Journal of the Eastern Asia Society for Transportation Studies, Vol.9, 2011

Evaluating Compactness of Cities by Energy Consumption Efficiency
Yanhong YIN
Ph.D Candidate
Graduate School of Science and Technology
Kumamoto University
2-39-1, Kurokami, Kumamoto
860-8555 Japan
Fax: +81-96-342-3541
E-mail: yanyangtian0627@yahoo.co.jp

Shoshi MIZOKAMI
Professor
Graduate School of Science and Technology
Kumamoto University
2-39-1, Kurokami, Kumamoto
860-8555 Japan
Fax: +81-96-342-3541
E-mail: smizo@gpo.kumamoto-u.ac.jp

Abstract: We present a microeconomic based quantitative analysis scheme to evaluate
compactness of cities by the energy consumption efficiency considering 1) the utility theory
based on personal consumption behaviors, and 2) a consistency between the level of utility
and energy consumption. By representing quality of life by utility, this study develops a CES
typed model to estimate the actual and minimum individual energy consumption for present
utility. Energy consumption efficiency index is introduced to analyze the compact level ofcities. We applied this model to the Kumamoto and Nagasaki region. Higher energy
consumption efficiency is found in Nagasaki which has more compact city structure and masstransit usage. Zones with higher energy consumption efficiency are mainly located in city
center and along mass-transit lines in both regions. Such findings suggest that more compact
urban structure and higher mass-transit usage can induce greater urban energy consumption
efficiency.
Key Words: compact city, energy consumption, utility, quality of life, CES

1. INTRODUCTION
Since the intensification of the global search for sustainable urban development in the late1980s, there has been growing support in compact city theories and policies. It is believed thiskind of higher density urban form attribute to less car trips and preservation of greens andarable land. Thinh et al. (2002) suggest compact city has two attributes: physical andfunctional. The physical compactness refers to the spatial configuration of land-use
development within the city, the functional compactness to the density and mix of daily
activity (Thinh et al. 2002). In seeking to provide empirical suggestions for compact city
planning strategy, many studies seek indicators for urban compactness. Measurement andevaluation of compactness of cities are mainly conducted on these two attributes. Thinhcreates a database of land-use patterns and evaluates the physical compactness of 116 German
Regional Cities (Thinh et al. 2002). While some researchers analyze maps or satellite images
like remote sensing images to evaluate the urban signature and compactness (Li et al. 2008;
Guindon and Zhang, 2007). Others analyze the compactness measurements based on densityand daily activity (Chen et al. 2008).
Our research attempts to analyze the compact city from the view of energy consumption basedon two reasons. Firstly, from the physical point, compact urban spatial configuration affects
the total amount of energy consumption. Secondly, density and intensity of activities, such as
traffic, are major factors influencing energy consumption. Furthermore, growing concerns
about urging oil prices and greenhouse gases produced by burning fossil fuels require theurban development to minimize the usage of resources, spatial displacement of environment

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Journal of the Eastern Asia Society for Transportation Studies, Vol.9, 2011

and improve energy consumption efficiency (Burgess, 2000; Williams, 1999). The amount ofenergy consumption is very important and effective index to evaluate the compactness ofcities.
Energy consumption is closely related to actual land-use and transportation. Importantly, itaffects the quality of life from the individual viewpoint. Aoyama et al. (2006) proposed a
micro-economic model to seek a representative consumer’s traffic pattern that minimizes
energy consumption while keeping the present mobility level. He also investigated the urban
structures and transportation policies in order to realize such traffic pattern. It is a good try tosolve the energy consumption problem based on the individual mobility through some kind of
micro-economic model. However, his research limits to personal mobility. How to estimate
the minimum energy consumption without declining quality of life will no doubt be more
helpful in urban sustainable development.
Two main aims are included in this study: 1) development an index to evaluate the urban
compactness based on energy consumption; 2) estimation the energy consumption on present
quality of life. Four sections are included in this paper. In the section 2, we show thedevelopment of a model to estimate the minimum energy consumption. In section 3, we apply
this model to Kumamoto and Nagasaki regions in Japan, to analyze energy consumption andenergy consumption efficiency. The section 4 presents conclusion and discussion.

2. METHODOLOGY
2.1 Model Framework
The term utility, which had been interpreted in 20th century economics, describes thesatisfaction experienced by a person through the consumption or use of a commodity. We use
utility to describe quality of life in purely economic terms. Utility is a measurable quantity andis a value function (or scale of preference) to describe consumer behavior. People are assumed
to maximize the utility to achieve the present level of quality of life. Maximum utility isachieved by consuming various kinds of goods, like food, clothes, house, trips et al..
Consuming goods is also actually a process of energy consumption. The problem in ourmodel is how to estimate the minimum energy consumption at maximum utility and find thecorresponding amount of goods.
Some assumptions are needed in order to formulate the model.
1. As transportation sector is a bigger contributor to energy consumption, we classified all
goods into two types: mobility goods and composite goods. Mobility goods include car
trips and mass transit trips. Composite goods are all other goods except mobility goods.
We assume that the representative consumer in zone i consumes three types of goods:
composite goods and trips by car and mass transit. The demands are shown as x1i , x2Ci andx2Mi , respectively.
2. The mobility level x2i is a function of the number of trips by car x2Ci, and trips by masstransit x2Mi.
3. Utility ui, which reflects the level of quality of life, is defined as a function of these threekinds of goods.
4. Representative consumer in zone i is assumed to maximize his/her utility and mobility byconsuming different amount of goods under the income budget constraint.
5. All the income is spent on consuming goods without saving.

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Journal of the Eastern Asia Society for Transportation Studies, Vol.9, 2011

We developed our model framework shown as Equation (1). We would like to explore
activities that minimize the energy consumption Ei on the maximum utility level ui*.

min

{ x1 i , x2 Ci , x2 Mi }( x , x )x

E = ∑ E = ∑ (e x + e tiis.t. u ( x , x , x
i

1i

1

i

2 Ci

1i

2 Ci

2 2 Ci

2 Mi

+et

2 Ci

3 2 Mi( x , x )x )
2 Ci

2 Mi

2 Mi

) = u , ∀i

(1)

∗

2 Mi

i

The total energy consumption E is a multi-objective function of Ei, which means average
individual daily energy consumption in zone i. e1, e2, e3 are energy consumption unit of eachgood. t2Ci, t2Mi are average time of each car trip and mass transit trip, which are functions ofcar and mass transit trips.
2.2 Definition of Utility Function
How to express the utility function is very important. First, we assume that there is a
substitutive relation between the number of car trips and mass transit trips. The mobility levelcan be defined as a function of them. Meanwhile, a substitution relationship also exists
between the amount of composite goods and mobility goods. For representing these two kindsof relationships, a nested type CES (Constant Elasticity of Substitution) function is used
(Kanemoto et al., 2006). The structure is shown in Figure 1. The actual functional form ofutility and mobility is expressed as Equation (2) and (3).
Utility u i

Composite goods x1i

σ1

α1

Mobility goods x 2 iα2σ2
α 2C α 2 M Trips by mass transit x 2 Mi

Trips by car x 2Ci

Figure 1 Structure of utility functionu ( x , x ) = {α x σ( 1 −1) / σ 1

i

1i

2i

1

1i

+α x σ( 1 −1) / σ 1

2

{

2i

}

σ1 /( σ −11 )(2)

x 2i ( x 2Ci , x 2 Mi ) = α 2C x 2'σCi−1) / σ + α 2 M x 2(σMi−1) / σ
2

2

2

2

}

σ 2 /(σ 2 −1)(3)Here, σ1 and σ2 are the elasticity of substitution between two goods at the first and second
stages. Further, α1 and α2 are the share parameters for composite goods and mobility goods,
while α2C and α2M are those for car trips and mass transit trips, respectively.
2.3 Present Utility Level
The following procedure is introduced to calculate the present utility level. At first,
maximizing mobility level subject to transportation budget constraint is formulated shown as
Equation (4). Revealed mobility level is defined as maximum mobility level, which isdetermined by the number of trips by car and mass transit. x*2Miare the optimal solutions of thenumber of trips by mode M (car or mass transit), and x*2i is the revealed mobility level, shownin Equation (5), (6), respectively.

max : x = {α x σ(

x 2 Ci , x 2 Mi

2i

s.t.

2C

2 −1 ) / σ 22 Ci+α x σp x +p x
2 Ci

2 Ci

(

2M

2 Mi

715

2 Mi

2 −1 ) / σ 2

2 Mi

≤I

2i

}

σ 2 /( σ 2 −1 )(4)

Journal of the Eastern Asia Society for Transportation Studies, Vol.9, 2011

x

*
2 Mi

α
= 
p


I
 σ σσσ
α p +α p

2M

2i

2 Mi

2

1−

2C

2 Ci

2

1−

2M

2 Mi

2

(5)

2

x = (α σ p σ + α σ p σ ) σ ⋅ I
*

2

1− 2

2

1− 2

2i

2C

2 Ci

2M

2 Mi

1/(

(6)

2 −1 )

2i

Utility maximization problem subject to income constraint is shown in Equation (7).The
demand function of the composite goods and revealed mobility are written analytically as thesolution of the utility maximization problem as Equation (8).
max : u = {α x σ(i

x1 i , x2 i

1

1 −1 ) / σ 11i+α x σ(2p x +p x ≤I

s.t.

1i

1i

2i

1 −1 ) / σ 1

2i

2i

}

σ 1 /( σ 1 −1 )

(7)

i

α 
I
x =   σ σσσ
 p α p +α p
*

k

i

ki

1− 1

1

ki

(8)

1− 1

1

1i

1

2i

2

p1i, p2i, p2Ci, p2Mi are the prices in zone i for composite goods, mobility goods, car trips andmass transit trips, respectively. Further, Ii is the individual income and I2i is the individualtransportation budget, each in zone i.
From Equations (5), (6) and (8), the optimal number of trips in zone i by car and mass transit
can be calculated as Equation (9). Substituting (8), (9) into utility function, the present utility
level can be obtained.

x

∗

2 Mi

α
= 
p

σ2

2M

1

2

2 Mi

−1

σ σ
σ
 σ σ σ α (α p + α σ p σ ) σ α σ p σ + α σ (α σ p σ + α σ p σ ) σ  I



2

1−

2C

2 Ci

2

2

1−

2M

2 Mi

2− 1
1− 2

2

1−

1

1

1

1

1

2

2

1−

2C

2 Ci

2

2

1−

2M

2 Mi

2

1−
1−

1

2

i

(9)

2.4 Energy Consumption Efficiency Index
In order to evaluate the compact level of cities, energy consumption efficiency is introduced.
Two kinds of index are analyzed: estimated actual UEi and estimated optimal UEi*, which are
shown in Equation (10), (11). Weighted index of energy consumption efficiency, UE and UE*,are applied to reflect the regional actual and optimal energy consumption efficiency level,
shown in (12) and (13).
UEi =

ui

*

(10)

Ei
*
ui
*
UEi = *Ei

(11)

UE = (1 / P ) ⋅ ∑ UEi ⋅ Pi

(12)

UE * = (1 / P ) ⋅ ∑ UEi ⋅ Pi

(13)

i

*

i

Here, ui*is the maximum utility, and Pi is the population, all in zone i. Further, Ei, Ei* areestimated actual and minimum energy consumption in zone i.

3. APPLICATION TO KUMAMOTO AND NAGASAKI METROPOLITAN REGIONS

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Journal of the Eastern Asia Society for Transportation Studies, Vol.9, 2011

3.1 Study Area
We chose Kumamoto and Nagasaki metropolitan regions for our study. Both regions arelocated in Kyusyu island in south of Japan. Kumamoto is a little bigger region, with apopulation of 970,380 in 1997, compared to 726,112 in Nagasaki in 1996. Two cities(Kumamoto and Uto), fourteen towns and one village are in Kumamoto metropolitan region,and the core city is Kumamoto city with a population of 0.67 million and area 267 km2.
Nagasaki metropolitan region covers three cities (Nagasaki, Isahara, Omura) and four towns.
Nagasaki city is the center city with population of 0.44 million and area 241 km2 (Figure 2).

Figure 2.a Kumamoto metropolitan region

Figure 2.b Nagasaki metropolitan region

The zone marked by white is Kumamoto Station

The zone marked by white is Nagasaki Station

Km2
90

Person600,000
550,000

Person/km2
14000

80

13000

70

12000

60

11000

500,000
450,000
400,000
350,000

10000

50

9000

300,000
40

250,000
200,000

8000

30

150,000

7000

20

6000

10

5000

0

4000

100,000
50,000
0
1965

1970

1975 1980
Year
Population of DID in Kumamoto
Area of DID in Kumamoto

1985

1990

1995

1965 1970 1975 1980 1985 1990 1995 2000
Year
Popupation density of DID in Kumamoto

2000

Population of DID in Nagasaki

Popupation density of DID in Nagasaki

Area of DID in Nagasaki

Figure 3.a Population and area of DIDs

Figure 3.b Population density of DIDs

According to the Japan Statistics Bureau and Statistics Center, a densely populated district(DID), is defined as a district that has a population density over 4,000 inhabitants per square
kilometer and a combined population of more than 5,000. With the tendency of urbanizationand the flow of population into major urban spheres, it is projected that the population andarea of DIDs will continue to grow up, although at a progressively slow pace in developed
countries. The phenomenon is also taken place in Kumamoto and Nagasaki regions, whereconsistently increasing population of DID, the area of DIDs, and yearly decreasing population
density of DIDs, are shown in Figure 3. Both regions are proceeding a process of urban
growth and urban sprawl. However, compared two regions, Nagasaki regions shows a slow
speed of urban sprawl and seems remaining a relatively more compact urban structure than
Kumamoto from the viewpoint of smaller DID area and high population density in city center.

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Journal of the Eastern Asia Society for Transportation Studies, Vol.9, 2011

3.2 Data
We apply this model to Kumamoto and Nagasaki at almost same time period, in 1997 and1996, when person trip surveys were conducted. The trip data used in this paper are from
Kumamoto personal trip survey (PTS) 1997, Nagasaki PTS 1996, supplied by Kumamoto
Metropolitan Regional Urban Transport Planning and Consultation Organization, Nagasaki
Metropolitan Regional Urban Transport Planning and Consultation Organization. Some basic
information of the PTS is shown in Table 1. Residents in Kumamoto are more car-dependence
and travel far than the ones in Nagasaki. It can be shown as higher car ownership rate, more
average car trips and longer trip length. In Nagasaki, fewer trips are generated each day, andthe percentage of trips by mass transit, including railway, light subway, bus, is the relatively
higher.
Table 1 Information about related PTS
Kumamoto (1997)
177 zones

Nagasaki (1996)
88 zones

970,380

726,112Car ownership rate(vehicle/1000 person)

569

442

Average trips（one day/person ）

2.47

2.38

Average trip length (km/trip)

6.81

2.66

Average car trips (one day/person )

1.44

0.94

Average mass transit trips (one day/person )

0.18

0.33

Other mode trips( one day/person )

0.85

1.11

7.29%

13.87%

Traffic zones
Population

Mass transit trip share

In order to estimate the model and investigate the individual energy consumption in eachzone, many kinds of data are needed.

Number of trips by car and mass transit (trips/person·day) are aggregated from original
dataset of personal trip survey. We focus on only the trip purpose of commute,business, shopping and returning home trips.

Average travel time by car and mass transit from zone i to every other zones isobtained by trip assignment results of road and mass transit networks.
Generalized cost by car and mass transit consists of two kinds of cost here. One is thetime cost, which is the result of multiplying the value of time and trip time. According
to statistical report from Japanese Road Bureau, Ministry of Land, Infrastructure andTransport (MLIT), the time value for car trip is 38.11 yen/min·person, and for masstransit trip is 40 yen/min·person. The other kind of cost is the price of each trip. We
can get the running fee unit (yen/km·vehicle) data from statistical report by MLIT,
considering the fees related to running distance, including oil, tyre, tube, maintenance,
vehicle depreciation. We transfer this data to our car trip price p2Cij as this way:
p2Ci (yen/person·trip) =running fee unit (yen/km·vehicle)
× minimum distance from zone i to j (km/trip)/ average number of passengers (persons/vehicle)
The number of passengers in each car is set to 1.21 according to the report. The priceof mass transit trip p2Mij is determined by the mass transit fare.

It is difficult to obtain the zonal income data since only the total income in each town
and city is available from Kumamoto Prefecture Government and Nagasaki Prefectural

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Journal of the Eastern Asia Society for Transportation Studies, Vol.9, 2011

Government. As a positive relationship observed from land price and income level, we
distribute the total income among zones according to the zonal price ratio of land
confronting major roads and railway, given the land price data by Japanese National
Tax Agency.
The composite goods energy consumption unit e1 (kcal/yen) is calculated as the resultof dividing the all energy each household consumed (kcal/household·month) by thehousehold monthly expenditures except the transport fee, given by Japanese Statistics
Bureau of Ministry of Internal Affairs and Communications and EDMC (Handbook ofEnergy& Economic Statistics in Japan). Car trip and mass transit trip energy
consumption unit e2, e3 (kcal/trip·min) have relationship not only with the running
distance, but also with speed. Here we transfer the trip distance energy consumption
unit (kcal/trip·km), which is available from statistical report by MLIT, to trip timeenergy consumption (kcal/trip·min). Having the data of weighted average speed(km/min) of all trips, the result of e2, e3 can be calculated and are listed in Table 2.
Similar energy consumption unit for composite good are found in two regions.
Nagasaki shows bigger energy unit for car trips and mass transit trips.
Table 2 Energy consumption unit
Composite goods e1（kcal/Yen）
Car trip e2（kcal/trip·min）
Mt trip e3（kcal/ trip·min）

Kumamoto(1997)
3.64
197.18
18.16

Nagasaki(1996)
3.51
256.5920.09

3.3 Procedure of Estimating Minimum Energy Consumption
We estimate the minimum energy consumption according to the stepwise as shown in Figure
4. The procedure is as follows:

Figure 4 Calculation flow of minimum energy consumption
Step 1: As the numbers of car and mass transit trips by zone can be calculated from mobility

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Journal of the Eastern Asia Society for Transportation Studies, Vol.9, 2011

maximization process, so the present utility level can be evaluated by Equation (2).
Step 2: By using the evaluation model, which minimizes energy consumption for present
utility level, we can calculate the corresponding amount of three kinds of goods: trips by car
x2Ci , trips by mass transit x2Mi, and composite goods x1i.
Step 3: The trips x2Ci and x2Mi given by step 2, are distributed to zones to form OD matrixesof mode by using a destination choice model. It will be mentioned later.
Step 4: Compare the OD matrixes with the original ones before the destination choicemodel. If x2Ci and x2Mi converge, stop and calculate the minimum energy consumption;otherwise, proceed to step 5.
Step 5: Assignments of OD matrix of car trips and mass transit trips are done.
Step 6: We solve the model again with a renewed costs, p2Ci, p2Mi, and travel times t2Ci, t2Mi.
Step 7: Return to Step 2.
3.4 Results
We compared the results of estimated actual and minimum energy consumption (Table 3).
More than 70% of the estimated actual energy is consumed by composite goods. The actualenergy share of car trips is over 20% in both regions. However, this value is a little bigger inKumamoto, 2.37% higher than in Nagasaki. The energy share of mass transit trips in Nagasaki
is 1.69%, higher than Kumamoto (2.47% to 0.41%). There is a big reduction in estimatedminimum energy consumption, more than 10% cut compared to the actual energy in bothregions. It is possible to reduce 5300kcal individual daily energy consumption in Kumamotoby decreasing 81.2% of energy consumption by car trips and increasing mass transit trips fourtimes. In Nagasaki, the goal of cutting 12.8% of energy consumption can be achieved by
reducing 87.8% of energy for car trips and increasing energy share in composite goods andmass transit trips by 5.7% and 175% respectively. Big energy share of composite goods(nearly 90%), relative higher energy share of mass transit trips and reduced car trips energy
share contribute to minimum energy consumption in both regions. The main attributors toachieve the minimum energy consumption goal are increasing energy share of composite
goods and mass transit trips, and decreasing energy share of car trips. Compared the estimatedactual and minimum energy consumption, Nagasaki shows a smaller difference than
Kumamoto, with a decreasing rate of 12.8% to 14.2% (Table 3).
Table 3 Estimated actual and minimum individual daily energy consumption
Kumamoto
Estimated
actualTotal energy consumption(kcal/person·day)

3.72×104

Energy for composite goods(kcal/person·day)

2.72×104

Energy for car trips(kcal/person·day)
Energy for mass transit trips(kcal/person·day)
Energy share of composite goods
Energy share of car trips
Energy share of mass transit trips

9.87×103
1.52×10273.12%
26.48%
0.41%

Estimated
minimum
3.19×104(-14.2%)
2.93×104(7.7%)
1.85×103(-81.2%)
7.89×102(419.0%)91.74%
5.79%
2.47%

Nagasaki
Estimated
actual2.81×104
2.08×104
6.79×103
5.92×102
73.79%
24.11%
2.10%

Estimated
minimum
2.45×104(-12.8%)2.2×104(5.7%)
8.22×102(-87.8%)
1.63×103(175%)
89.99%
3.36%
6.65%

Note: the figure in () shows the increasing percentage of estimated minimum compared to estimated actual energy consumption

We investigated the energy consumption efficiency at regional and zone levels. Larger thevalue of index is, more compact the city is. The difference between estimated actual and720

Journal of the Eastern Asia Society for Transportation Studies, Vol.9, 2011

optimal energy consumption efficiency, △ UE*= UE-UE* (estimated actual energy
consumption efficiency minus optimal energy consumption efficiency), is calculated tocompare the achievement level of optimal energy consumption efficiency.
From Table 4, individual utility level in Kumamoto is higher than in Nagasaki. It is the same
as expected since lower income level in Nagasaki with the average income 6,286
yen/person·day compared to 8,290 yen/person·day in Kumamoto. The actual energy
consumption efficiency is higher in Nagasaki region. It is interesting to observe that Nagasaki
region shows higher estimated actual energy consumption efficiency, but with lower estimatedoptimal energy consumption efficiency. The difference between estimated actual and optimalenergy consumption efficiency, is bigger in Kumamoto (0.032 compares to 0.028 in
Nagasaki). Nagasaki is more compact than Kumamoto with higher estimated actual energy
consumption efficiency. This is consistent with results suggested by other evaluation method,such as population density. Higher population density of DIDs means more compact urban
structure of Nagasaki mentioned in 3.1. Moreover, Nagasaki region seems to be much easily
to reach the goal of optimal energy consumption efficiency than Kumamoto.
Table 4 Estimated actual and optimal energy consumption efficiency

Utility
Total energy consumption(kcal/person·day)
Energy consumption efficiency
Difference between estimated actualand optimal efficiency △UE*

Kumamoto
Estimated
actual6,966

Estimated
optimal
6,966

Nagasaki
Estimated
actual
5,289

Estimated
optimal5,289

37,27631,88828,15424,496

0.187

0.218

0.188

0.216

-0.032-0.028Figure 5 and Figure 6 show the space distribution of estimated zonal actual energy
consumption efficiency, estimated zone optimal energy consumption efficiency, network andpopulation density in the Kumamoto and Nagasaki region. Although a few zones with higher
estimated actual energy consumption efficiency are found in suburban or rural area, the energy
consumption efficiency decreases with the distance to the city center. Zones along the masstransit lines are higher energy efficient. For zonal estimated optimal energy consumption
efficiency results, zones with higher values are mainly concentrated in the city center.

Figure 5 Estimated zone actual energy consumption efficiency; estimated zone optimal energy
consumption efficiency, network and population density in Kumamoto in 1997

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Journal of the Eastern Asia Society for Transportation Studies, Vol.9, 2011

Figure 6 Estimated zone actual energy consumption efficiency; estimated zone optimal energy
consumption efficiency, network and population density in Nagasaki in 1996

4. CONCLUSIONS
Representing quality of life by utility, the present level of quality of life can be expressed by
the maximum utility. A microeconomic model is developed to estimating the minimum energy
consumption on maximum utility represented by consumption of composite goods, trips by
car and mass transit. Energy consumption efficiency index is introduced to compare compact
level of cities. By applying the model into Kumamoto and Nagasaki metropolitan region, theresults proved that greater energy consumption efficiency corresponds to more compact urban
structure in Nagasaki. More compact urban structure and higher mass transit usage can induce
greater energy consumption efficiency.
The methodology of this paper is important since it gives a research framework to estimate theenergy consumption on maximum utility from microeconomic viewpoint. Its result is valuable
to give suggestions for policy making in light of reducing the energy consumption while
keeping individual quality of life.

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