42

CHAPTER 3

MODEL FOR ASSESSMENT OF EFFICIENCY OF BUS

DEPOTS USING DATA ENVELOPMENT ANALYSIS

3.1 INTRODUCTION

The concept of productivity involves relationship in terms of the

quantified output obtained from any system and input resources utilized for

the smooth running of the operation of the system. Productivity broadly

relates to the efficient and effective use of existing resources with constraints

inherent in the business of producing goods or services. It is determined by

dividing the output by the inputs. When the productivity of two firms is

compared, the more productive firm produces more output with the same

inputs or it produces the same ouput with less inputs. Productivity

improvement is one of the basic functions of any mangement.

The bus transit system has gained significance to handle the urban

traffic. In most of the metropolitan cities in India, for a long time the bus

depots of the transit system have always been planned and regulated just

according to experiences.This has resulted in serious problems such as lower

service efficiency, inefficient operations and administration and low bus

route spacing coverage, etc. At the same time, with the acceleration of the

urban socio-economic development, the public desires to have higher quality

and new services from the transit system. In order to appropriately deploy

buses, make full use of transit resources, and provide convenient and good

service to passengers, it is necessary to assess the performance of bus depots

43

to provide a decision-making foundation for the management for sustained

operation. In this study an attempt has been made to develop a model to

assess the efficiency of bus depots of a metropolitan city using Data

Envelopment Analysis (DEA) and also apply it to a real case.

3.2 LITERATURE

Some of the earlier studies related to the performance assessment of

transport sector is presented below. Hensher and Daniels (1995) have

measured the performance of bus transport by means of ratio analysis and

econometric methods. Sing (2000) has used index number approach to

estimate the growth and relative level of productivity of 21 state transport

undertakings.The regression analysis has also been used to investigate the

source of growth and differences in levels of productivity. Hjalmarsson and

Odeck (1996) assessed the performance of trucks used in road construction

and maintenance using DEA. Sing and venkatesh (2002) have compared the

efficiency of 21 state transport udertakings by the estimation of Stochastic

Frontier production using the method of maximum lklihood. Joneth and

Darinka (2004) calculated the efficiency of British bus transport industry by

using DEA. A heteroskedastic error component model with unbalanced panel

data has been used by Kumbhakar et al. (1996) to measure the total factor

productivity growth and technical change in passenger transport. DEA is also

applied to various sectors such as healthcare, education, banks, etc. But in

India, the studies based on DEA are relatively very few. Bhatt et al. (2001)

applied DEA to assess the performance of healthcare services provided by

hospitals in the state of Gujarat in India. Kumar and Verma (2002) used DEA

for the study of the performance of Indian public sector banks. Shanmugam

and Kulshreshta (2002) used DEA to determine the efficiency of thermal

power plants. Most of the recent work has focused on technical efficiency

patterns (Borger et al. (2002), Brons et al. (2005)).

44

Chu et al. (1992) advised that performance analysis needs to be

done using multiple measures.

Previous research indicates that a very few researchers have applied

DEA to study and analyse the performance of bus transport depots especially

in India. In this study an attempt has been made to analyse the performance of

bus depots using DEA. DEA is a non-parametric analysis model for

measuring the relative efficiencies of a homogenous set of decision-making

units (DMUs). In this study both technical and scale efficiencies of the depots

have been computed and their significance with respect to the performance of

depots has been analysed.

3.3 DATA ENVELOPMENT ANALYSIS (DEA)

Data Envelopment Analysis was initiated by Charnes et al. (1978)

in their seminal paper. The paper was operationalised and extended by means

of linear programming production economic concepts of empirical efficiency

put forth some twenty years earlier by Farrell (1957). DEA was initially

developed as a method for assessing the comparative efficiencies of

organizational units known as decision-making units (DMUs). It involves the

use of mathematical linear programming methods to construct a

non-parametric frontier over the data so as to be able to calculate the

efficiencies relative to these frontiers.

According to Charnes et al. (1978), the efficiency of any DMU is

obtained as the maximum of the ratio of weighted output (virtual output) to

weighted input (virtual input) subject to the condition that the similar ratio for

every DMU be less than or equal to unity. This fractional programming

problem is known as classical CCR ratio model named after Charnes, Cooper

and Rhodes. Variables in DEA model are input/output weights. The weight of

45

any input/output provides a measure of the relative contribution of that

input/output to the overall value of efficiency. The weights are derived

directly from the data in a manner that assigns the best set of weights to each

DMU. The fractional programming problem is transformed into ordinary LPP

by normalizing the denominator of the fractional programming objective

function. Thus, the objective of the transformed LPP is to maximize virtual

output subject to the unit virtual input while maintaining the condition that

virtual output cannot exceed virtual input for every DMU. This is known as

CCR multiplier model. The optimal weights may (and generally will) vary

from one DMU to another DMU. The efficient frontier is determined by the

combination of the data of the other DMUs for whatever weights are applied

to their inputs and outputs. No other common set of weights will give a more

favorable rating relative to the reference set. This means that an inefficient

DMU with a set of weights would also be inefficient with any other set of

weights.

To solve the above LPP, many computational difficulties arises.

Hence generally the dual of this LPP, which is called CCR envelopment

model, is used to obtain the solution. The efficiency score obtained by

envelopment model reflects the radial distance from the estimated production

frontier to the DMU under consideration.The non-zero slacks and (or) radial

efficiency score lesser than unity identify the sources and amounts of any

inefficiency that may exist in the DMU. So, a DMU is called fully efficient if

it is not possible to reduce any input or increase any output without increasing

some other input or reducing other output. When a DMU is CCR inefficient,

then there must be at least one DMU for which virtual output is strictly equal

to the virtual input. The set composed by these types of CCR efficient DMUs

is known as the reference set or the peer group to that inefficient DMU. One

version of a CCR model aims to minimize inputs while satisfying at least the

given output level. This is called the input oriented model. There is another

46

type of model called the output-oriented model that attempts to maximize

outputs without requiring more of any of the observed input values.

Another basic model of DEA is BCC model, which is given by

Banker et al. (1984). The primary difference between BCC model and CCR

model is the convexity constraint, which represents the returns to scale.

Returns to scale reflects the extent to which a proportional increase in all

inputs increases output. The CCR model is based on the assumption that

constant returns to scale exists at the efficient frontiers whereas BCC assumes

variable returns to scale frontiers. CCR efficiency is known as the Technical

Efficiency (TE) whereas BCC efficiency is known as the Pure Technical

Efficiency (PTE) (Cooper et al. 2000). The efficiency assessed by BCC

model is pure technical efficiency. If a DMU scores a value of both

CCR-efficiency and BCC-efficiency as unity, it is operating in the Most

Productive Scale Size (MPSS). The impact of scale-size on efficiency of a

DMU is measured by scale efficiency. Inefficiency in any DMU may be

caused by the inefficient operation of the DMU itself (BCC-inefficiency) or

by the disadvantageous conditions under which the DMU is operating

(scale-inefficiency). Scale efficiency (SE) is estimated by dividing the

CCR-efficiency by the BCC-efficiency for a DMU. As TE of a DMU can

never exceed its PTE, SE is equal to 1. It suggests that a DMU is less

productive when we control scale size which means that scale of operation

does impact the productivity of the DMU. Scale efficiency measures the

divergence between the efficiency rating of a DMU under CCR and BCC

model.

Before applying DEA, some precautions are to be taken:

1. No hypothesis testing is possible in DEA, so data accuracy

must be given priority.

47

2. In order to make sufficient discrimination between DMUs,

sample-size should be adequate. It should be at least three

times greater than the sum of input-output variables.

3. Zero and negative values of any input or output should be

avoided. Variables in the model should be as few as

possible.

3.4 MODEL DESCRIPTION

3.4.1 CCR Model

Suppose that the performance of the homogeneous set of N

decision-making units (DMUn n=1,2...N) be measured by DEA. The

performance of DMUn is characterized by a production process of I inputs

(xim i=1...I) to yield J outputs (yjn j=1...J). According to Charnes et al. (1978),

the ratio of the virtual output to the virtual input of any DMUk is to be

maximized with the condition that the ratio of virtual output to virtual input of

every DMU should be less than or equal to unity. The mathematical model of

Fractional DEA program is given below.

1

1

max

J

jm jm

j

m I

im im

i

v y

E

u x

=

=

=

�

� (3.1)

1

1

subject to

0 1; 1,2, ,

, 0; 1,2, , ; 1,2, ,

J

jm jnj

I

im ini

jm im

v y

n N

u x

v u i I j J

=

=

�

≤ ≤ =

�

≥ = =

�

� �

(3.2)

48

Em is the efficiency of the m th

DMU,

yjm is j th

output of the m th

DMU,

vjm is the weight of that output,

xim is i th

input of the m th

DMU,

uim is the weight of that input, and

yjn and xin are j th

output and i th input of the n

th DMU

The above model is popularly known as the classical CCR ratio

model named after Charnes, Cooper and Rhodes. The theory of fractional

linear programming (Charnes and Cooper 1962), makes it possible to replace

the above model with an equivalent linear programming problem by

imposing the condition:

�=

=

I

i

imim xu1

1 (3.3)

which provides

jm

J

j

jmm yvEMax �=

=

1

(3.4)

Subject to

11

=�=

I

i

imim xu (3.5)

.N.1,2.nfor01 1

=≤� −= =

� in

J

j

I

i

imjnjm xuyv (3.6)

JjIiuvimjm

,,2,1;,,2,1;0, �� ==≥

The above model is run N times to identify the relative efficiency

scores of all the DMUs. Each DMU selects input and output weights that

maximize its efficiency score. In general, a DMU is considered to be efficient

49

if it results in a score of 1 and a score of less than 1 implies that it is

inefficient.

Benchmarking in DEA

Min � (3.7)

Subject to

Iixx imin

N

n

n ...2,101

=∀≤−�=

θλ (3.8)

Jjyy jmjn

N

n

n ...2,101

=∀≥−�=

λ (3.9)

�n� 0 ∀ n= 1,2....N

�n - dual variable , � – Efficiency score

The dual variables indicate the fractional representation of

individual to the composite unit. Based on the above model, a test DMU is

inefficient if a composite DMU (Linear combination of units in the set) can be

identified which utilizes less input than the test DMU while maintaining at

least the same ouput levels. The units involved in the construction of the

composite DMU can be utlized as benchmarks for improving the efficient set

DMU.

3.4.2 BCC Model

Another version of DEA is BCC model given by Banker et al.

(1984). As already pointed out the primary difference between BCC model

and CCR model is the convexity constraint, which represents the returns to

scale. Returns to scale reflects the extent to which a proportional increase in

all inputs increases outputs. In the BCC model �n‘s are now restricted to

50

summing to one (1

1N

n

n

λ=

=� ) which is known as convexity constraints. The

BCC model measures only pure technical efficiency for each DMU.

Technical efficiency assessed by BCC model is pure technical efficiency

because it has net of any scale effect. The impact of scale-size on efficiency

of a DMU is measured by scale efficiency.

efficiency VRS Its

efficiency CRS ItsDMU a of efficiency Scale =

The technical efficiency (TE) of a DMU can never exceed its pure

technical efficiecny (PTE). All the three efficiencies (technical, pure

technical and scale) are bounded by zero and one.

3.5 APPLICATION OF MODEL

The model has been applied to assess the performance of bus

depots of a Metropoliton Transport corporation(MTC) of Chennai city, India.

At present MTC operates its fleet of buses from 17 depots across the Chennai

city. Three inputs and one output have been used in this model. The data

collected for the year 2008 – 2009 is shown in Table 3.1.

51

Table 3.1 Observed data of depots in MTC-Chennai

Depot Name

Fleet Size

(Nos)

Total

Staff

(Nos)

Fuel

Consumption

(kiloliters)

Passenger

Kilometers

(kms)

D1 200 625 452595 1937877

D2 138 486 274761 1233933

D3 112 427 217797 988122

D4 150 512 262703 1092725

D5 175 569 331607 1487694

D6 199 623 471145 2043481

D7 120 454 277299 1064660

D8 155 524 308909 1418722

D9 155 524 289875 1318145

D10 201 627 383316 1604565

D11 126 459 252374 1108201

D12 142 495 242549 1093630

D13 134 477 245390 1098283

D14 118 441 215890 0955798

D15 118 440 235093 1012370

D16 150 513 262703 1092725

D17 141 492 273201 1087358

52

3.5.1 Inputs

Three inputs have been considered in this study as the most

important in producing the output. Fleet size (FS) comprises the number of

buses held in the depot. It is a representative of the capital input. Total staff

(TS) refers to the total number of employees worked in a depot. It represents

the labour input. The fuel consumption (FC) ( kiloliters) is the total fuel

consumed in the depot during the study period. It represents material input.

3.5.2 Output

In this study, only a single output, namely passenger kilometers

produced by the above three inputs is selected. Passenger kilometer is

bascially revenue passenger kilometers.

The extent of relationship between input and output variables has

been analysed using regression analysis. It is found that the output variable

has good correlation with these input variables ( r = 0.97). The descriptive

statistics of inputs and output is given in Table 3.2.

3.5.3 Model Specification

The transport depot is assumed as an economic firm which strives

to maximize its revenue by utilizing its inputs in a given environment.

Input-oriented model has been employed, i.e, how much resource can be

reduced without changing the outputs produced to make the depots efficient.

Constant Return to Scale (CRS) model of DEA is used for calculating

technical efficiency and Variable Return to scale (VRS) model of DEA is

used to evaluate pure technical efficiency. The efficiency scores based on

53

DEA techniques are derived by using the software package named Data

Envelopment Analysis Programming,Version 2.1(DEAP 2.1) .

Table 3.2 Descriptive Statistics of input-output variables

Fleet Size

(No‘s)

Total

Staff

(No‘s)

Fuel

Consumption

(kiloliters)

Passenger

Kilometers

(kms)

Maximum 201 627 273201.00 1092725.50

Minimum 112 440 215890.00 955798.80

Average 148.82 510 291600.41 1272840.56

SD 20.45 42.98 13174.94 31477.47

No. of Depots 17 17 17 17

3.5.4 Results and Discussion

The efficiency score (TE, PTE and SE) of the 17 depots of Chennai

MTC Ltd., for the year 2008-09 obtained from CRS and VRS input oriented

models along with reference set, peer weights and peer counts are presented

in Table 3.3.

54

Table 3.3 Output from CRS and VRS Models

Depots

CRS Technical Efficiency VRS Pure Technical Efficiency

Efficiency

score Peer

Peer

Weight

Peer

Count

Efficiency

Score Peer

Peer

Weight

Peer

Count

D1 0.978 D8,D6 0.225,

0.792

0 0.980 D6,

D8

0.831,

0.169

0

D2 0.978 D8 0.870 0 0.988 D6,

D8,

D3

0.438,

0.054

0.508

0

D3 0.988 D8 0.696 0 1.000 D3 1.000 7

D4 0.906 D8 0.770 0 0.913 D8,

D3

0.243,

0.757

0

D5 0.977 D8 1.049 0 0.986 D6,

D8

0.110,

0.890

0

D6 1.000 D6 1.000 4 1.000 D6 1.000 5

D7 0.878 D8,D6 0.103,

0.449

0 0.986 D3,D6 0.927,

0.073

5

D8 1.000 D8 1.000 15 1.000 D8 1.000 9

D9 0.990 D8 0.929 0 0.992 D8,

D3

0.766,

0.234

0

D10 0.920 D6,D8 0.121,

0.956

0 0.932 D6,

D8

0.297,

0.703

0

D11 0.958 D8,D6 0.758,

0.016

0 0.979 D6,

D3

0.114,0.886 0

D12 0.982 D8 0.771 0 0.990 D8,

D3

0.245,

0.755

0

D13 0.975 D8 0.774 0 0.983 D8,

D3

0.256,

0.744

0

D14 0.964 D8 0.674 0 1.000 D14 1.000 0

D15 0.938 D8 0.714 0 0.981 D3,

D6

0.977,0.023 0

D16 0.906 D8 0.770 0 0.913 D8,

D3

0.243,

0.757

0

D17 0.867 D8 0.766 0 0.905 D6,

D3

0.906,0.094 0

MEAN 0.953 0.972

55

3.6 TECHNICAL EFFICIENCY (TE)

TE scores are calculated through CRS Model. Table 3.3 shows that

out of 17 depots, two depots [D6, D8] are relatively technically efficient

(efficiency score =1) and thus form the efficient frontier. The remaining

15 depots are relatively less efficient as they have efficiency score below one.

The lower the TE scores for a depot, the higher the scope for it to reduce

inputs (while maintaining output level) relative to the best practice depot in

the reference set. The average of TE score works out to be 0.953, which

implies that on an average a depot can reduce its resources by 4.7% to obtain

the existing level of output. Out of 17 depots, 6 depots have an efficiency

score lower than the average efficiency score and 11 depots have higher than

the average efficiency.

3.7 PURE TECHNICAL EFFICIENCY (PTE)

CRS model is based on the assumption of constant returns to scale

which does not consider scale-size of depot to be relevant in assessing TE.

Therefore, in order to know whether inefficiency in any depot is due to

inefficient operations or due to unfavourable conditions displayed by the size

of depot, VRS efficiency (PTE) is required. Usually VRS efficiency is

always greater or equal to CRS efficiency (TE). Hence, the number of depots

on the frontier under VRS model is always greater than or equal to the

number of depots on the frontier under CRS model.

Table 3.3 also provides details about DEA results drawn from VRS

model. It is evident from the table that out of 17 depots, four are efficient

(VRS Score = 1), i.e, none of these have scope to further reduce inputs for

maintaining the same output level. The remainin 13 depots are relatively

inefficient. The efficiency score obtained by this model is known as PTE as it

56

measures how efficiently inputs are converted into output, irrespective of the

size of the depots. The average PTE works out to be 0.972. This means that

given the scale of operation, on average, a depot can reduce its inputs by

2.8% . Out of the 17 depots, 4 depots have an efficiency score lower than the

average efficiency score and 13 depots have higher than the average

efficiency.

PTE is concerned with the efficiency in converting input to

output, given the scale size of the depot. It is observed that D3, and D14 are

poor in CRS Technical efficiency but efficient in pure technical efficiency.

This indicates that these depots are able to convert their inputs into outputs

with 100% efficiency but their overall efficiency (TE) is low due to their scale

size disadvantage (low scale efficiency). D8 has the highest peer count of 9

and D6 and D7 have the same peer count of 5 and D3 has a peer count of

7(Table 3.3). Therefore, these depots can be considered as the best practice

depots.

3.8 SCALE EFFICIENCY (SE)

A comparison of the results obtained from CRS and VRS models

gives an assessment of whether the size of the depot has an influence on its

TE. Scale efficiency is the ratio of TE to PTE score. If the value of SE score

is one, then the depot apparantly operates at an optimal scale. If the value is

less than one, then the depot operates at either small or big relative to its

optimum scale size. The fourth column of Table 3.4 shows the SE score of

the depots.

The result presented in Table 3.4 show that out of 17 depots, only

2 depots are scale efficient (D6 and D8) while the remaining 15 depots are

scale inefficient.The average SE is 0.980. It means that on an average a

57

depot may be able to decrease the input by 2% maintaining the same output.

Out of the 17 depots, 5 depots have an efficiency score lower than the

average efficiency score and 12 depots have score higher than the average

efficiency.

Table 3.4 Relative Efficiencies, Scale Efficiencies and Returns to Scale

TE CRS

Efficiency

PTE VRS

Efficiency

Scale

Efficiency

Returns to

Scale

D1 0.978 0.980 0.998 DRS

D2 0.978 0.988 0.990 IRS

D3 0.988 1.000 0.988 IRS

D4 0.906 0.913 0.992 IRS

D5 0.977 0.986 0.991 DRS

D6 1.000 1.000 1.000 CRS

D7 0.878 0.986 0.891 IRS

D8 1.000 1.000 1.000 CRS

D9 0.990 0.992 0.988 IRS

D10 0.920 0.932 0.987 DRS

D11 0.958 0.979 0.978 IRS

D12 0.982 0.990 0.992 IRS

D13 0.975 0.983 0.992 IRS

D14 0.964 1.000 0.964 IRS

D15 0.938 0.981 0.956 IRS

D16 0.906 0.913 0.992 IRS

D17 0.867 0.905 0.957 IRS

Mean 0.953 0.972 0.980

Column five of Table 3.4 presents the returns to scale of the depots

concerned. Returns to scale reflects the extent to which output varies with a

proportional increase in all inputs. Constant Returns to Scale (CRS) happens

when a propotional increase in the value of all inputs results in the same

58

propotional increase in outputs of the depot. Increasing Returns to Scale (IRS)

happens when a proportional increase in all inputs results in more than

proportional increase in outputs whereas decreasing Returns to Scale (DRS)

happens when proportional increase in all inputs results in less than

proportional increase in output.

It is observed from Table 3.4 that only 2 depots, D6 and D8,

have CRS (operates on optimum scale size) and 3 depots (D1, D5, D10) have

DRS and remaining 12 depots operate under IRS. Figure 3.1 shows

depot-wise DEA Efficiency Score of MTC, Chennai.

Figure 3.1 Depot-wise DEA Efficiency Score of MTC Chennai

3.9 INPUT/OUTPUT TARGETS FOR INEFFICIENT DEPOTS

Each of the inefficient depots can become overall efficient by

adjusting its operations to the associated target point determinied by the

effiecient depots that define its reference frontier. Table 3.5 presents the target

values of all inputs and outputs for the inefficient region alongwith percentage

reduction in inputs in terms of CRS model. It can be observed from the

Table3.5 that on average, approximately 9.1% of total fleet, 12.3% of total

59

staff and 5.8% of fuel consumption can be reduced if all the inefficient depots

operate at the level of efficient depots. The numbers in bracket of Table 3.5

are the percentage reductions in the corresponding inputs and percentage

additons in the corresponding output to make the region efficient. Column 5

of Table 3.5 shows the target value of output with zero increase for the

corresponding reduction in the input variables. For example, the present

passenger kilometers of D1 can be attained with a reduction of 3.8% in fleet

size, 2.2% reduction in employee size and 2.2% reduction in fuel

consumption. This indicates that the management of these depots should

concentrate on the effective utlization of the three input resources.

Table 3.5 Target values of input and output variables under CCR

input model

Inefficient

Region

Target Values of Input Variables Target Values

of Output

variables

Passenger

Kilometers

Fleet Size (No.) Employee Size

(No.)

Fuel consumption

(Kiloliter)

D1 192.499 (3.8) 611.351 (2.2) 442710.759 (2.2) 1937877

D2 134.811 (2.3) 455.749 (6.2) 268673.503 (2.2) 1233933

D3 107.956 (3.6) 364.959 (14.5) 215151.227(1.2) 988122

D4 119.384 (20.7) 403.594(21.2) 237927.22 (9.4) 1092725.5

D5 162.535 (7.1) 549.475 (3.4) 323926.792 (2.3) 1487694

D6 199.000 (0) 623.000 (0) 471145.000 (0) 2043481

D7 114.356 (12.2) 382.573 (26.4) 233935.524 (12.2) 1064660

D8 155.000 (0) 524.000 (0) 308909.000 (0) 1418722

D9 144.012 (7.1) 486.852 (7.1) 287009.614 (1) 1318145

D10 172.364 ( 14.2) 576.674 (8) 352549.323 (8) 1604565

D11 120.682 (4.2) 407.176 (11.3) 241721.416 (4.2) 1108201

D12 119.483 (15.9) 403.928 (18.4) 238124.276 (1.8) 1093630

D13 119.991 (10.5) 405.647 (15.0) 239137.409 (2.5) 1098283

D14 104.424 (11.5) 353.021(19.9) 208113.080 (3.6) 0955798

D15 110.605 (6.3) 373.915 (15.0) 220430.926 (6.2) 1012370

D16 119.384 (20.4) 403.594 (21.3) 237927.224 (9.4) 1092725

D17 118.797 (15.7) 401.612 (18.4) 236758.627 (13.3) 1087358

Average 135.6(9.1) 451.7(12.3) 277664(5.8)

60

3.10 SENSITIVITY ANALYSIS

To investigate the robustness of the efficiency scores, sensitivity

analysis has been carried out. This has been done by removing the efficient

depots (D6 and D8) from the reference set. Accordingly, the following

changes Table3.6 have resulted. From Table 3.6 we observe that D1,D2,D3

and D9 have become efficient. This is because of the removal of D6 and D8.

The mean techinical efficiency score after removing D6 and D8 is 96.4% and

the mean pure technical efficiency is 97.5%. Hence the management can

concentrate more on the remaining depots to improve their perfromance.

Table 3.6 Change of reference sets in the models

Efficient

depots

removed

Mean

Technical

efficiency

New

reference set

(CRS Model)

Mean pure

Technical

efficiency

New referenc set

(VRS Model)

D6, D8 96.4% D1,D2,D3,D9 97.5% D1,D2,D3,D5,D9,D14

3.11 CONCLUSION

In this study, an attempt has been made to measure the technical

and scale efficiency of the depots of MTC, Chennai, India, using DEA. A

three input and one output DEA model has been developed with fleet size,

number of employees and fuel consumption as inputs and passenger

kilometers as output. The model has been applied to evaluate 17 bus depots of

Metro Transport Corporation of Chennai city, India. The model provides

relative efficiencies and bench marks (Peer group).

61

The study reveals that only 2 depots [D6, D8] have the maximum

degree of efficiency. The overall mean TE of the depots is found to be

95.3%. This indicates that on an average 4.7% of the technical potential of the

depot is not in use. This implies that these depots have the scope of

producing the same output with inputs of 4.7% less than the existing level.

The efficient depots are D6 and D8 while D17 is the most inefficient depot.

The results of the VRS model shows that out of 17 depots, 4 depots

(about 29% of the depots) have PTE equal to one, indicating the conversion

efficiency of inputs into output. These depots are D3, D6, D8 and D14. Also,

out of these, two depots (D3 and D14) are technicaly inefficient due to

scale-size effect.

It is also observed that out of 17 depots, 2 are with CRS , 12 with

IRS and 3 with DRS. From Table 3.6, it is also evident that on average the

relatively inefficient depots have to reduce their fleet strength by 9.1%,

employee size by 12.3% and fuel consumption by 5.8% relative to the best

practice depot.

This study has discussed how DEA can be applied to evaluate the

degree of efficiency of the depots. Thus, these results give an indication on

the degree of effciency of depots in the process of transforming inputs into

output. The conclusion on the efficiency of depots needs to be taken with

some care. The results also depend upon the choice of inputs and output and

the way the DEA model measures efficiency.