Journal of the Eastern Asia Society for Transportation Studies, Vol. 6, pp. 519 - 528, 2005

BUS INDUSTRY EVALUATION METHOD PER ROUTE
Ryuji KAKIMOTO
Associate Professor
Dept. of Architecture and Civil Engineering
Kumamoto University
2-39-1 Kurokami, Kumamoto,
860-8555, Japan
Fax: +81-96-342-3507
E-mail: kakimoto@gpo.kumamoto-u.ac.jp

Shoshi MIZOKAMI
Professor
Dept. of Architecture and Civil Engineering
Kumamoto University
2-39-1 Kurokami, Kumamoto,
860-8555, Japan
Fax: +81-96-342-3507
E-mail: smizo@gpo.kumamoto-u.ac.jp

Abstract: Transport density and the rate of revenue and costs are usually applied to assessment to
expend public subsidy in operating bus service. However, these indexes overlook factors such as
business effort as bus services supply under minimum costs. Then, the aim of this paper is to develop
an evaluation method of business management condition per bus route in order to distinguish thesubsidized bus route efficiently. This method reflects operating condition for inside and outsidebusiness environment of bus route. This method is applied to the evaluation of 45 bus routes inKumamoto city. Consequently, each bus route is classified under 16 categories. Roughly speaking, 20
bus routes are inexpensive and profitable, 6 bus routes are inexpensive and unprofitable, 2 bus routes
are expensive and profitable, 17 bus routes are expensive and unprofitable.
Key Words: deregulation of bus business, public subsidy, evaluation of business efforts, productivity

1. INTRODUCTION
Regulations to adjust supply and demand of bus service are repealed, and subsidization for local bus
was modified because of a partial amendment of the Road Transport Law in 2002. Former
subsidization was conditional on cross subsidy but is changed to a subsidy system per bus route.
Several issues are raised by this modification. New low-fare bus services are expected in urban area.
However, disorder is also foreseen because of excessive competition between bus companies. On theother hand, since bus companies can discontinue routes with deficit easily, unprofitable routes may bediscontinued rapidly, and bus services for daily transport in local areas may be lost. Unprofitable bus
routes need to be kept by public subsidy if they are indispensable for living there. However,subsidization without planning will cause financial trouble and may spoil business efforts. Therefore,characteristics of bus routes have to be evaluated to subsidize the bus industry appropriately.
When the public subsidy for bus industry is determined, transport density and the rate of revenue andcosts are usually employed to assess bus transit operation. However, these indexes overlook factors
such as business effort as bus services supply under minimum costs. Since these indexes are calculated
from operation outputs which are fare revenues and number of passengers, it seems problematic thatbus business is evaluated by only these indexes.
In this situation, the evaluation and the improvement of a bus business management were proposed to
the following studies. Haraguchi and Takayama et al. (2001) constructed the evaluation system ofplanning the bus route network. This system searches the optimal bus route network by considering thenumber of bus schedule and bus drivers. Tamazawa and Tokunaga (2002) created simulation model in519

Journal of the Eastern Asia Society for Transportation Studies, Vol. 6, pp. 519 - 528, 2005

order to evaluate bus priority measures for increasing the level of bus service. Sugio and Isobe (2001)
developed the supporting tool for public transportation system by applying GIS. This study uses
Route-Potential and Marginal-Population-Depended for the index that a route is evaluated. Sugio andIsobe et al. (1999) clarified relationships between business environment and management policies.
They proposed the desirable management policies suited by various bus-route types, and divided thebus routes into several bus-groups considering the key concept of business/public characters andpotential/actual stage. Takeuchi and Yamada (1991) developed the route potential as a measurement forthe public subsidy to bus business. They distinguished the bus route that may be subsidized, andmanage the productivity under the subsidized system by using this measurement.
There are not many studies about treating the management and the public subsidy of bus business. For
this reason, the aim of this paper is to develop an evaluation method of business management condition
per bus route in order to distinguish the subsidized bus route efficiently. The improvement policy
according to business management condition in each bus route is also proposed.

2. GROUPING CONCEPT OF BUS ROUTES
Sugio and Isobe et al. (1999) take bus business environment form two angles of business and public.
The business and the public of each bus route are evaluated by actual operating condition and potential
operating condition. The bus routes are divided several bus groups according to the evaluation. They
also propose four management policies, which are “Increase passenger”, “Cut in costs”,“Rationalization of bus route formation”, and “Public subsidy”, in order to improve a management ofbus business. The concept of business/public characters and potential/actual stages is introduced tointerpret correspondence between the bus groups and the management policies.
In this paper, we make reference to the above study, but more managerial viewpoint is introduced to
the grouping concept of bus route in order to improve bus business management. Bus routes areclassified by inside and outside management environment of each bus route. Inside management
environment indicates whether managerial resources are used effectively. In addition to management
condition which means balance of revenue and costs, productivity of bus route should be considered as
one of the evaluation indexes. Then, productivity and management condition of bus route are used forthe indexes of inside management environment. The rate of actual passenger number to potential
demand, which we call attractiveness of passenger, may be used as index of business effort for getting
passengers. Potential demand and public of bus route act for the indexes of outside management
environment. The productivity, potential demand and management condition usuallycorrelate to each other under efficient operation of bus route respectively. Therefore, if allof the bus routes operate efficiently, it may be meaningless to define such indexes. These indexes aredefined on assumption that inefficient operation of bus route exists and the aim of defining suchindexes is to identify the inefficient bus routes and quicken the improvement of them.
The attractiveness of passenger and productivity of bus route compose a plane of business effort.
Management condition and public compose a plane of business environment. Bus routes are classified
according to these two planes. Figure 1. a) shows plane of business effort. The horizontal axis is therate of attractiveness of passenger, and the vertical axis is productivity. Figure 1.b) shows plane ofbusiness environment. The horizontal axis is management condition, and the vertical axis is public.
Plane of business effort is composed of four quadrants which are BE1, BE2, BE3 and BE4. Plane ofbusiness environment is also composed of four quadrants which are ME1, ME2, ME3 and ME4. In
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this paper, each bas route is characterized according to a combination of the quadrants on two planes
and is classified.
Basic concept of the improvement policy is that business management condition of each bus routeshould be improved toward BE1 on the plane of business effort and toward ME1 or ME2 on the planeof business environment. The bus route is a proper object of subsidy basically when a bus routebelongs to BE1 and ME3 or ME4 on two planes. In this paper, we try to apply this grouping concept tobus routes of private company K in Kumamoto prefecture, and propose the improvement policy.

Productivity
BE4

PublicBE1ME4Management
Condition

Attractiveness
BE3

BE2

ME1

ME3

ME2

a) Plane of Business Effortb) Plane of Business Environment
Figure 1. Conceptual Figure of Bus Route Grouping

3. PRODUCTIVITY ANALYSIS OF BUS BUSINESS
3.1 Translog Cost Function
The cost minimization framework is applied to analyzing productivity of the bus industry. A translog
type cost function is selected for this purpose. The translog function is one of the families of flexible
function, which may be interpreted either as an exact function or an approximation to arbitrary function
by Taylor’s series expansion up to second degrees. The translog function is flexible in that it places no apriori restriction on its own structure and the structure of production process (Viton P., 1981). The
flexibility allows us to perform statistical tests of various restrictions against those imposed structure. A
second order, n -factor, m -output, translog cost function is defined as follows.
n
m
1 n n
ln C = α0 + ∑αi ln Pi + ∑ βi ln Qi + ∑∑γ ij ln Pi ln Pj
2 i =1 j =1
i =1
i =1
(1)
n m
1m m
+ ∑∑δij ln Pi ln Qj + ∑∑ε ij ln Qi ln Qj
2 i =1 j =1
i =1 j =1
Where, C is total costs, Pi is price of input, Qi is output, and α 0 , α i , β i , γ ij , δ ij , ε ij are parameters. In
this paper, the number of passenger QJ and the vehicle-miles QS are employed as output, and thelabor price PW , the unit cost of repair PR , and the unit cost of fuel and oil PF are employed as
price of input. A symmetry and homogeneity constrains are imposed to translog cost function.
Furthermore, since data are not enough for estimating the parameters, fifth and sixth terms in Equation(1) are neglected. Therefore, Equation (1) is transformed as follows.

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Journal of the Eastern Asia Society for Transportation Studies, Vol. 6, pp. 519 - 528, 2005

ln C − ln PF = α 0 + αW (ln PW − ln PF ) + α R (ln PR − ln PF ) + β J ln QJ + β S ln QS− γ WR (ln PW − ln PR ) 2 / 2 − γ WF (ln PW − ln PF ) 2 / 2 − γ RF (ln PR − ln PF ) 2 / 2(2)∑ α i = 1, ∑ γ ij = 0, ∑ γ ij = 0, γ ij = γ ji , ( i, j = W , R, F )iij

According to Shephard’s lemma, the derived demand functions of production are simply the partial
differentials of the cost function with respect to corresponding factor price. Therefore, the sharefunctions of the labor prices and the cost of repairs are obtained by differentiating Equation (2) withrespect to the logarithm of the labor prices PW and the unit cost of repairs PR as follows.
UW = αW + γ WR (ln PR − ln PW ) − γ WF (ln PW − ln PW )(3)

U R = α R + γ WR (ln PW − ln PR ) − γ RF (ln PR − ln PF )(4)

It has been widely known that the optimal method of estimating all the parameters is to jointly estimate
the translog cost function and the factor share equations as a system. For such a system estimation does
not neglect additional information that can be derived from the cost and the share equations. All theparameters of the share equations simultaneously with the cost function are estimated.
The translog cost function of private bus company K in Kumamoto prefecture is estimated. The data toestimate parameters are used tables of the bus transit operating cost factor for twelve years from 1991
to 2002. The estimated parameters are shown in Table 1. Since the parameters β J and β S of
outputs are positive, the cost increases when the number of passenger or the vehicle-miles increases.
Considering the parameters α W , α R and α F of factor prices, the coefficient of the labor prices
W is only negative. This result is the opposite of an empirical assumption. Other parameters without
2γ RF clear 5% level of significant. Since R of each equation is also enough, the estimated equations
are good fitness. Wald statistic about homogeneity is χ 2 distribution with 5 degrees of freedom.
Since Waldlinear=5868.402 and Ｐ-value=0.000, homogeneity restriction is valid hypothesis.

Table 1. The Estimated Parameters of Costs Function
Coefficientt-value
α0
αW
αR
βJ
βS
γWR
γWF
γRF

6.378
-0.410
0.328
0.407
0.548
-0.094-0.1590.024

Eq. (2)
Eq. (3)Eq. (4)

R２
0.917
0.917
0.998

7.730
-2.199
3.990
4.471
5.534
-7.549-4.692
1.379
D-W
2.147
1.356
1.424

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Journal of the Eastern Asia Society for Transportation Studies, Vol. 6, pp. 519 - 528, 2005

3.2 Evaluation of Productivity by Cost Function

Operating ratio and level of bus fare are usually employed as the evaluation indexes of bus business.
These indexes are calculated through fare revenues and number of passengers without considering thelevel of business effort. These indexes are the total values as a bus company and can not evaluate
productivity per bus route.
The estimated translog cost function can give the standardized cost of bus company K. The standard
cost of a bus route can be estimated by inputting the data of bus route into the cost function.
Productivity of a bus route is evaluated to compare the standard cost with the actual cost. Since only
1993’data of operating ratio per bus route are got, productivity of 45 bus routes of private bus company
K in 1993 is evaluated.
The number of passengers and the vehicle-miles per bus route need adjusting because the estimatedcost function yield cost of company unit. These data have to be expanded according to the rate of thevehicle-miles per bus route to the total vehicle-miles of bus company K. To sum up, each bus route isregarded as a company and the productivity of each bus route is evaluated.
The comparisons between the standard cost and the expanded real cost per bus route are shown in
Figure 2. Consequently, 26 bus routes are less and 19 bus routes are more than the standard cost, that is,
26 bus routes are inexpensive condition and 19 bus routes are expensive condition.

95

The actual costs(billion yen)

85

75

65

55

45

35
35

45

55

65

75

85

95

The standard costs(billion yen)

Figure 2. Comparison between The Standard Costs and the expanded Real Costs

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4. THE GROUPING OF BUS ROUTES AND IMPROVEMENT POLICY
4.1 The Grouping indexes of Bus Routes

In addition to the productivity in Chapter 3, attractiveness of passengers, public and operating ratio
need calculating in order to apply the grouping concept in Chapter 2.
(1) Attractiveness of Passengers
In this paper, an idea of route-potential (Takeuchi and Yamada, 1991) is simplified and is applied to
calculating the attractiveness of passengers. Attractiveness of passengers means the ratio of actual
passenger number to potential demand per kilometer and the actualization level of potential demand.
Attractiveness of passengers is calculated as follows.

First, trip generation potential in a sphere of bus stop is calculated. A sphere of bus stop means a circle
with the radius of 500 meter as bus stop is the center. The data of a sphere of bus stop include thepopulation, number of employee by industries, student and sickbed, and number of other facilities’ user
in the circle. Multiply the trip generation potential and average frequency of trip generation and shareratio of bus transit together, and the product is potential of bus stop. The data of average frequency of
trip generation and share ratio of bus transit are got from C zone data of person trip survey inKumamoto city area. The former is 2.47 trips/person, and the later is 0.041.
Second, the potential of bus stop on any route are summed up, and the total divided by number ofoverlapping bus routes is the route potential. A weighted average of the route potential by service
frequency divided by a weighted average of operating kilometer by service frequency is the routepotential per kilometer in each bus route.
The attractiveness of passengers of the bus route is evaluated to compare the route potential per
kilometer with actual passenger number per kilometer.
(2) Public
Here, to show significance of bus transit for daily life along the bus route is regarded as showing public.
Number of people who can not consume public transit service without the bus route is called Limited
Dependent Population.

Those who can not drive a car because of no driving license, too young or too old are considered to be
dependent on public transit. Thus the people is divided into three age groups; young age group is form
0 to 14 years old, middle age group is from 15 to 64 years old, old age group is more than 65 years old.
The population of each age group is surveyed along each bus route, and population ratio of each age
group is calculated.
Multiplying these ratios and population in each circle, population of each age group in each circle iscalculated. Then, giving added weight to the population of each age group, Total Limited Dependent
Population is calculated according to Equation (5). This Total Limited Dependent Population
represents public. If Total Limited Dependent Population of a bus route is lager than an average ofTotal Limited Dependent Population, public is judged high.
TLP = αx1 + β x 2 + γx 3

(5)Where, x1 , x 2 and x 3 are population of young age group, population of middle age group and524

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population of old, old age group respectively. α , β and γ are public intense coefficient of eachage group. These coefficients are got from person trip survey in Kumamoto city area (Kumamoto
Transport Plan Council, 1999), bus transit share ratio of middle age group is standardized as 1.0. The
public intense coefficient of each age group is shown in Table 2.
Table 2. Weight Coefficients of PublicYoung Age Population
α
0.31
Middle Age Populationβ
1.00
Old Age Populationγ2.38(3) Management Condition
The operating ratio of each bus route represents management condition whether each bus route is in theblack or red. Here, operating ratio indicates operating expenses as a percentage of operating revenue.
4.2 Grouping of Bus Route45 bus routes of private bus company K are classified according to a combination of the quadrants on
the two planes of business effort and business environment. The result is shown in Table 3.
The bus routes belonging to ME4 are 9. They need examining business management condition in moredetail as targets for public subsidy because the public is high and the operating ratio is more than
100 %. However, all of them need improving the business effort because no route belongs to BE1 andME4. The bus route belonging to BE2 and ME4 is 1. The attractiveness of passengers is high and the
productivity is less than the average in it. Therefore, this bus route will be subsidized publicly undercondition that the operating cost is cut and the productivity is increased. The bus routes belonging to
BE4 and ME4 are 4. Since the productivity is high and the attractiveness of passenger is less than the
average in them, they will get public subsidies provided that they make efforts to increase passengers.
The bus routes belonging to BE3 and ME4 are 4. Since they lack business efforts, they need making
effort to increase passengers and cut in cost without public subsidy.
The bus routes belonging to ME3 are 14. Judging from only operating ratio as usual, these routes aretargets of public subsidy because of the red. However, they need making business efforts because thepublic is low in them and they belong to BE2, BE3 and BE4. If these are in the red and are improved
toward BE1, the routes will be subsidized publicly with rationalizing the formation.

Business Effort
Total

Table 3. Grouping of Bus Routs
Business Environment
ME1
ME2
ME3
ME4
BE1
9
1
0
0
BE2
0
2
7
1
BE3
0
0
5
4
BE4
6
4
2
4
15
7
14
9

total
10
10
9
16

In this way, a target of public subsidy can be narrowed efficiently by characterizing each bus routeaccording to a combination of the quadrants on the two planes, and then the business effort will be
stimulated, if necessary.
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4.3 Proposal of Improvement

Principal component analysis is executed for primary variables determining bus operating condition
because concrete improvements of each bus route are found. As accumulated proportion is more than
70% and eigenvalue is more than 1.0, the first three components are examined. Here, standardized
variables are used in this analysis. Factor loadings of the first three components are shown in Table 4.
The first principal component gives heavy weight to vehicle-miles, travel time, the first bus time, thelast bus time and frequency bus and thus represents “level of service”. The second component
represents “speediness”, with average speed, number of bus stop and interval of bus stop weighted
heavily. The third component represents “localness of bus route”. Because vehicle-miles, travel time,
average speed and number of bus stop are weighted positive, frequency of bus, number of route
overlapping and the last bus time are weighted negative, the score of local bus route tends to get bigger.

Vehicle-miles
Travel time
Average speed
Number of bus stop
Interval of bus stop
The first bus time
The last bus time
Frequency of bus
Total travel distance
Number of overlapping
Accumulated
Eigenvalue

Table 4. Factor Loading
Second component
First component
0.81
0.25
0.88
-0.03
-0.14
0.79
0.45
-0.68
0.10
0.86
-0.55
-0.06
0.69
-0.12
0.85
0.09
0.94
0.15
0.49
-0.04
42.76
62.09
4.28
1.93

Third component
0.49
0.37
0.39
0.41
-0.18
0.25
-0.31
-0.33
0.00
-0.41
73.73
1.16

Table 5. shows the average score of principal components by the group according to the business effort
and the business environment. Judging from characteristics of each group leaded from the score andthe business management condition in the previous section, the improvement goals and the policies arearranged in Table 6.
The productivity, the attractiveness of passenger and the management condition are well in the bus
routes belonging to (BE1, ME1) and (BE1, ME2). Thus the business management condition issatisfactory. However, more operating revenues are expected by improving factors of “speediness” inthe local bus route whose score of “localness of bus route” is low.
The attractiveness of passenger and the management condition are well but the productivity is not wellin the bus routes belonging to (BE2, ME2). These need cutting in cost to improve the productivity.
The productivity and the management condition are not well in the bus routes belonging to (BE2,
ME3) and (BE2, ME4). These need improving the management condition and the productivity. Since
the scores of “level of service” and “speediness” tend to be high in the bus routes belonging to (BE2,ME3), these need cutting in cost to improve the productivity. The bus route belonging to (BE2, ME4)
needs cutting in cost and increasing passengers by improving factors of “speediness” to improve theproductivity.
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BE1
BE2
BE3
BE4

Table 5. Average Principal Component Score of Each Bus Route Group
Level of service
Speediness
Localness
ME1 ME2 ME3 ME4 ME1 ME2 ME3 ME4 ME1 ME2 ME3－－ -0.70 -0.01 －－ -0.19 -1.16 －0.59 0.37－
0.69 0.26 0.35－
1.13 1.46 -1.03 －0.27 -0.41－－ -1.22 0.48－－
0.46 0.08－－
0.39
0.32 -0.66 -1.04 -0.56 -0.92 -0.24 0.17 -0.40 0.25 -0.66 -0.46
Table 6. Improvement target and policy of each group
ME1
ME2
ME3
Goal
PolicyGoal
PolicyGoal
PolicyBE1

To improve
management
condition

To improve
speediness inlocal route

To improve
management
condition

To improve
speediness inlocal route

BE2

＊＊＊

＊＊＊

To increase
productivity

To cut in cost

BE3

＊＊＊

＊＊＊

＊＊＊

＊＊＊

To increase
passenger

To improve
speediness inlocal route,
To improve
LOS in urban
route

BE4

To increase
passenger

To improve
LOS＊＊＊
To improve
management
condition,
To increase
productivity
To increase
passenger,
To increase
productivity
To improve
management
condition,
To increase
passenger

ME4
－
1.04
0.82
0.26

ME4
Goal

Policy

＊＊＊

＊＊＊

＊＊＊

To cut in cost

To increase
productivity

To cut in cost，
To improve
speedinessTo cut in cost，
To improve
LOS

To increase
passenger,
To increase
productivity

To cut in cost,
To rationalize
bus routeformation

To improve
LOS

To improve
management
condition,
To increase
passenger

To improve
LOS，Toimprove
speediness

All of the productivity, the attractiveness and the management condition are not well in the bus routes
belonging to (BE3, ME3) and (BE3, ME4). Thus they are required to make quite a business effort. The
sore of “level of service” is low in the routes belonging to (BE3, ME3). They need improving factorsof “level of service” to improve the attractiveness of passengers and the productivity. The sores of“level of service” and “speediness” are not low in the route belonging to (BE3, ME4). They needbasically rationalizing their formation to improve the attractiveness of passengers and the productivity.
The productivity and the management condition are well but the attractiveness of passenger is not wellin the bus routes belonging to (BE4, ME1) and (BE4, ME2). Thus they need improving theattractiveness of passengers. The score of “speediness” is low in all 6 bus routes belonging to (BE4,
ME1). 4 local bus routes in them are expected to increase passengers by improving factors of“speediness”. On the other hand, 2 urban bus routes in them need improving the attractiveness ofpassenger by improving factors of “level of service” rather than “speediness”. The bus routes
belonging to (BE4, ME2) are mostly urban bus route, and need improving factors “level of service” toincrease passengers.
The productivity is well but the management condition and the attractiveness of passengers are notwell in the bus routes belonging to (BE4, ME3) and (BE4, ME4). Thus they need improving themanagement condition by increasing passengers. They need improving factors of “level of service” toincrease passengers because the score of “level of service” is low in all of them.

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5. CONCLUSION

The grouping method according to business management condition of bus route is proposed. Business
management condition of each bus route can be indicated according to a combination of the plane ofbusiness effort and the plane of business environment.
This method is applied to the evaluation of 45 bus routes of private bus company K in Kumamoto city.
Consequently, each bus route is classified under 16 categories. Roughly speaking, 20 bus routes are
inexpensive and profitable, 6 bus routes are inexpensive and unprofitable, 2 bus routes are expensive
and profitable, 17 bus routes are expensive and unprofitable.
Furthermore, the characters of bus route are summarized by principal component analysis, because
business management elements of each bus route are characterized efficiently. The result of thisprincipal component analysis and grouping of bus route according to business management condition
are combined, and the improvement policies of management are proposed. Through this method, thesubsidized bus route can be distinguished efficiently, and the improvement policy can be shown for thebus routes without public subsidy definitely. These results will be helpful in assessing business
management condition when public subsidy is expended in operating bus service.

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