CHAPTER 5 The Case Study 1
5.5 Conclusions
Using station-level data of TMTC and KKTC for the years 2000 and 2002, respectively, this study applies a hyperbolic graph efficiency approach to test for “return to the dollar” and the technical and allocative efficiencies of service provided in 15 stations of the firms before and after privatization. Moreover, this study has demonstrated how performance, with respect to the geographical characteristics of the area in which bus stations operate, varies by region.
Whereas the POE has average profit margins of about 4.1%, the former SOE incurred losses with total costs exceeding total revenues by 19% on average. However, given the absence of market information on prices, an allocative efficiency index was employed to measure price distortions using data on observed costs and revenues. Perhaps in an attempt to cover the inefficiency-induced losses, both SOE and POE apparently resorted to distorting relative output prices with respect to input prices; the distortion being more pronounced in POE than in its counterpart. In other words, there was a substantial upgrade in “return to the dollar” for the entire sample of stations after privatization. The decomposition of the “return to the dollar” indicates that this increase in profit margin was mostly due to allocative progress rather than to an improvement in technical efficiency. On the other hand, the aforementioned results are also confirmed by the statistical test which shows a statistically significant increase in TE, simultaneous with an insignificant increase in AE. This suggests that the KKTC converted its input resource into outputs more effectively than its predecessor, while its ability to distort relative output prices with respect to input prices remained constant. The main reason for the latter is that although the cost savings of KKTC, such as reduced pay and wages, appear to have come about through performance improvement, the average fare rate has also fallen as a result of competitive pressure. The decrease both in input and output prices resulting from this, resulted in an
unchanged AE following privatization. Furthermore, the changes in the three measures among three different station types were also analyzed and demonstrated a consistent origin of these changes in profit margins. The stations of the northern region virtually dominated the other station types in all three efficiency dimensions. In a final analysis, the inverted U-shaped relationship between the “return to the dollar”, TE, and AE for all the sample stations against fleet size suggests that stations of approximately 40-70 vehicles are of optimal size.
CHAPTER 6 The Case Study 2
─ Measuring the Risk-Adjusted Efficiency of Taiwan Motor Transport Company Before and After Privatization
6.1 Introduction
In the theory of production it is common to assume that outputs are strongly disposable.
Classical DEA models, as described e.g., in Charnes et al. (1994), rely on the assumption that inputs have to be minimized and outputs have to be maximized. However, it was mentioned already in the seminal work of Koopmans (1951) that production may also generate undesirable outputs like smoke pollution or waste.
This study intends to employ a directional distance function that incorporates both desirable and undesirable outputs to measure the impact of Taiwan Motor Transport Company’s (TMTC’s) privatization on its station-level efficiency changes. The directional distance function allows us to consider both the desirable production output, “goods”, and the undesirable production output, “bads”, in order to measure the linkage between “goods”
and “bads” and to assess the level of production inefficiency that gives rise to opportunities in improving efficiency and overall performance simultaneously.
By introducing entrepreneurship and related productivity benefits into bus operations such as downsizing, reducing cost bases, empowering operation management (as will be seen below), the decreasing rate of desirable output (here referred to as vehicle-kilometers) was small in proportion to those of various inputs in the new owner (Kuo Kuang Motor Transport Company, KKTC). This may reveal that efficiency improved following privatization. While evaluating the performance of bus operators, however, transport risks
as either internalities or externalities imposed by bus operators upon both users and non-users of the particular mode concerned are needed to be considered simultaneously as undesirable outputs, so as to calculate the overall risk-adjusted efficiency (See e.g., Mester 1996; Chang 1999). Otherwise, the true measure of efficiency could be overestimated or underestimated.
6.2 Model formulation
In this section the model used is explicitly set up to evaluate production in efficiency, and the approach applied is based on the frontier production function. Färe et al. (1989) were the first to apply classic output-oriented DEA analysis to check for production congestion using radial efficiency measures for equiproportional increases of desirable and undesirable outputs. However, the symmetric treatment of outputs in terms of their disposability characteristics looses its justification if one or some of the outputs produced are undesirable goods (2002).
Following this approach, Färe et al. (1998) took a step forward by treating desirable and undesirable outputs asymmetrically. These authors define measures that allow desirable and undesirable production to vary by the same proportion, but desirable outputs are proportionally increased while undesirable ones are simultaneously decreased. The essence of the method is to compute the opportunity cost of transforming the production process from one where all outputs are strongly disposable to one which is characterized by a weak disposability of undesirable outputs.
The goal of this study is to assess the undesirable by-product performance of a set of decision making units (here, DMU refers to stations) by grading their ability to produce the largest equiproportional increase in desirable output and decrease in the undesirable output.
Such an evaluation is done through a comparative technique known as DEA which enables the analyst to determine the success of a station in attaining the objective.
This approach establishes a relationship between outputs, U, and inputs, X . Given a vector of inputs, X , the production correspondence is defined as,
( ) {
X U UP = can be produced by X
}
(6.1) If the output vector U may be partitioned into goods and bads, U =( )
y,b , then the directional distance function increases the good output and decreases the bad (Boyd et al.2001). The directional output distance function is defined as
(
x y b g) { ( ( )
y b g)
P( )
X}
D0 , , , =sup β : , +β⋅ ∈ (6.2) Figure 6.1 illustrates the directional distance function. The output set is denoted by
( )
XP , the good output by y , and the bad by b. The inequality Z⋅Y ≥ y0 allows for feasible vertical extensions south of the poly tope, reflecting weak disposability of the undesirable outputs. The weak output set is the region OFBCDE. The inequality Z⋅B≥b0 allows for a strong disposability of undesirable outputs, so that in Figure 6.1 the strong output set is the region OABCDE. The region OABF represents production possibilities that are feasible under strong disposability of all outputs, but not feasible under weak disposability of undesirable outputs.
Figure 6.1 Directional Distance Function for Desirable and Undesirable Output Performance
G( by, )
x(bads) , )
(y b
g = −
y (goods) I
E A
F H
B C
D
O
( )
X PThe directional output distance function takes
( )
y,b in the g direction and places it on the boundary at H or I , depending on whether the technology exhibits free or weak disposal of bad output. The directional distance function under weak disposability, where(
y b)
g = ,− , can be estimated from the following linear programming problem:
0 ,
max0
≥
θ≥ z θ (6.3) subject to
(
1)
y0 Yz⋅ ≥ +θ (6.4)
(
1)
b0 Bz⋅ = −θ (6.5)
x0
X
z⋅ ≤ (6.6) The program defines the production frontier using the observed combinations of inputs and outputs
(
X,Y,B)
to evaluate inefficiencies of other individual stations(
x0,y0,b0)
, based on the frontier.6.3 The data
The TMTC station-level data in the period of 2000 and KKTC data for 2002 are used in this study. For each DMU (station) in the sample, four traditional inputs are used for the assessment of efficiency, which are measured in physical units: (1) number of buses in the active fleet (
x
1), (2) number of employees (x
2), (3) liters of fuel consumed (x
3), and (4)kilometers of network length (
x
4). The single (desirable) output measure is vehicle-kms ( y ).Two types of risk indicators are introduced together as the measure of the undesirable outputs. These two indicators are selected to account for the safety quality and riskiness of a station’s output. The first one is the amount of accident compensation, including monetary
compensation for the fatalities and victims, cost of medical treatment for persons involved in accidents, repair of property damage, costs for legal and court procedures, and others.
The second risk measure is the accident liability insurance which is regarded as a provision for risk insurance and is taken here as an output since it is in the form of legal insurance to cover risks that bus or road users might be exposed to if these insurances were not made.
In the interest of analysis these two risk indicators are combined into a single undesirable output measure, and termed as accident and insurance costs (b). A further series, differences in service area population of each station, is added to these measures as an environmental (input) variable to reflect the differences in potential demand impacting on intercity service outputs, but outside of the control of the station management. The intention is to prevent DMUs in remote areas from being disadvantaged in an assessment of relative efficiency over time. The imposed constraint to reflect the above environmental impact can be defined as Z⋅E ≤e0 , where E denotes the observed matrix of the environmental variable.
The whole sample therefore consists of the 15 stations (denoted by S1~S15) of both TMTC and KKTC, along with two years of input and output data (2000 and 2002). All these related data are used to calculate the comparison of the before and after effects of privatization on efficiency. A preliminary examination of summary data before and after privatization reveals the operating changes that have been instituted at TMTC and KKTC, as well as the markets’ response to their service offers (Table 6.1). In terms of resources, the KKTC has cut the number of employees by 40%, the number of vehicles by 36%, the liters of fuel used by 24%, and the network length by 22% as compared to TMTC over the study period. Regions on average had a population of 1,467,232 with a standard deviation of 1,232,266 in 2002. Although the number of service area population has slightly increased by 1.0%, the amount of desirable outputs (vehicle-kilometers) has decreased by 12% and undesirable outputs (accident and insurance costs) decreased by 24%, respectively.
Table 6.1 Data Summary for TMTC and GGBC Station
Desirable Undesirable Environmental Inputs
output output variable
NetworkFleet Employees Fuel Vehicle- Accident and Service Area length kilometers Insurance costs Population
(vehicles) (persons) (103 liters) (km) (103) (103 NT$) (103 persons) TMTC
(2000)
Max 169.0 436.0 10,246.9 4,492.1 24,358.0 7,037.3 4,977.4 Min 24.0 47.0 757.7 508.3 2,197.8 341.6 245.3 Mean 83.5 199.3 3,566.5 1,431.9 8,879.0 2,233.8 1,451.5
Std 40.4 107.9 2,447.7 1,067.3 5,813.3 1,891.6 1,221.5 GGBC
(2002)
Max 142.0 318.0 8,144.8 4,449.9 23,794.9 8,317.5 5,020.4 Min 14.0 33.0 493.5 335.5 1,664.9 257.2 244.0 Mean 53.6 112.1 2,696.4 1,111.1 7,563.5 1,694.9 1,467.2
Std 36.8 80.6 2,068.9 1,032.8 5,742.1 2,046.6 1,232.3 Percent Change
of Mean -35.8 -43.8 -24.4 -22.4 -14.8 -24.1 +1.1
6.4 Results and discussions
The results of a comparison of the directional distance function and standard DEA model to estimate efficiencies of TMTC before and after privatization are set out in Table 6.2. Note that all the efficient scores should be larger than or equal to 1.0 and that a lower score indicates a more efficient status. However, the efficiency level can be increased in order for the station to achieve a best practice level. An efficiency score of 1 means that the firm is efficient (or equivalent on the frontier).
Looking at the first column, the performance of a station is evaluated on the basis of its ability to expand transit service production with given inputs, regardless of what happens to the risk exposure. The standard efficiency indices diverge from 1.000 to 1.465 with a mean level of 1.195. The results are very different when station performance is judged on the basis of the ability to increase outputs and reduce risk simultaneously.
Table 6.2 Comparison of Directional Distance Function and Standard DEA Model to Estimate Efficiencies of the TMTC before and after Privatization
Station Standard DEA Model
with Envirnmental variable Dorectional Distnace function
Rate Rank Rate Rank
Average Efficiency 1.195 1.135
GGBC
Average Efficiency 1.047 1.024
Total Average
Efficiency 1.121 1.079
Column 4 reports the efficiency scores obtained from the directional distance function.
This is a stringent standard, and by this criterion the efficiency indices range from a low of 1.000 to 1.302 with a mean level of 1.135. Therefore, a general feature of interest is that efficiency levels for many of the TMTC and KKTC stations appear to be higher under the standard model compared to those under the directional distance function. This may suggest that the stations in the sample are less efficient relative to the relaxed standard than to the
more stringent standard. This is due to the incorporation of transport risks as outputs, and also because of the assumption of weak disposability of undesirable outputs which enables the technology to envelop the data more closely.
It is worth noting that a ranking of station performance by a standard model which ignores risk exposures is very much different from a ranking of station performance by a directional distance function which acknowledges risk exposures. This confirms the finding in Fare et al (1989) that failure to credit stations for risk reduction can severely distort the ranking of station performance.
Based on the results derived from a directional distance function, this study now focuses on the evaluation of the risk-adjusted efficiency changes at the station-level of TMTC before and after privatization. As can be seen from the third column of Table 6.2, there are differences in the mean efficiency score between the pre- and post- privatization periods, as POE is found to be superior to its predecessor. The overall mean efficiency index for TMTC computed across the stations, is 1.135, however, corresponding figures for the KKTC as a whole are 1.024. In contrast to only 3 out of 15 stations operating efficiently before privatization, 11 out of 15 stations are deemed as efficient following privatization.
The above comparison of both the average efficiency scores and the numbers of efficient units before and after TMTC’s privatization provides empirical evidence that POE’s operation outperformed the previous SOE’s operation. On the whole, the above findings indicate that TMTC’s privatization has produced a clear improvement in efficiency enhancement and as such may be considered to be a source of cost reduction.
6.5 Conclusions
The purpose of this article is to apply the directional distance function which incorporates both desirable and undesirable outputs to examine the effects of privatization
on TMTC’s efficiency changes. This method allows desirable and undesirable production to vary by the same proportion, but desirable outputs are proportionally increased while undesirable ones are simultaneously decreased. Transport risks as undesirable outputs are, for the first time, taken into account to measure the overall risk-adjusted efficiency before and after privatization.
As regards mean efficiency score and ranking order, the results of the comparison between the standard DEA model and the directional distance function implies that the latter appears to be more suited to this empirical study. The empirical findings demonstrate that, in terms of both the number of efficient units and the average efficiency scores, TMTC’s privatization has had a noticeable impact on KKTC’s efficiency enhancement and as such may be considered to be a source of cost reduction.
CHAPTER 7 The Case Study 3
─ The Joint Determination of Efficiency in Multi-Mode Bus Transit
7.1 Introduction
Improving performance has been widely held to be one of the principal objectives in most transportation organizations. Hence, it is an appropriate way to measure and compare performance with peer groups, with particular reference to the efficient use of resources. As mentioned in Section 1.1 of Chapter 1, however, some transportation organizations may engage in various activities (services) simultaneously, a problem then arises with respect to how the resource can be assigned in an equitable or optimal way to the various activities.
On the other hand, why comprehensive studies on productivity, efficiency, and quality of urban transportation systems need to be capable of handling each mode separately can easily be highlighted by focusing on the important technological and operational differences between the various modes currently in use within urban areas. Also, there is currently, at least, a vast disparity between the levels of utilization of the various urban travel modes－a disparity that is frequently at the center of inefficiency of major system components. All these three factors therefore call for a separate accounting system that will permit the analyst to discover, understand, and illuminate accurately the situation at any given moment and the reasons behind any overall system rating (Tomazins, 1975).
A number of studies have been presented recently, both from a practical organizational standpoint and from a costs research perspective, to deal with this problem (see for example, Golany et al. 1993; Golany and Tamir 1995; Beasley 1995, 2003; Mar Molinero 1996;
Tanassoulis 1996, 1998; Fare et al. 1997; Mar Molinero and Tsai 1997; Tsai and Mar Molinero 1998, 2002; Cook et al. 1999; Cook et al. 2000; Fare and Grosskopf 2002).
Among them, the multiactivity DEA model, a novel refinement of the conventional DEA approaches, for the joint determination of efficiencies in the DEA context, was proposed by Beasley (1995) and subsequently revised by Mar Molinero (1996) and Tasi and Mar Molinero (1998, 2002). Specifically, the multiactivity model is used for evaluating efficiencies of organizations that engage in several activities simultaneously. DMUs in this situation may have some inputs and outputs among all the activities, and in doing so, estimate the efficiency with which a given organization carries out each activity.
This study intends to apply the multiactivity model to explore the efficiency of individual services within different but highly homogeneous multimode transit firms in Taiwan. There are three reasons for this. First, the multiactivity model was designed, in particular, to estimate the efficiency achieved by organizations which face several production functions using shared inputs. Second, to the present author’s knowledge, few DEA studies relating to multimode transit agencies deal with the shared input problem in a proper way. For example, Viton (1997, 1998) analyzed the efficiency of U.S. multimode bus transit systems operating conventional motor-bus (MB) and demand-responsive (DR) services using DEA. However, the allocation problems of the system costs data appear to have been ignored.
Third, in the present study of the 60 bus companies in Taiwan, 24 of them, operated both highway bus services (HB) and urban bus services (UB) in 2001. Due to dissimilarities in operation characteristics (e.g., headway, frequency, vehicle capacity, load factor, cycle time, and others), which imply different production technologies between these two services, they construct different production functions themselves. Moreover, because of some input resources imposed on the multimode transit firm such as technical labors are devoted to both types of activities (services), they need to decide how to allocate across different
DMUs for the joint (simultaneous) determination of the efficiencies of both services, respectively.
In applying DEA to bus firms, one requires the input and output measures for each service to be specified. The conventional DEA model evaluates the efficiency with which a DMU transforms inputs into outputs. It assumes that DMU is equally efficient in all its activities. However, there are cases in which a DMU faces several production functions.
This happens when a DMU is engaged in several activities simultaneously. For example, a transit firm may operate both highway bus services and urban bus services. A transit firm which is efficient at HB may not be efficient in UB, and hence the evaluation of the efficiency of a firm which faces two production functions using shared inputs needs to be solved. As indicated by Diez-ticio and Mancebon (2002), this method was proposed with the object of providing a solution to a weakness in the conventional DEA model, due to its incapacity to evaluate the efficiency of firms which carry out various activities whilst sharing common resource. The main problem is that what is by nature heterogeneous is treated in a homogenous manner, which could lead to a significant degree of distortion in the interpretation of the results. However, how can one determines how efficient each service is at each of its two basic functions, highway bus services and urban bus services?
This happens when a DMU is engaged in several activities simultaneously. For example, a transit firm may operate both highway bus services and urban bus services. A transit firm which is efficient at HB may not be efficient in UB, and hence the evaluation of the efficiency of a firm which faces two production functions using shared inputs needs to be solved. As indicated by Diez-ticio and Mancebon (2002), this method was proposed with the object of providing a solution to a weakness in the conventional DEA model, due to its incapacity to evaluate the efficiency of firms which carry out various activities whilst sharing common resource. The main problem is that what is by nature heterogeneous is treated in a homogenous manner, which could lead to a significant degree of distortion in the interpretation of the results. However, how can one determines how efficient each service is at each of its two basic functions, highway bus services and urban bus services?