9.

2. Literature Review Due to the importance of road safety, and its vital impacts on the societies’ financial and human life, this field has been investigated widely among both practitioners and academia. Indeed, with growing challenges, more literature have been devoted to investigating road safety in recent decade in order to mitigate the harmful consequences of a global challenge. Researchers apply different indicators and models to evaluate road safety in different regions. Generally, evaluation of alternatives is mostly a multi criteria decision making (MCDM) problem. Since evaluation of alternatives involving multiple appropriate and even conflicting quantitative and qualitative criteria. For evaluating road safety, many research applied various MCDM techniques and criteria. For example, Nenadić (2019) applied five quantitative and two qualitative traffic safety criteria in a hybrid MCDM model consist of Full Consistency Method (FOCUM) and Weighted Aggregate Sum Product Assessment method (WASPAS). Bham et al., (2019), in order to locate hotspots or high-crash locations on the highways, and consequently improve the road safety considering extra factors such as crash injuries severity, and issues with statistical distribution of crash data applied composite rank measure based on PCA. Haghighat (2011) used Group Analytic Hierarchy Process (GAHP) for obtaining the weights of main and sub-main criteria influencing road safety in Bushehr province of Iran. Then applied Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) for final ranking of roads safety. Chen et al., (2015) used entropy TOPSIS-road safety risk with combining all safety performance indexes (SPIs) into an overall index to evaluate road safety risks in 31 provinces of China. Bao et al. (2012) applied SPI which is related to crashes and injuries data in a hierarchy fuzzy TOPSIS model to evaluate the road safety in a set of European countries. They claimed that the SPI can evaluate road safety concepts better than single indicators. Shen et al. (2012) combined hierarchy structured safety performance indicators (SPI) with DEA model to benchmark 28

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European countries. One of the weaknesses of the aforementioned applied MCDM techniques is that these techniques are not suitable for benchmarking purposes. However, as mentioned in introduction, by benchmarking, units compared with the best performance, ones and can learn from the best performers to improve their own efficiency. Among MCDM techniques, DEA as a powerful decision making method has been successfully applied in road safety assessment (Ganji et al., 2019). Since, ranking alternatives is not the only purpose of DEA and it can be applied for benchmarking. Therefore, one of the mostly applied model for evaluating road safety is DEA technique. For instance, Shen et al. (2015) proposed a DEA-RS model with three inputs of population, passenger kilometer and passenger cars and two outputs of fatalities and serious injuries to evaluate road safety performance of 10 European countries. In order to rank European countries, they applied weight restriction method in DEA model. Bastos et al., (2015) assessed road safety of 27 Brazilian states as well as 27 EU countries using three fatalities per hundred thousand inhabitants, fatalities per billion passenger kilometer travelled (mortality rate) and fatalities per ten thousand vehicles as a composite indicator using DEA. Ganji et al., (2019) assessed Iranian road safety performance by proposing a novel double-frontier cross-efficiency method (CEM) taking into account both optimistic and pessimistic points of view, simultaneously. In this regard, six inputs of police station, road maintenance depot, emergency medical service, equipment and vehicles, camera and road with lightening systems and one output of fatality risk have been considered. They indicated that using double frontier CEM leads to the more real results. Shah et al., (2019) applied DEA method for identify risky and safe segments of a homogeneous highway. Indeed, they proposed a methodology to analyze road safety performance by using a combination of DEA with the decision tree (DT) technique. For assessing Decision Making Units (DMUs), DEA applies a series of linear programming to determine the efficient frontier and DMUs are free to choose their input and output variable weights in order to be efficient (Omrani, 2013). Indeed, DMUs are completely flexible to choose their input and output weights. However, weight flexibility could be considered both weakness and strength of DEA simultaneously. The weight flexibility is weakness of DEA, since in evaluations, some input and output variables take the zero or extreme values which makes the interpretation of impacts of such variables on efficiency scores difficult (Liu, 2014). On the other hand, interpreting the inefficient units is the strength of weight flexibility of the DEA model. Since it indicates that, units are unable to be on efficient frontier even they were free to choose input and output variables’ weights. In the other

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words, inefficiency of units is meaningful and justifiable. In order to dealing with weaknesses of weight flexibility, incorporating decision makers’ judgements in evaluations and improving distinguish power of the DEA model, in literature, four approaches of common weights (Roll et al., 1991), weight restriction (Dyson and Thanassoulis, 1988), cone ratio (Charnes, et al., 1990) and assurance region (AR) (Thompson et al., 1986) have been proposed. In this study, for dealing with mentioned weaknesses of conventional DEA and incorporating the DMs’ judgement a novel group BWM- DEA- RS model has been proposed. As mentioned before, for including DMs’ preferences a group BWM model is applied. In real world applications, there are different MCDM techniques to incorporate DMs’ subjectivity in decision making process such as AHP (Saaty, 1980), Step-wise Weight Assessment Ratio Analysis (SWARA) (Keršuliene et al., 2010), Full Consistency Method (FUCOM) (Pamučar et al., 2018) and BWM (Rezaei, 2015). Mi et al., (2019) mentioned that BWM is one of the most cited (3rd) outranking methods which applies pairwise comparison in evaluations since 2014 and it is predicted the growing application of BWM will continue in future. In comparison with other widely applied outranking methods such as AHP, BWM uses structured way in performing pairwise comparison. Moreover, BWM has filled the gap of using complex and huge number of pairwise comparison and keeping consistency in establishing decision matrix/vector. Mardani et al., (2017) also compared the SWARA as a group decision making method with AHP and pointed out that SWARA technique applies less pairwise comparison (n-1). Moreover, consistency is ensured in SWARA since criteria are ranked descending. Also newly proposed approach, FOCUM, with (n-1) pairwise comparison generates more consistent results than AHP and BWM models. However, the mathematical model of BWM and the normalization constraint n

w i 1

i

 1 for criteria made it applicable in integrating with DEA and mathematical models.

Due to the strengths of BWM, this method has been applied in several papers since presented by Rezaei (2015). For instance, Badi and Ballem (2018) used modified BWM and Multi-Attribute Ideal-Real Comparative Analysis (MAIRCA) methods to select the select the best medical suppliers among available alternatives in Libya. Omrani et al., (2018) in order to find the optimal combination of power plant alternatives, applied an integrated multi response Taguchi, neural network, fuzzy BWM and TOPSIS approach. In another study, Omrani et al., (2019) applied BWM to incorporate DMs’ judgement in DEA and common weight DEA models. They used their model to investigate the efficiency of electricity distribution companies in Iran. Tian et al., (2019) for improving the classic failure mode and effect analysis (FMEA) model, used fuzzy BWM for weighting the risk factors. Pamučar et al., (2018) applied a new

6

integrated interval rough number (IRN) approach based on the BWM and Weighted Aggregated Sum Product Assessment (WASPAS) method along Multi-Attributive Border Approximation Area Comparison (MABAC) to evaluate Third-party logistics (3PL) providers. Aboutorab et al., (2018) in order to consider uncertainty in BWM, integrated Z-numbers and BWM and used their model to address supplier development problem. For a comprehensive review of application of BWM technique in decision making problems, readers can refer to Mi et al. (2019).

3. Methodology In this section, the proposed model is presented. The methodology of this paper is based on the BWM and DEA. The BWM is used for finding weights of inputs and outputs. The BWM assigns the weights of criteria based on the preferences of a DM. However, an extended form of BWM as group BWM has been applied to assign the weights based on the preferences of a group of DMs. In order to incorporating DMs’ preferences into DEA model, the objective function and constraints of the group BWM are added to DEA model. The proposed group BWM-DEARS model is solved by using min-max approach. The results of min-max approach are the inputs and outputs weights which can be used in calculating the efficiency scores. The steps of proposed group BWM-DEA-RS is depicted in graphic abstract clearly.

3.1. Data envelopment analysis-based road safety (DEA-RS) DEA is a nonparametric method that uses linear programming to measure the efficiency of DMUs with multiple inputs and multiple outputs. In DEA, efficiency is defined as a ratio of weighted sum of outputs to a weighted sum of inputs. The data form a frontier and DMUs which are on the frontier are evaluated as efficient. Output-oriented DEA models maximize output for a given quantity of input factors, Contrariwise, input-oriented models minimize input factors required for a given level of output. The input oriented DEA-CCR model is as follows (Charnes et al., 1978):

7

 oCCR  max

m s

 wy

io

i

i  m 1

st : m s



i  m 1

m

wi yij   wi xij  0, j  1,..., n

m

w x i 1

(1)

i 1

1

i io

wi  0,i  1,..., m  s

In model (1), jth DMU uses m inputs

x1 j ,..., xmj

score of DMU under evaluation denotes as o

CCR

for producing s outputs y(m1) j ,..., x(ms) j . Also, the efficiency

.

The model (1) is not appropriate for evaluating the road safety (Shen et al., 2012). As Shen et al. (2012) expressed, in DEA-based road safety model, we want the output, i.e., the number of road fatalities to be as low as possible with respect to the given input levels. In other words, in DEA-based road safety model proposed by Shen et al. (2012), efficient DMUs are those with minimum output levels in a given input levels. The DEA-based road safety (DEARS) model proposed by Shen et al. (2012) is as follows:

m

 oDEA RS  max  wi xio i 1

st : m

 wi xij  i 1

m s

 wy

i  m 1

i

io

m s

 wy

i  m 1

i

ij

 0, j  1,..., n

(2)

1

wi  0,i  1,..., m  s

In model (2), jth DMU have m inputs DMU under evaluation denotes as o

x1 j ,..., xmj

DEARS

and s outputs y(m1) j ,..., x(ms) j . Also, the road safety score of

.

8

3.2. Group Best-Worst Method (Group BWM) Assigning the real weight of criteria is very important in decision making problems, since some methods solution affected by criteria weights significantly (Pamučar et al., 2018). Different MCDM techniques have been proposed to assign the weight of criteria such as AHP, SWARA, FOCUM and BWM which are usually resulted in subjectivity in decision makings. The widely used method in assigning the weights in literature is AHP. However, AHP suffers from some shortages such as huge number of pairwise comparison, and inconsistency in DMs’ preferences. Taking into the account of AHP weaknesses, researches introduced new techniques to improve the weighting of criteria. For example, Pamučar et al., (2018) introduced FOCUM which generates criteria weights with less error than AHP for two reasons. First, FOCUM requires ( n  1) pairwise comparison,

while AHP needs

n  ( n  1) pairwise 2

comparison. Second, the constraints defined when calculating the optimal values of criteria. Indeed, FOCUM enables DMs to measure the errors via Deviation from Full Consistency (DFC) index and validate the model. For more detail readers can refer Pamučar et al., (2018). Another popular method for determining weights is BWM. The BWM determines the weight of criteria using pairwise comparison. Indeed, like AHP, BWM assign the weights based on the preferences of DMs. However, BWM has advantages in compared with AHP such as less pairwise comparison and higher consistency ratio (Zhao et al.,2019). For example, for a set of n criteria, while BWM applies

(2  n )  3 , which is less than AHP technique. However, to compare BWM and FOCUS models, more investigations is necessary. The final BWM model is as model (3). It is important to note that the steps of the BWM are completely explained in Rezaei (2015 and 2016) and readers for more details can refer to them.

min  r s.t : {| wi  aiW wW |}r   r , i  1,..., n {| wB  aBi wi |}r   r , i  1,..., n n

w i 1

i

(3)

1

wi  0,

j  1,..., n

Where the preference of the best criterion over ith criteria for rth DM is criterion for rth DM is

aiW . 9

aBi and preference of ith criteria on worst

The initial BWM proposed by Rezaei (2015 and 2016) in order to determine weights of criteria, taking into accounts of the preference of a DM. In this section, it is assumed that there are K DMs who want to consider their judgments. If there are K DMs, the model (3) can be expressed as a multiple objectives programming model (4) as follows:

min{1 ,  2 ,...,  K } s.t : {| wi  aiW wW |}k   k , i  1,..., n, k  1,...K {| wB  aBi wi |}k   k , i  1,..., n, k  1,..., K n

w i 1

i

(4)

1

wi  0,

j  1,..., n

Where the symbol

{}k just shows the constraints related to the kth DM. In model (5), the objective functions are

homogeneous and can be summed easily. Hence, the model (4) is converted to a single objective programming model (5) for considering the DMs’ preferences, simultaneously.

min 1   2  ...   K s.t : {| wi  aiW wW |}k   k , i  1,..., n, k  1,...K {| wB  aBi wi |}k   k , i  1,..., n, k  1,..., K n

w i 1

i

(5)

1

wi  0,

j  1,..., n

The results of model (5) are the weights related to the indicators based on the DMs’ judgments.

3.3. The proposed group BWM- DEA-RS model In this section, the novel group BWM-DEA-RS model is proposed. The DEA-RS model (2) has an equality m s

constraint

 wy

i  m 1

i io

 1 which is different with the normalized equality constraint

n

w  1 of the group BWM i 1

(5). Consider the DEA model (6) as follows:

10

i

m

max  wi xio   oDEA RS i 1

m s

 wy

i  m 1

i

io

s.t : m

 wi xij   jDEA RS i 1

m s

w i 1

i

m s

 wy

i  m 1

i

0

ij

j  1,..., n

(6)

1

wi  0, i  1,..., m  s

Where

 jDEARS is

the efficiency score estimated for jth DMU in DEA-RS model (2). m s

normalization constraint



i  m 1

wi yio  1

m s

has been replaced by

In model (6), the

 wi  1. The normalization constraint i 1

m s

w 1 i 1

i

is similar to the weights normalization in BWM. Zohrehbandian et al. (2010) proved that the optimal solution of the models (2) and (6) are the same. In other words, the weights generated by the models (2) and (6) are same. Due to m s

the existence of normalization constraint

 w  1in both model (6) and group BWM (5), the DEA model (6) is i 1

i

considered for combination with BWM. The proposed bi-objective group BWM-DEA model can be written as follows:

m

m s

i 1

i  m 1

max f1   wi xio   oDEA RS

 wy

i io

max f 2  1   2  ...   k s.t : m

m s

i 1

i  m 1

 wi xij   jDEA RS

 wy

i ij

 0, j  1,..., n (7)

m s

 w 1 i 1

i

{ wB  aBi wi }k   k , i  1,..., m  s, k  1,..., K { wi  aiW wW }k   k , i  1,..., m  s, k  1,..., K wi  0, i  1,..., m  s

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In model (7), the first objective function and the first constraint are belong to the DEA-RS model (2). The second objective function, the third and the fourth constraints are belong to the group BWM. The second constraint m s

 w  1is belong to both DEA-RS and group BWM. The constraint | wB  aBi wBi |  is easily transformed to i 1

i

two linear constraints

wB  aBi wBi   and aBi wBi  wB   .

Model (7) is a bi-objective programming model which can be solved via some multiple objectives programming models such as parametric method, constraint-, min-max approach, goal programming and etc. In this paper, the min-max approach has been used for solving the model (7) as follows:

m s   m    min max   f1*    wi xio   oDEA RS  wi yio   ,  f 2*   1   2  ...   k    i  m 1  i 1     s.t : m

m s

i 1

i  m 1

 wi xij   jDEA RS

 wy i

ij

 0, j  1,..., n (8)

m s

 w 1 i 1

i

{ wB  aBi wi }k   k , i  1,..., m  s, k  1,..., K { wi  aiW wW }k   k , i  1,..., m  s, k  1,..., K wi  0, i  1,..., m  s

Where

f1*

and

f2*

objective functions

are the ideal values of first and second objective functions. For calculating

f1

and

f2

f1*

and

f2*

, the

are optimized on the constraints of model (7), separately. In other words, for

obtaining the ideal value for f1 , the objective function f2 is eliminated from the model (7) and the model is solved by using the objective function f1 . Also, the ideal value for

f2 is obtained by eliminating the objective function f1

from the model (7). It is clear that the min-max model (8) is easily converted to a linear model (9) as follows:

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min  s .t : m s  m  f 1*   w i x io   0DEA  RS  w i y io    i  m 1  i 1  * f 2   1   2  ...   k    m

m s

i 1

i  m 1

w i x ij   jDEA RS m s

w i 1

i

w

i

y ij  0, j  1,..., n (9)

1

{w B  aBi w i }k   k , i  1,..., m  s , k  1,..., K {w B  aBi w i }k   k , i  1,..., m  s , k  1,..., K {w i  aiW w W }k   k , i  1,..., m  s , k  1,..., K {w i  aiW w W }k   k , i  1,..., m  s , k  1,..., K w i  0, i  1,..., m  s

*

*

*

*

The linear group BWM-DEA-RS model (9) is solved and the optimal weights ( w1 ,..., wm , wm1,..., wms ) are obtained for inputs and outputs. Then, the efficiency score of jth DMU is calculated by equation (10) as follows:

m

BWM  DEA RS  Group  j

w x

i 1 m s



i  m 1

* i ij

(10)

wi* yij

4. Numerical example In this section, in order to illustrate proposed group BWM-DEA-RS model (10) a numerical example is presented and solved. The property of provided example is presented in Table (1). As presented in Table (1) two inputs of C1 and C2 and two undesirable outputs of C3 and C4 are considered to evaluate five DMUs. ---------------------------------------------Table 1 about here ---------------------------------------First, the best, the worst, the preferences of the best criterion over all criteria and all criteria over the worst criterion are determined. Two DMs have been asked to specify their preferences, separately. The preferences are shown in Table (2).

13

---------------------------------------------Table 2 about here ---------------------------------------BWM weights for each DM and group BWM weights based on both DMs preferences are calculated and presented in Table (3). The group BWM model for determining criteria weights is as follows:

Min f  1   2 ; | w 4  6w 1 | 1 ; | w 4  4w 2 | 1 ; | w 4  3w 3 | 1 ; | w 2  2w 1 | 1 ; | w 3  3w 1 | 1 ; | w 3  4w 1 |  2 ; | w 3  7w 2 |  2 ; | w 3  2w 4 |  2 ; | w 1  3w 2 |  2 ; | w 4  5w 2 |  2 ; w 1  w 2  w 3  w 4  1; w 1 ,w 2 ,w 3 ,w 4  0; According to the Table (3), group BWM generates weights based on the two DMs preferences and tries to satisfy all DMs, simultaneously. The weights generated by BWM and group BWM are reported in columns 2, 3 and 4 of Table (3). ---------------------------------------------Table 3 about here ----------------------------------------

Now, group BWM-DEA-RS model (9) is applied to measure the efficiency scores of DMUs. The two objectives model (7) for evaluating first DMU is expressed as follows:

14

Max f1  180 w1  187 w2  1 (53w3  65w4 ); Max f 2  1   2 ; s.t : 180 w1  187 w2  1 (53w3  65w4 )  0; 174 w1  175w2  0.8548*(62 w3  73w4 )  0; 130 w1  144 w2  0.9275*(44 w3  71w4 )  0; 190 w1  120 w2  1*(83w3  62 w4 )  0; 166 w1  140 w2  0.7311*(75w3  80 w4 )  0; | w4  6 w1 | 1 ; | w4  4 w2 | 1 ;

(12)

| w4  3w3 | 1 ; | w2  2 w1 | 1 ; | w3  3w1 | 1 ; | w3  4 w1 |  2 ; | w3  7 w2 |  2 ; | w3  2 w4 |  2 ; | w1  3w2 |  2 ; | w4  5w2 |  2 ; w1  w2  w3  w4  1; w1 , w2 , w3 , w4  0;

In DEA-RS model, DMUs are free to choose the weights of inputs and outputs to maximize their scores. Indeed, DEA-RS considers no DMs’ judgment in calculation. However, in group BWM-DEA-RS model, the weights are obtained based on the DMs preferences. The weights generated by group BWM-DEA-RS model for each DMU are provided in the Table (3). These weights can be used for efficiency estimating of each DMU. The efficiency scores obtained from DEA-RS model (2) and group BWM-DEA-RS model (9) are presented in Table (4). The group BWM-DEA-RS model generates efficiency scores equal or less than DEA-RS model (2). Since the preferences of DMs are considered as additional constraints into DEA-RS model. Moreover, as can be seen, only the score of DMU1 is equal to 1 which means that the distinguish power of DEA-RS has been improved in the proposed group BWM-DEA-RS model. In summary, the proposed model tries to maximize DMUs efficiency scores by incorporating a group of DMs opinions in decision making process. ---------------------------------------------Table 4 about here ----------------------------------------

15

5. An application in road safety of Iranian provinces In this section, the proposed group BWM-DEA-RS model is used for evaluating the road safety in 31 provinces of Iran. Iran is one of the worst performance countries in terms of road incidents. Thus, policy makers in Iran are planning to evaluate and improve the conditions of driving based on the experienced scientific methods. Iran has planned to reduce the number of fatalities up to 10% per year. However, in comparison with global statistics, the situation of Iran in road safety is still poor. Hence, the policy makers want to evaluate road safety performance in different provinces to benchmark and identify the provinces with the strongest and weakest performance and compare them with other provinces. So poor performance provinces can cover their weaknesses by learning from best performance provinces and improve their road safety situation. Iran has 31 provinces consist of small and low populated provinces such as Ilam, Chaharmahal & Bakhtiari, and big populated provinces such as Razavi Khorasan and Esfahan. The provinces are located in different geographical locations with different characteristics. Briefly, north part of Iran is covered with condensed forest and mountains which make it difficult for constructing free/ high ways. West and northwestern parts of Iran covered by cold mountains. Like north of Iran, mountains covered places have dangerous and narrow roads which decrease the road safety of provinces in such regions. The other provinces located in the center, east and south parts of Iran, have arid and semi-arid climate with vast deserts. In such areas of Iran, population is scattered and road facilities (e.g. length of free/highways) are more than other parts of Iran. For more detail a simple map of environmental features of Iran is presented in Fig.1. ---------------------------------------------Fig.1 about here ---------------------------------------In terms of development, Omrani et al., (2019) examined the Human Development Index (HDI) for provinces of Iran. Although HDI rankings provides insufficient and intangible information for analyzing road safety, it may help readers to better understand the socioeconomic situation of provinces of Iran. For more detail, enthusiasm reader can refer to Omrani et al., (2019). Moreover, Fig.2 indicates the population distribution and provinces of Iran. ---------------------------------------------Fig.2 about here ---------------------------------------5.1. Data Selection of input and output variables is very crucial in DEA applications. However, there is no firm consensus on which variables best describe the road safety efficiencies. In previous studies, researchers have used different indicators for comparing road safety of the countries, regions and etc. For instance, Shen et al. (2012) and Shen et al.

16

(2013) used population, passenger kilometer and passenger automobiles as inputs and fatalities as output. Egilmez et al. (2013) used registered vehicles, highway safety expenditures, licensed drivers, VMT, overall road condition, total road length, and safety belt usage as the input variables and the number of fatalities as the only output variable. Ganji et al., (2019) applied six inputs of equipment and vehicles, police station, emergency medical service, road maintenance depot, camera and road with lightening systems and one output of fatality risk. In this study, according to the data availability and previous road safety studies, we have applied six most used indicators of passenger kilometer, tone kilometer, free/highway length (km), number of registered automobile, number of speed camera and population as inputs and three indicators of number of fatalities, number of injuries and number of crashes as outputs for estimating the efficiency scores of road safety in provinces in Iran. Briefly, the input and output variables definitions are as follow. 5.1.1. Inputs 

Passenger kilometer: The average number of passenger along 100 km road



Tone kilometer: The average of loads transporting along 100 km road



Free/highway length (km): The total length of free/highway in each province



Number of registered automobile: The total number of cars plus two-wheelers in each province



Number of speed camera: The total number of fixed speed cameras in each province.



Population: Average of inhabitants for two consecutive years

5.1.2. Outputs 

Number of fatalities: Total number of persons who were dying immediately or within 30 days from injuries sustained in a collision.



Number of injuries: Total number of persons who receive hospital services after collision and dismissing after treatment



Number of crashes: Total number of collisions reported to the traffic police in each province

Provided data series involves annual data on 31 provinces observed in 2015. These data are retrieved from Iran Road Maintenance & Transportation Organization (www.rmto.ir). The raw data are reported in Table (5). ---------------------------------------------Table 5 about here ---------------------------------------6. Results and discussion

17

In this section, the proposed group BWM-DEA-RS model is applied to measure the road safety efficiency scores in 31 provinces of Iran. The results of this section can help policy makers to have a better picture of road safety risks in Iran and improve it by taking preventative and intervention actions. First, DEA-RS model is used to evaluate the efficiency scores of provinces. Then, by incorporating opinions of a group of experts into proposed group BWMDEA-RS model, road safety efficiency scores of provinces are re-evaluated. The efficiency scores generated by DEA-RS and group BWM-DEA-RS models are presented in Table (6). In the following, the results of each model are discussed, separately. ---------------------------------------------Table 6 about here ----------------------------------------

6.1. DEA-RS results In this section, using six inputs number of registered automobile, population, speed control camera, free/high way length, passenger per kilometer, ton per kilometer and three undesirable outputs road accidents fatalities, injuries and number of crashes, the road safety efficiency scores of provinces are evaluated. In order to obtain the efficiency scores, DEA-RS model (2) is executed for each province. The DEA-RS model (2) is data-oriented and evaluates the score of provinces just base on the data. The results of DEA-RS are presented in Table (6). According to the DEARS results, 10 provinces out of 31 provinces with efficiency scores of 1 have the best performance in the safety of roads. These best performance provinces are located on the efficient frontier. In order to maximize the efficiency scores, DEA choose the weights of inputs and outputs, freely. Determining 10 provinces with score of 1 as efficient DMUs represents the poor performance of DEA-RS model in distinguishing DMUs. The other provinces with efficiency scores less than 1 are inefficient and should improve their performance. Kohgiluye & Boyerahmad province with efficiency scores of 0.4194 has the worst performance in the safety of roads. Kermanshah and Gilan provinces with scores of 0.4900 and 0.4925 are the second and third worst provinces in road safety respectively. The scores of worst performance provinces show that they still have great challenges in improving the safety of roads. The mean of efficiency scores in DEA-RS model is equal to 0.7871 which shows that the efficiency of 14 provinces are less than average performance. For better understanding the model, numerical form of DEA-RS for the first DMU is presented in Appendix 1.

6.2. Group BWM results

18

In this phase, just before executing group BWM-DEA-RS model, the best, the worst, the preference values of the best criterion over all criteria and the preference values of the all criteria over the worst criterion are defined. For this purpose, reference pairwise comparisons are performed based on the expert team opinions consist of three members with sufficient work experiences in traffic police department and two experts from the Iran Road Maintenance & Transportation Organization. The preference values are the outcome of the mentioned team closely working and are acceptable for all team members. Table (7) shows the preferences of five DMs, separately. According to the DMs’ opinions, number of road fatalities is the most important index in evaluating the safety of roads. However, the least important index varies based on DMs’ opinions. Based on the each DM preferences, a set of weights are obtained by using BWM (3) which have been presented in the Table (8). Last column of Table (4) is devoted to the weights of group BWM (6). The group BWM (6) generates the weights of criteria by considering all DMs judgment, simultaneously. According to the group BWM, number of road accident fatalities index with the weight of 0.3154 is the most importance for DMs group. ---------------------------------------------Table 7 about here ------------------------------------------------------------------------------------Table 8 about here ---------------------------------------For better understanding the model, numerical form of group BWM for the criteria is presented in Appendix 2.

6.3. Group BWM-DEA-RS results In this phase, the DEA-RS scores and DMs’ preferences are integrated in group BWM-DEA-RS model (10). The group BWM-DEA-RS model is used to re-evaluate the road safety efficiency scores of provinces. This model is based on both data and preferences of a group of decision makers. In fact, group BWM-DEA-RS model tries to maximize efficiency scores by considering DMs judgment on inputs and outputs criteria. According to the Table (7) preferences and DEA-RS scores, group BWM-DEA-RS is applied to evaluate provinces efficiency in terms of road safety. Calculated scores are presented in Table (8). According to the results, Tehran and Hormozgan provinces with efficiency scores of 0.9999 have the best performance in road safety in Iran. Sistan & Baluchestan and Kerman provinces with efficiency scores of 0.9998 and 0.9996 are in the second and third ranks, respectively. Obviously, group BWM-DEA-RS model has improved the distinguish power of DEA and generated almost complete ranking of provinces. In the bottom of the Table (8), Kohgiluye & Boyerahmad province with the score of 0.4194 has the most unsafe roads in Iran. North Khorasan and Kermanshah are the second and third unsafe provinces in roads with the

19

scores of 0.4560 and 0.4881, respectively. The mean of efficiency scores is equal to 0.7772 which shows decrease in comparison to DEA-RS scores. The results conform to the provinces situation. For instance, according to the results reported in Table (8), Tehran has the most population, registered automobiles and passenger in Iran. In addition to mentioned indexes, also Tehran is among three provinces which has the highest number of speed camera and ton kilometers. Since Tehran is the capital province of Iran, hence, it has great importance in terms of economic and political development. So, it was expected that Tehran devotes the highest input indexes values to itself. Despite of high value of inputs indexes, Tehran performance in outputs indexes is acceptable. Considering high amount of automobiles, population and passengers in Tehran, number of fatalities, for example, are low in comparison to other provinces. So, Tehran efficiency score is the highest among other provinces. Moreover, Kohgiluye & Boyerahmad is one of the smallest provinces in Iran which located on the Zagros mountain range. This province is known as one of the less developed provinces in Iran, too. This factors lead to a low values of inputs indexes for Kohgiluye & Boyerahmad province. For example, due to the geographical position, constructing lengthy free/high ways is impossible. In addition, Kohgiluye & Boyerahmad province has poor performance in outputs which is not proportional to inputs indexes values. High values for output indexes relative to inputs low values lead to lowest efficiency score among 31 provinces. For better understanding the model, numerical form of group BWM-DEA-RS for the first DMU is presented in Appendix 3.

7. Validation In this section, for validating the result of the proposed group BWM-DEA-RS model, two approaches of principal component analysis (PCA) and numerical taxonomy have been applied and results are compared. In brief, PCA is a popular approach in reducing the number of variables and analyzing DMUs (Azadeh et al., 2009). The PCA model, aims to define new variables according to the linear combination of original variables and scoring DMUs based on new principle components. In this study, for validating group BWM- DEA- RS results, PCA approach has been applied, since according to the Zhou (1998) PCA and DEA contribute to more consistent results. The steps of PCA are discussed in Azadeh et al. (2009). On the other hand, numerical taxonomy is appropriate model to discriminate homogenous and non-homogenous units. The numerical taxonomy ranks units according to the distance matrix. The distance matrix will be obtained

20

by computing the distance of every two DMUs for each new measures (Rossi and Thomas, 2001). The steps of numerical taxonomy method are discussed in Azadeh et al. (2009). In the following, the results and ranking of applying group BWM- DEA- RS, PCA and numerical taxonomy approaches have been indicated in the Table (9). ---------------------------------------------Table 9 about here ----------------------------------------

It should be noted that new indicators for applying into PCA and numerical taxonomy are obtained by dividing each input variable on all outputs separately (Azadeh et al., 2009). For observing the correlation between three different models, Spearman correlation test is performed and results approves the high correlation between three models rankings. For example, correlation between the group BWM- DEA- RS and PCA is 0.895 at the 0.01 level which indicates that the proposed group BWM- DEA- RS final ranking is valid. The Spearman correlation test results are presented in Table (10). ---------------------------------------------Table 10 about here ----------------------------------------

8. Remarks for policy makers Globally, the number of road traffic deaths has irreparable socioeconomic consequences on the societies. In general, the number of road traffic deaths is considered as a development index in most countries. In our paper, also this index plays a major role in efficiency evaluations. As mentioned before, a significant part of the accidents and fatalities are both preventable and predictable. Policy makers in Iran try to reduce fatalities and improve the safety of roads by intervention policies. In summary, the intervention policies should include of policies to encourage investment on roads infrastructures, encourage automotive industries to produce more safe automobiles, policies to place fatality reduction target, encourage drivers to obey the traffic rules, evaluate the safety of roads periodically, monitoring the actions are taken and etc. In addition, according to the group BWM-DEA-RS results, it is observed that the provinces that are located in mountainous and forest areas of Iran such as Kohgiluye & Boyerahmad, Kermanshah and Gilan, have less road safety. Inversely, provinces that are located in desert, vast and center areas of Iran, such Razavi Khorasan, Kerman and Esfahan, have better road safety performances. The provinces which are located in desert, vast and center areas of Iran are larger and more developed than remaining provinces. These areas have higher free/high ways length and

21

speed camera. As mentioned before, the weights of free/high ways length and camera inputs are more than other input indexes. So, it is recommended to policy makers to improve the safety of roads in all provinces, try to build new free/high ways between provinces plus to enhance the number of speed cameras on the roads. Intervention policies and extending infrastructures such freeways and speed cameras will help drivers to have safe driving. Moreover, applying the proposed model indicates that number of fatalities plays a major role in provinces final ranking. Implementing restrictive rules for using seat belts, enhancing the safety of nationally produced automotive, using mass media for learn drivers appropriate driving behaviors, and increasing emergency medical services to deliver medical services in a shorter time could tangibly improve the road safety in poor performance provinces of Iran. Local policy makers using the results of the proposed model and recommendations have been made in this study can improve their provinces road safety situation and decrease the financial loss and fatality rate in long term. At last, since a combination of data and subjectivity of a group of DMs has been considered to estimate the efficiency scores of DMU simultaneously, the results are more reliable than traditional DEA-RS model. Thus, DMs enable to better evaluate the DMUs and apply the proposed model in measuring efficiency scores of DMUs in any managerial problem.

9. Conclusion and summary Road traffic deaths are the main cause of death among people and predicted to become the seventh leading cause of deaths by 2030. If no preventative action has taken, road safety will remain a great public health challenge for countries. Overcoming this serious issue requires that countries to address road safety issue as much as possible. Evaluating road safety performance of regions is a valuable way to improve road safety performance. The policy makers can compare the regions and learn of best-performer units to improve the performances of others. In this study, a novel model is proposed to evaluate the road safety performances of Iranian provinces. In proposed model, judgment of a group of decision makers is considered in DEA model. In our proposed model, both DMs’ preferences and data affected to decision making process. Importance of indexes is obtained by considering a group of DMs’ opinion. Another feature of proposed model is increasing the distinguish power of conventional DEA which will help decision makers to recognize the really best performer units. The proposed model is applied to investigate road safety performances of 31 provinces of Iran. The data for six inputs passenger kilometers, number of automobiles, ton kilometers, population, free/high way length, speed camera and three outputs number of

22

fatalities, injuries and crashes are collected to determine the best province. According to DMs preferences, number of fatalities is the most important index, while population and speed camera is the less important ones. Also, based on the results of the proposed group BWM-DEA-RS model, developed provinces of Iran such as Tehran have better performance in comparison with undeveloped provinces located in the mountainy and forest areas in terms of road safety. For validating the results of the proposed group BWM-DEA-RS model, two PCA and Taxonomy approaches were applied and results compared. The spearman correlation test approves high correlation between models’ results. Finally, to improve the road safety performances, recommendations have been made for policy makers. Constructing road facilities, emergency medical services centers, learning critical driving behaviors through mass media are some of the recommendations have been made according to the results of the proposed model in this study. The proposed approach has a great potential in measuring the efficiency of organizations where the preferences of DMs are crucial. For example, when the Bank managers want to know about the branches performance with the common weights obtained according to their preferences. Other sectors such as hospitals, electricity distribution companies, air ports, telecommunication companies and etc. can also benefit from the proposed model in measuring efficiency. For future studies, alternative approaches for incorporating DMs’ preferences such as FOCUM can be applied. The FOCUM is a newly proposed model that has a great potential in applying into decision making problems. Also, combining group BWM with other DEA models such as super-efficiency, network and additive DEA may be the interest of researchers in the field. Also considering ambiguity and uncertainty, in either DEA model or BWM may read to the more reliable and real results in future studies.

Acknowledgment The authors would like to thank Prof. Paolo Carbone, the Editor-in- Chief, and Dr. Amy Marconnet, the Editor of Measurement, and three reviewers for their insightful comments and suggestions. As results this paper has been improved substantially.

References

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Fig.1. Mountain, Desert and Rainforest zones of Iran

29

Fig.2. Provinces of Iran with population distribution (Person in Square Kilometer)

30

Table 1: The data for numerical example DMU

Inputs

Outputs

C1

C2

C3

C4

1

180

187

53

65

2

174

175

62

73

3

130

144

44

71

4

190

120

83

62

5

166

140

75

80

31

Table 2: The DMs’ preferences for numerical example DM 1 2

Criteria

Best &Worst Criteria

C1

C2

C3

C4

Best (C4)

6

4

3

1

Worst (C1)

1

2

3

6

Best (C3)

4

7

1

2

Worst (C2)

3

1

7

5

32

Table 3: The weights generated by BWM, group BWM and group BWM-DEA-RS BWM

Group BWM-DEA-RS

(DM1)

(DM2)

Group BWM

w1

0.0847

0.1414

0.1061

0.0959

0.1622

0.0949

0.2098

0.2508

w2

0.1526

0.0652

0.1516

0.1548

0.0941

0.1315

0.0513

0.0023

w3

0.2034

0.5109

0.2122

0.2073

0.1285

0.7155

0.0547

0.245

w4

0.5594

0.2827

0.5304

0.5418

0.6151

0.0579

0.6841

0.5017

Weights

33

(DMU1)

(DMU2)

(DMU3)

(DMU4)

(DMU5)

Table 4: The efficiency scores generated by DEA-RS and group BWM-DEA-RS models DMU

Efficiency Scores DEA

Group BWM-DEA-RS

1

1

1

2

0.855

0.845

3

0.928

0.879

4

1

0.980

5

0.731

0.717

34

Table 5: Road safety data for provinces of Iran Inputs

Outputs

Provinces Passengerkilometer

Tonkilometer

Free/High way length

Registered automobile

Speed camera

Population

Fatalities

Injuries

Crashes

3’310

17’396

587

42’459

27

3’909’652

470

15’415

12’364

2’233

6’528

302

40’105

0

3’265’219

444

11’429

6’794

Ardabil

1’058

2’240

137

14’201

13

1’270’420

145

4’031

2’162

Esfahan

7’180

45’057

2’094

106’856

105

5’120’850

239

24’697

7’135

Alborz

1’171

2’132

176

10’470

21

2’712’400

182

8’368

5’689

Ilam

1’790

1’905

87

8’286

4

580’158

110

3’485

1’538

Bushehr

1’418

6’724

639

31’393

46

1’163’400

241

4’901

2’028

Tehran

13’197

26’719

650

448’419

79

13’267’637

315

41’384

10’304

1’044

4’407

226

13’063

4

947’763

192

3’733

1’169

2’215

8’902

404

9’027

47

768’898

175

3’436

1’716

11’229

28’670

1’261

124’395

88

6’434’501

731

27’632

8’152

778

2’120

169

13’920

16

863’092

192

4’207

1’901

Khuzestan

3’662

41’870

1’188

94’609

22

4’710’509

627

18’943

5’826

Zanjan

1’537

6’230

313

14’726

20

1’057’461

222

5’304

2’769

East Azerbaijan West Azerbaijan

Chaharmahal & Bakhtiari SouthKhorasan Razavi Khorasan North Khorasan

Semnan

4’262

14’761

717

10’481

49

702’350

238

4’395

3’537

Sistan & Baluchestan

2’995

8’119

243

26’428

24

2’775’014

693

6’228

3’015

Fars

6’229

24’464

1’590

106’452

136

4’851’274

1’076

24’900

9’086

Qazvin

2’125

7’857

578

17’540

24

1’273’761

307

6’126

2’284

Qom

2’817

10’855

420

23’871

39

1’292’283

218

8’669

2’271

Kurdistan

1’440

4’980

226

15’452

0

1’603’011

324

5’624

4’021

Kerman

3’102

30’700

1’784

52’313

31

3’164’718

697

13’624

2’693

Kermanshah

2’067

5’859

379

22’419

0

1’952’434

333

10’803

5’445

Kohgiluye& Boyerahmad

680

2’607

110

7’946

4

713’052

144

4’395

2’152

Golestan

1’528

3’532

247

29’713

4

1’868’819

237

9’412

3’020

Gilan

2’317

5’919

475

33’445

16

2’530’696

509

12’475

8’104

Lorestan

2’057

11’213

489

25’351

42

1’760’649

390

8’684

4’488

Mazandaran

2’182

7’247

818

48’165

8

3’283’582

461

15’418

5’590

Markazi

2’623

14’317

745

22’866

26

1’429’475

434

7’255

5’680

Hormozgan

1’377

28’853

705

40’019

40

1’776’415

290

3’123

2’761

Hamedan

2’598

7’916

583

27’883

11

1’738’234

359

7’470

2’948

Yazd

1’608

25’324

686

34’464

36

1’138’533

134

7’500

1’530

35

Table 6: The results of DEA-RS and Group BWM-DEA-RS models

East Azerbaijan

Efficiency Scores DEAGroup BWMRS DEA-RS 0.6550 0.6533

West Azerbaijan

0.6941

0.6916

Qazvin

0.8045

0.7992

Ardabil

0.7817

0.776

Qom

0.9395

0.9304

Esfahan

1

0.9991

Kurdistan

0.6246

0.6215

Alborz

0.8959

0.8926

Kerman

1

0.9996

Ilam

0.9144

0.9102

0.4900

0.4881

Bushehr

1

0.9459

0.4194

0.4157

Tehran Chaharmahal & Bakhtiari South Khorasan

1

0.9999

Kermanshah Kohgiluye& Boyerahmad Golestan

0.5742

0.5718

0.8076

0.8017

Gilan

0.4925

0.4909

1

0.9986

Lorestan

0.5624

0.5282

Razavi Khorasan

1

0.9995

Mazandaran

0.6404

0.6379

North Khorasan

0.5630

0.456

Markazi

0.6006

0.5962

Khuzestan

0.8316

0.8309

Hormozgan

1

0.9999

Zanjan

0.5832

0.5816

Hamedan

0.7948

0.7911

Semnan

1

0.9992

Yazd

1

0.9995

Sistan &Baluchestan

1

0.9998

Mean

0.7871

0.7772

Provinces

Provinces Fars

36

Efficiency Scores DEAGroup BWMRS DEA-RS 0.7316 0.6882

Table 7: Preference values of the best criterion over all the criteria and all criteria over worst criterion DM

1

2

3

4

5

Best &Worst Criteria Best (Fatalities) Worst (Population) Best (Fatalities) Worst (Speed camera) Best (Fatalities) Worst (Population) Best (Fatalities) Worst (Speed camera) Best (Fatalities) Worst (Registered automobile)

Passengerkilometer

Tonkilometer

Free/High way length

Registered automobile

Speed camera

Population

Fatalities

Injuries

Crashes

6

6

5

4

8

9

1

2

3

5

4

6

6

3

1

9

8

7

5

6

4

3

8

7

1

2

3

5

3

4

5

1

2

8

7

6

4

5

6

4

7

8

1

2

2

5

4

4

5

2

1

8

7

6

4

6

5

4

9

7

1

2

3

5

4

5

6

1

3

9

8

7

6

5

4

9

7

8

1

2

3

6

4

5

1

2

3

9

8

7

37

Table 8: The weights generated by BWM, Group BWM and Group BWM-DEA-RS models for inputs and outputs BWM

Group BWMDEA-RS (Mean)

DM1

DM2

DM3

DM4

DM5

Group BWM

w1

0.0638

0.0710

0.0854

0.0913

0.0649

0.0724

0.0818

w2

0.0638

0.0592

0.0683

0.0609

0.0779

0.0724

0.0041

Free/High way

w3

0.0766

0.0888

0.05695

0.0731

0.0973

0.0724

0.1177

Registered automobiles Speed camera

w4

0.0958

0.1184

0.0854

0.0913

0.0247

0.0490

0.0008

w5

0.0479

0.0276

0.0488

0.0261

0.0556

0.0280

0.1353

population

w6

0.0255

0.0507

0.0284

0.0522

0.0486

0.0280

0.0003

Fatalities

w7

0.3067

0.2881

0.2847

0.3002

0.3060

0.3154

0.4639

Injuries

w8

0.1916

0.1776

0.1708

0.1827

0.1947

0.2172

0.0720

Crashes

w9

0.1277

0.1184

0.1708

0.1218

0.1298

0.1448

0.1236

Criteria

Weights

Passenger kilometer Ton kilometer

38

Table 9: Results of applying group BWM-DEA, PCA and Taxonomy DMU

Group BWM-DEA

PCA

Taxonomy

Score

Rank

Score

Rank

Score

Rank

East Azerbaijan

0.6533

19

-0.84983

27

17.81374

24

West Azerbaijan

0.6916

17

-0.80124

24

18.21112

27

Ardabil

0.776

16

-0.34377

17

17.11971

18

Esfahan

0.9991

6

2.132593

2

12.05374

1

Alborz

0.8926

11

-0.76801

23

18.06164

26

Ilam

0.9102

10

-0.48908

18

17.66934

21

Bushehr

0.9459

8

0.407022

8

14.69644

7

Tehran Chaharmahal & Bakhtiari South-Khorasan

0.9999

1

4.48297

1

12.28392

3

0.8017

13

-0.1447

13

16.71134

16

0.9986

7

0.451615

7

14.52614

5

Razavi Khorasan

0.9995

4

0.708394

6

15.22538

9

North Khorasan

0.456

28

-0.83624

26

17.79984

23

Khuzestan

0.8309

12

0.268353

9

15.68634

10

Zanjan

0.5816

23

-0.70745

21

17.20582

19

Semnan

0.9992

5

0.241882

11

14.88499

8

Sistan & Baluchestan

0.9998

2

0.243764

10

16.44348

14

Fars

0.6882

18

-0.25358

14

16.38683

13

Qazvin

0.7992

14

-0.2872

16

16.2469

12

Qom

0.9304

9

0.114357

12

15.78499

11

Kurdistan

0.6215

21

-0.9862

28

18.30438

28

Kerman

0.9996

3

0.78596

5

14.62356

6

Kermanshah Kohgiluye& Boyerahmad Golestan

0.4881

27

-1.16416

29

18.60145

30

0.4157

29

-1.31569

31

18.85072

31

0.5718

24

-0.62267

19

17.88782

25

Gilan

0.4909

26

-1.18332

30

18.54323

29

Lorestan

0.5282

25

-0.74082

22

17.23194

20

Mazandaran

0.6379

20

-0.70022

20

17.70152

22

Markazi

0.5962

22

-0.80823

25

17.08799

17

Hormozgan

0.9999

1

1.955306

3

12.23909

2

Hamedan

0.7911

15

-0.26009

15

16.62862

15

Yazd

0.9995

4

1.470309

4

12.69329

4

39

Table 10: The Spearman correlation test among different models rankings

Group BWMDEA-RS PCA

Group BWMDEA-RS

PCA

Taxonomy

1

0.895(*)

0.831(*)

-

1

0.953(*)

Taxonomy 1 *Correlation is significant at the 0.01 level

40

Appendix 1 D E A  R S

 o



M ax f



3310 w1

 17396 w 2

 587 w 3

 42459 w 4

 27 w 5

 3903652 w 6 ;

s .t : 3 3 1 0 w1  1 7 3 9 6 w 2  5 8 7 w 3  4 2 4 5 9 w 4  2 7 w 5  3 9 0 3 6 5 2 w 6  ( 4 7 0 w 7  1 5 4 1 5 w 8  1 2 3 6 4 w 9 )  0 ; 2 2 3 3 w1  6 5 2 8 w 2  3 0 2 w 3  4 0 1 0 5 w 4  0 w 5  3 2 6 5 2 1 9 w 6  ( 4 4 4 w 7  1 1 4 2 9 w 8  6 7 9 4 w 9 )  0 ; 1 0 5 8 w1  2 2 4 0 w 2  1 3 7 w 3  1 4 2 0 1 w 4  1 3 w 5  1 2 7 0 4 2 0 w 6  (1 4 5 w 7  4 0 3 1 w 8  2 1 6 2 w 9 )  0 ; 7 1 8 0 w1  4 5 0 5 7 w 2  2 0 9 4 w 3  1 0 6 8 5 6 w 4  1 0 5 w 5  5 1 2 0 8 5 0 w 6  ( 2 3 9 w 7  2 4 6 9 7 w 8  7 1 3 5 w 9 )  0 ; 1 1 7 1 w1  2 1 3 2 6 w 2  1 7 6 w 3  1 0 4 7 0 w 4  2 1 w 5  2 7 1 2 4 0 0 w 6  0 (1 8 2 w 7  8 3 6 8 w 8  5 6 8 9 w 9 )  0 ; 1 7 9 0 w1  1 9 0 5 w 2  8 7 w 3  8 2 8 6 w 4  4 w 5  5 8 0 1 5 8 w 6  (1 1 0 w 7  3 4 8 5 w 8  1 5 3 8 w 9 )  0 ; 1 4 1 8 w1  6 7 2 4 w 2  6 3 9 w 3  3 1 3 9 3 w 4  4 6 w 5  1 1 6 3 4 0 0 w 6  ( 2 4 1 w 7  4 9 0 1 w 8  2 0 2 8 w 9 )  0 ; 1 3 1 9 7 w1  2 6 7 1 9 w 2  6 5 0 w 3  4 4 8 4 1 9 w 4  7 9 w 5  1 3 2 6 7 6 3 7 w 6  ( 3 1 5 w 7  4 1 3 8 4 w 8  1 0 3 0 4 w 9 )  0 ; 1 0 4 4 w1  4 4 0 7 w 2  2 2 6 w 3  1 3 0 6 3 w 4  4 w 5  9 4 7 7 6 3 w 6  (1 9 2 w 7  3 7 3 3 w 8  1 1 6 9 w 9 )  0 ; 2 2 1 5 w1  8 9 0 2 w 2  4 0 4 w 3  9 0 2 7 w 4  4 7 w 5  7 6 8 8 9 8 w 6  (1 7 5 w 7  3 4 3 6 w 8  1 7 1 6 w 9 )  0 ; 1 1 2 2 9 w1  2 8 6 7 0 w 2  1 2 6 1 w 3  1 2 4 3 9 5 w 4  8 8 w 5  6 4 3 4 5 0 1 w 6  ( 7 3 1 w 7  2 7 6 3 2 w 8  8 1 5 2 w 9 )  0 ; 7 7 8 w1  2 1 2 0 w 2  1 6 9 w 3  1 3 9 2 0 w 4  1 6 w 5  8 6 3 0 9 2 w 6  (1 9 2 w 7  4 2 0 7 w 8  1 9 0 1 w 9 )  0 ; 3 6 6 2 w1  4 1 8 7 0 w 2  1 1 8 8 w 3  9 4 6 0 9 w 4  2 2 w 5  4 7 1 0 5 0 9 w 6  ( 6 2 7 w 7  1 8 9 4 3 w 8  5 8 2 6 w 9 )  0 ; 1 5 3 7 w1  6 2 3 0 w 2  3 1 3 w 3  1 4 7 2 6 w 4  2 0 w 5  1 0 5 7 4 6 1 w 6  ( 2 2 2 w 7  5 3 0 4 w 8  2 7 6 9 w 9 )  0 ; 4 2 6 2 w1  1 4 7 6 1 w 2  7 1 7 w 3  1 0 4 8 1 w 4  4 9 w 5  7 0 2 3 5 0 w 6  ( 2 3 8 w 7  4 3 9 5 w 8  3 5 3 7 w 9 )  0 ; 2 9 9 5 w1  8 1 1 9 w 2  2 4 3 w 3  2 6 4 2 8 w 4  2 4 w 5  2 7 7 5 0 1 4 w 6  ( 6 9 3 w 7  6 2 2 8 w 8  3 0 1 5 w 9 )  0 ; 6 2 2 9 w1  2 4 4 6 4 w 2  1 5 9 0 w 3  1 0 6 4 5 2 w 4  1 3 6 w 5  4 8 5 1 2 7 4 w 6  (1 0 7 6 w 7  2 4 9 0 0 w 8  9 0 8 6 w 9 )  0 ; 2 1 2 5 w1  7 8 5 7 w 2  5 7 8 w 3  1 7 5 4 0 w 4  2 4 w 5  1 2 7 3 7 6 1 w 6  ( 3 0 7 w 7  6 1 2 6 w 8  2 2 8 4 w 9 )  0 ; 2 8 1 7 w1  1 0 8 5 5 w 2  4 2 0 w 3  2 3 8 7 1 w 4  3 9 w 5  1 2 9 2 2 8 3 w 6  ( 2 1 8 w 7  8 6 6 9 w 8  2 2 7 1 w 9 )  0 ; 1 4 4 0 w1  4 9 8 0 w 2  2 2 6 w 3  1 5 4 5 2 w 4  0 w 5  1 6 0 3 0 1 1 w 6  ( 3 2 4 w 7  5 6 2 4 w 8  4 0 2 1 w 9 )  0 ; 3 1 0 2 w1  3 0 7 0 0 w 2  1 7 8 4 w 3  5 2 3 1 3 w 4  3 1 w 5  3 1 6 4 7 1 8 w 6  ( 6 9 7 w 7  1 3 6 2 4 w 8  2 6 9 3 w 9 )  0 ; 2 0 6 7 w1  5 8 5 9 w 2  3 7 9 w 3  2 2 4 1 9 w 4  0 w 5  1 9 5 2 4 3 4 w 6  ( 3 3 3 w 7  1 0 8 0 3 w 8  5 4 4 5 w 9 )  0 ; 6 8 0 w1  2 6 0 7 w 2  1 1 0 w 3  7 9 4 6 w 4  4 w 5  7 1 3 0 5 2 w 6  (1 4 4 w 7  4 3 9 5 w 8  2 1 5 2 w 9 )  0 ; 1 5 2 8 w1  3 5 3 2 w 2  2 4 7 w 3  2 9 7 1 3 w 4  4 w 5  1 8 6 8 8 1 9 w 6  ( 2 3 7 w 7  9 4 1 2 w 8  3 0 2 0 w 9 )  0 ; 2 3 1 7 w1  5 9 1 9 w 2  4 7 5 w 3  3 3 4 4 5 w 4  1 6 w 5  2 5 3 0 6 9 6 w 6  ( 5 0 9 w 7  1 2 4 7 5 w 8  8 1 0 4 w 9 )  0 ; 2 0 5 7 w1  1 1 2 1 3 w 2  4 8 9 w 3  2 5 3 5 1 w 4  4 2 w 5  1 7 6 0 6 4 9 w 6  ( 3 9 0 w 7  8 6 8 4 w 8  4 4 8 8 w 9 )  0 ; 2 1 8 2 w1  7 2 4 7 w 2  8 1 8 w 3  4 8 1 6 5 w 4  8 w 5  3 2 8 3 5 8 2 w 6  ( 4 6 1 w 7  1 5 4 1 8 w 8  5 5 9 0 w 9 )  0 ; 2 6 2 3 w1  1 4 3 1 7 w 2  7 4 5 w 3  2 2 8 6 6 w 4  2 6 w 5  1 4 2 9 4 7 5 w 6  ( 4 3 4 w 7  7 2 5 5 w 8  5 6 8 0 w 9 )  0 ; 1 3 7 7 w1  2 8 8 5 3 w 2  7 0 5 w 3  4 0 0 1 9 w 4  4 0 w 5  1 7 7 6 4 1 5 w 6  (1 9 2 w 7  3 1 2 3 w 8  2 7 6 1 w 9 )  0 ; 2 5 9 8 w1  7 9 1 6 w 2  5 8 3 w 3  2 7 8 8 3 w 4  1 1 w 5  1 7 3 8 2 3 4 w 6  ( 3 5 9 w 7  7 4 7 0 w 8  2 9 4 8 w 9 )  0 ; 1 6 0 8 w1  2 5 3 2 4 w 2  6 8 6 w 3  3 4 4 6 4 w 4  3 6 w 5  1 1 3 8 5 3 3 w 6  (1 3 4 w 7  7 5 0 0 w 8  1 5 3 0 w 9 )  0 ; 470 w

7

15415 w

8

12364 w

9

1;

w1 , w 2 , w 3 , w 4 , w 5 , w 6 , w 7 , w 8 , w 9



0 ;

41

Appendix 2 M in f2 | w 7



1   2

 6 w1

|

  3

1 ; | w 7

  4  6 w 2

  5 ; |

1 ; | w 7

 5 w 3

|

1 ; | W 7

|w 7  8 w 5 |  1 ;

|w 7  9 w 6 |  1 ;

|w 7  2 w 8 |  1 ;

|w 7  3 w 9 |  1 ;

|w1  5 w 6 |  1 ;

|w 2  4 w 6 |  1 ;

|w 3  6 w 6 |  1 ; |w 4  6 w 6 |  1 ;

|w 5  3 w 6 |  1 ;

|w 8  8 w 6 |  1 ;

|w 9  7 w 6 |  1 ;

|w 7  5 w1 |  2 ; |w 7  6 w 2 |  2 ;

|w 7  4 w 3 |  2 ;

|w 7  8 w 5 |  2 ; |w 7  7 w 6 |  2 ;

|w 7  2 w 8 |  2 ; |w 7  3 w 9 |  2 ;

|w1  5 w 5 |  2 ;

|w 3  4 w 5 |  2 ;

|w 2  3 w 5 |  2 ;

|w 7  3 w 4 |  2 ;

|w 4  5 w 5 |  2 ;

|w 6  2 w 5 |  2 ;

|w 8  7 w 5 |  2 ; |w 9  6 w 5 |  2 ;

|w 7  4 w1 |  3 ;

|w 7  5 w 2 |  3 ;

|w 7  6 w 3 |  3 ;

|w 7  4 w 4 |  3 ;

|w 7  7 w 5 |  3 ; |w 7  8 w 6 |  3 ;

|w 7  2 w 8 |  3 ;

|w 7  2 w 9 |  3 ;

|w1  5 w 6 |  3 ; |w 2  4 w 6 |  3 ;

|w 3  4 w 6 |  3 ; |w 4  5 w 6 |  3 ;

|w 5  2 w 6 |  3 ; |w 8  7 w 6 |  3 ;

|w 9  6 w 6 |  3 ;

|w 7  4 w1 |  4 ; |w 7  6 w 2 |  4 ; |w 7  5 w 3 |  4 ; |w 7  4 w 4 |  4 ; |w 7  9 w 5 |  4 ; |w 7  7 w 6 |  2 ;

|w 7  2 w 8 |  4 ; |w 7  3 w 9 |  4 ;

|w1  5 w 5 |  4 ; |w 2  4 w 5 |  4 ; |w 3  5 w 5 |  4 ; |w 4  6 w 5 |  4 ; |w 6  3 w 5 |  4 ; |w 8  8 w 5 |  4 ;

|w 9  7 w 5 |  4 ;

|w 7  6 w1 |  5 ; |w 7  5 w 2 |  5 ;

|w 7  4 w 3 |  5 ; |w 7  9 w 4 |  5 ;

|w 7  7 w 5 |  5 ; |w 7  8 w 6 |  5 ; |w 7  2 w 8 |  5 ;

|w 7  3 w 9 |  5 ;

|w1  6 w 4 |  5 ; |w 2  4 w 4 |  5 ; |w 3  5 w 4 |  5 ; |w 5  2 w 4 |  5 ; |w 6  3 w 4 |  5 ;

|w 8  8 w 4 |  5 ;

|w 9  7 w 4 |  5 ;

w1  w 2  w 3  w 4  w 5  w 6  w 7  w 8  w 9  1 ; w1 , w 2 , w 3 , w 4 , w 5 , w 6 , w 7 , w 8 , w 9



0 ;

42

 4 w 4

|

1 ;

Appendix 3 M a x f1  3 3 1 0 w 1  1 7 3 9 6 w 2  5 8 7 w 3  4 2 4 5 9 w 4  2 7 w 5  3 9 0 3 6 5 2 w 6  0 . 6 5 5  ( 4 7 0 w 7  1 5 4 1 5 w 8  1 2 3 6 4 w 9 ) ; M a x f2   1   2   3   4   5 ; s .t : 3 3 1 0 w1  1 7 3 9 6 w 2  5 8 7 w 3  4 2 4 5 9 w 4  2 7 w 5  3 9 0 3 6 5 2 w 6  0 . 6 5 5  ( 4 7 0 w 7  1 5 4 1 5 w 8  1 2 3 6 4 w 9 )  0 ; 2 2 3 3 w1  6 5 2 8 w 2  3 0 2 w 3  4 0 1 0 5 w 4  0 w 5  3 2 6 5 2 1 9 w 6  0 . 6 9 4 1 ( 4 4 4 w 7  1 1 4 2 9 w 8  6 7 9 4 w 9 )  0 ; 1 0 5 8 w1  2 2 4 0 w 2  1 3 7 w 3  1 4 2 0 1 w 4  1 3 w 5  1 2 7 0 4 2 0 w 6  0 . 7 8 1 7  ( 1 4 5 w 7  4 0 3 1 w 8  2 1 6 2 w 9 )  0 ; 7 1 8 0 w1  4 5 0 5 7 w 2  2 0 9 4 w 3  1 0 6 8 5 6 w 4  1 0 5 w 5  5 1 2 0 8 5 0 w 6  1 ( 2 3 9 w 7  2 4 6 9 7 w 8  7 1 3 5 w 9 )  0 ; 1 1 7 1 w1  2 1 3 2 6 w 2  1 7 6 w 3  1 0 4 7 0 w 4  2 1 w 5  2 7 1 2 4 0 0 w 6  0 . 8 9 5 9  ( 1 8 2 w 7  8 3 6 8 w 8  5 6 8 9 w 9 )  0 ; 1 7 9 0 w1  1 9 0 5 w 2  8 7 w 3  8 2 8 6 w 4  4 w 5  5 8 0 1 5 8 w 6  0 . 9 1 4 4  ( 1 1 0 w 7  3 4 8 5 w 8  1 5 3 8 w 9 )  0 ; 1 4 1 8 w1  6 7 2 4 w 2  6 3 9 w 3  3 1 3 9 3 w 4  4 6 w 5  1 1 6 3 4 0 0 w 6  1 ( 2 4 1 w 7  4 9 0 1 w 8  2 0 2 8 w 9 )  0 ; 1 3 1 9 7 w1  2 6 7 1 9 w 2  6 5 0 w 3  4 4 8 4 1 9 w 4  7 9 w 5  1 3 2 6 7 6 3 7 w 6  1 ( 3 1 5 w 7  4 1 3 8 4 w 8  1 0 3 0 4 w 9 )  0 ; 1 0 4 4 w1  4 4 0 7 w 2  2 2 6 w 3  1 3 0 6 3 w 4  4 w 5  9 4 7 7 6 3 w 6  0 . 8 0 6 7  ( 1 9 2 w 7  3 7 3 3 w 8  1 1 6 9 w 9 )  0 ; 2 2 1 5 w1  8 9 0 2 w 2  4 0 4 w 3  9 0 2 7 w 4  4 7 w 5  7 6 8 8 9 8 w 6  1 ( 1 7 5 w 7  3 4 3 6 w 8  1 7 1 6 w 9 )  0 ; 1 1 2 2 9 w1  2 8 6 7 0 w 2  1 2 6 1 w 3  1 2 4 3 9 5 w 4  8 8 w 5  6 4 3 4 5 0 1 w 6  1 ( 7 3 1 w 7  2 7 6 3 2 w 8  8 1 5 2 w 9 )  0 ; 7 7 8 w1  2 1 2 0 w 2  1 6 9 w 3  1 3 9 2 0 w 4  1 6 w 5  8 6 3 0 9 2 w 6  0 . 5 6 3  ( 1 9 2 w 7  4 2 0 7 w 8  1 9 0 1 w 9 )  0 ; 3 6 6 2 w1  4 1 8 7 0 w 2  1 1 8 8 w 3  9 4 6 0 9 w 4  2 2 w 5  4 7 1 0 5 0 9 w 6  0 . 8 3 1 6  ( 6 2 7 w 7  1 8 9 4 3 w 8  5 8 2 6 w 9 )  0 ; 1 5 3 7 w1  6 2 3 0 w 2  3 1 3 w 3  1 4 7 2 6 w 4  2 0 w 5  1 0 5 7 4 6 1 w 6  0 . 5 8 3 2  ( 2 2 2 w 7  5 3 0 4 w 8  2 7 6 9 w 9 )  0 ; 4 2 6 2 w1  1 4 7 6 1 w 2  7 1 7 w 3  1 0 4 8 1 w 4  4 9 w 5  7 0 2 3 5 0 w 6  1 ( 2 3 8 w 7  4 3 9 5 w 8  3 5 3 7 w 9 )  0 ; 2 9 9 5 w1  8 1 1 9 w 2  2 4 3 w 3  2 6 4 2 8 w 4  2 4 w 5  2 7 7 5 0 1 4 w 6  1 ( 6 9 3 w 7  6 2 2 8 w 8  3 0 1 5 w 9 )  0 ; 6 2 2 9 w1  2 4 4 6 4 w 2  1 5 9 0 w 3  1 0 6 4 5 2 w 4  1 3 6 w 5  4 8 5 1 2 7 4 w 6  0 . 7 3 1 6  ( 1 0 7 6 w 7  2 4 9 0 0 w 8  9 0 8 6 w 9 )  0 ; 2 1 2 5 w1  7 8 5 7 w 2  5 7 8 w 3  1 7 5 4 0 w 4  2 4 w 5  1 2 7 3 7 6 1 w 6  0 . 8 0 4 5  ( 3 0 7 w 7  6 1 2 6 w 8  2 2 8 4 w 9 )  0 ; 2 8 1 7 w1  1 0 8 5 5 w 2  4 2 0 w 3  2 3 8 7 1 w 4  3 9 w 5  1 2 9 2 2 8 3 w 6  0 . 9 3 9 5  ( 2 1 8 w 7  8 6 6 9 w 8  2 2 7 1 w 9 )  0 ; 1 4 4 0 w1  4 9 8 0 w 2  2 2 6 w 3  1 5 4 5 2 w 4  0 w 5  1 6 0 3 0 1 1 w 6  0 . 6 2 4 6  ( 3 2 4 w 7  5 6 2 4 w 8  4 0 2 1 w 9 )  0 ; 3 1 0 2 w1  3 0 7 0 0 w 2  1 7 8 4 w 3  5 2 3 1 3 w 4  3 1 w 5  3 1 6 4 7 1 8 w 6  1 ( 6 9 7 w 7  1 3 6 2 4 w 8  2 6 9 3 w 9 )  0 ; 2 0 6 7 w1  5 8 5 9 w 2  3 7 9 w 3  2 2 4 1 9 w 4  0 w 5  1 9 5 2 4 3 4 w 6  0 . 4 9 0 0  ( 3 3 3 w 7  1 0 8 0 3 w 8  5 4 4 5 w 9 )  0 ; 6 8 0 w1  2 6 0 7 w 2  1 1 0 w 3  7 9 4 6 w 4  4 w 5  7 1 3 0 5 2 w 6  0 . 4 1 9 4  ( 1 4 4 w 7  4 3 9 5 w 8  2 1 5 2 w 9 )  0 ; 1 5 2 8 w1  3 5 3 2 w 2  2 4 7 w 3  2 9 7 1 3 w 4  4 w 5  1 8 6 8 8 1 9 w 6  0 . 5 7 4 2  ( 2 3 7 w 7  9 4 1 2 w 8  3 0 2 0 w 9 )  0 ; 2 3 1 7 w1  5 9 1 9 w 2  4 7 5 w 3  3 3 4 4 5 w 4  1 6 w 5  2 5 3 0 6 9 6 w 6  0 . 4 9 2 5  ( 5 0 9 w 7  1 2 4 7 5 w 8  8 1 0 4 w 9 )  0 ; 2 0 5 7 w1  1 1 2 1 3 w 2  4 8 9 w 3  2 5 3 5 1 w 4  4 2 w 5  1 7 6 0 6 4 9 w 6  0 . 5 6 2 4  ( 3 9 0 w 7  8 6 8 4 w 8  4 4 8 8 w 9 )  0 ; 2 1 8 2 w1  7 2 4 7 w 2  8 1 8 w 3  4 8 1 6 5 w 4  8 w 5  3 2 8 3 5 8 2 w 6  0 . 6 4 0 4  ( 4 6 1 w 7  1 5 4 1 8 w 8  5 5 9 0 w 9 )  0 ; 2 6 2 3 w1  1 4 3 1 7 w 2  7 4 5 w 3  2 2 8 6 6 w 4  2 6 w 5  1 4 2 9 4 7 5 w 6  0 . 6 0 0 6  ( 4 3 4 w 7  7 2 5 5 w 8  5 6 8 0 w 9 )  0 ; 1 3 7 7 w1  2 8 8 5 3 w 2  7 0 5 w 3  4 0 0 1 9 w 4  4 0 w 5  1 7 7 6 4 1 5 w 6  1 ( 1 9 2 w 7  3 1 2 3 w 8  2 7 6 1 w 9 )  0 ; 2 5 9 8 w1  7 9 1 6 w 2  5 8 3 w 3  2 7 8 8 3 w 4  1 1 w 5  1 7 3 8 2 3 4 w 6  0 . 7 9 4 8  ( 3 5 9 w 7  7 4 7 0 w 8  2 9 4 8 w 9 )  0 ; 1 6 0 8 w1  2 5 3 2 4 w 2  6 8 6 w 3  3 4 4 6 4 w 4  3 6 w 5  1 1 3 8 5 3 3 w 6  1 ( 1 3 4 w 7  7 5 0 0 w 8  1 5 3 0 w 9 )  0 ;

43

| w7

 6 w 1 |  1 ; | w 7

 6w2

|  1 ; | w 7

 5w3

|  1 ; | W 7

|w 7  8 w 5 | 1 ; |w 7  9 w 6 | 1 ; |w 7  2 w 8 | 1 ; |w 7  3 w 9 | 1 ; | w1  5 w 6 |   1 ; | w 2  4 w 6 |   1 ; | w 3  6 w 6 |   1 ; | w 4  6 w 6 |   1 ; |w 5  3 w 6 | 1 ; |w 8  8 w 6 | 1 ; |w 9  7 w 6 | 1 ;

| w 7  5 w1 |   2 ; | w 7  6 w 2 |   2 ; | w 7  4 w 3 |   2 ; | w 7  3 w 4 |   2 ; |w 7  8 w 5 |  2 ; |w 7  7 w 6 |  2 ; |w 7  2 w 8 |  2 ; |w 7  3 w 9 |  2 ; | w1  5 w 5 |   2 ; | w 2  3 w 5 |   2 ; | w 3  4 w 5 |   2 ; |w 4  5 w 5 |  2 ; |w 6  2 w 5 |  2 ; |w 8  7 w 5 |  2 ; |w 9  6 w 5 |  2 ;

| w 7  4 w1 |   3 ; | w 7  5 w 2 |   3 ; | w 7  6 w 3 |   3 ; | w 7  4 w 4 |   3 ; |w 7  7 w 5 |  3 ; |w 7  8 w 6 |  3 ; |w 7  2 w 8 |  3 ; |w 7  2 w 9 |  3 ; | w1  5 w 6 |   3 ; | w 2  4 w 6 |   3 ; | w 3  4 w 6 |   3 ; | w 4  5 w 6 |   3 ; |w 5  2 w 6 |  3 ; |w 8  7 w 6 |  3 ; |w 9  6 w 6 |  3 ;

| w 7  4 w1 |   4 ; | w 7  6 w 2 |   4 ; | w 7  5 w 3 |   4 ; | w 7  4 w 4 |   4 ; |w 7  9 w 5 |  4 ; |w 7  7 w 6 |  2 ; |w 7  2 w 8 |  4 ; |w 7  3 w 9 |  4 ; | w1  5 w 5 |   4 ; | w 2  4 w 5 |   4 ; | w 3  5 w 5 |   4 ; | w 4  6 w 5 |   4 ; |w 6  3 w 5 |  4 ; |w 8  8 w 5 |  4 ; |w 9  7 w 5 |  4 ;

| w 7  6 w1 |   5 ; | w 7  5 w 2 |   5 ; | w 7  4 w 3 |   5 ; | w 7  9 w 4 |   5 ; |w 7  7 w 5 |  5 ; |w 7  8 w 6 |  5 ; |w 7  2 w 8 |  5 ; |w 7  3 w 9 |  5 ; | w1  6 w 4 |   5 ; | w 2  4 w 4 |   5 ; | w 3  5 w 4 |   5 ; | w 5  2 w 4 |   5 ; |w 6  3 w 4 |  5 ; |w 8  8 w 4 |  5 ; |w 9  7 w 4 |  5 ;

w1  w 2  w 3  w 4  w 5  w 6  w 7  w 8  w 9  1 ; w1 , w 2 , w 3 , w 4 , w 5 , w 6 , w 7 , w 8 , w 9

 0;

44

 4w4

|  1 ;

Declaration of interests

☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

Declarations of interest: none

45

Graphical Abstract

The model considers relative efficiency and DMs’ preferences at the same time Calculating weights using BWM Combining BWM and DEA to incorporate DMs’ preferences

Selecting inputs and outputs for road safety Using DEA to calculate efficiency

46

Solving biobjective model via min-max approach

Estimating efficiency of Iranian provinces based on integrated BWMDEA model

Highlights 

Developing DEA-based road safety model based on decision makers’ preferences.



Introducing a novel group BWM for considering DMs’ judgments, simultaneously



Estimating Final road safety efficiencies based on group BWM-DEA-RS model



Investigating road safety performance of provinces in Iran.

47