Preference Elicitation in Generalized Data Envelopment Analysis-In Search of a New Energy Balance in Japan

Peter Nijkamp (VU University Amsterdam)
Soushi Suzuki* (Hokkai-Gakuen University)

The recent dramatic change in energy supply in Japan has prompted a search for a newenergy-environment-economic efficiency policy, in which a compromise has to be foundbetween a sufficient supply of energy resources, the development of low carbon emission
technology, and a continuation of economic growth. The prefectures in Japan are regarded
as decision-making units (DMUs) which are responsible for the design of a new sustainableenergy balance in these regions. The main challenge is now to design an efficient energyenvironment-economic (EEE) system.
The present paper aims to develop a balanced decision-support tool for achieving anefficient energy supply in all Japanese prefectures. To that end, a new variant of Data
Envelopment Analysis (DEA) is presented, which is characterized by two integrated
features: (i) the use of a general Distance Friction Minimization (DFM) model to achieve
the most appropriate movement towards the efficiency frontier surface; (ii) the
incorporation of preference-based (PB) adjustments in efficiency policy strategies regarding
the input reduction or the output increase allocation of DMUs in order to balance rigorous
efficiency decisions with political priorities at the regional level. This paper illustrates thisnew methodology by means of an application to prefectural energy efficiency strategies inJapan.

Keywords: Data Envelopment Analysis (DEA); Distance Friction Minimization (DFM);
Preference Based (PB); Energy-Environment-Economic efficiency

JEL classifications: C00, R58, Q48

Preference Elicitation in Generalized Data Envelopment Analysis-In Search of a New Energy Balance in Japan
Peter Nijkamp (VU University Amsterdam)
Soushi Suzuki* (Hokkai-Gakuen University)

1. In Search of a New Energy Balance in Japan

DEA, including a short overview of DEA developments. This is

After the Fukushima nuclear catastrophe in Japan, the country

followed by an exposition of: (i) a Distance Friction

was faced with an unprecedented challenge in its energy policy:

Minimization (DFM) approach (in Section 3); and (ii) a

namely, to seek a new energy supply balance after thePreference-Based (PB) approach (in Section 4). Next, Section 5abandonment of nuclear power technology and supply. This

contains an empirical application of the above methodology tosudden transformation in energy supply policy called for anenergy policy at the prefectural level in Japan, including theintensive search for energy alternatives that could meet thepresentation of various research findings. Finally, Section 6

requirements of both supply efficiency and sustainable energy

makes some concluding remarks.

supply, while avoiding a situation of electrical power shortage.
Thus, the new energy policy of Japan has to find the right balance

2. Efficiency Improvement Projection in DEA

in the triangular relationship Energy - Environment - Economy,

A popular tool to judge efficiency in organizations is Data

governed by the policy objectives of electrical power savings,

Envelopment Analysis (DEA). Over recent years comparative

low carbon emissions, and the continuation of economic growth.

efficiency analysis has become a well-established field as part of

To meet these goals, a strategic foresight analysis of energy

a benchmarking exercise. DEA was originally developed tosupply in the country is necessary.

analyze the relative efficiency of a DMU, by constructing a

Although the national government in Japan is responsible forpiecewise linear production frontier, and then projecting thethe overall strategic design of future energy policy, the actual

performance of each DMU onto the frontier concerned. A DMU

implementation of energy policy takes place at the decentralized

located on the frontier is efficient, whereas a DMU that is not onlevel of 47 prefectures. These prefectures may be seen as decision

the frontier is inefficient. An inefficient DMU may then become

agents which may have to find a new balance in the supply of(more) efficient by reducing its inputs, or by increasing its outputs.

energy resources that would be efficient and environmentally-In the standard DEA approach, this is achieved by a uniform

sustainable. These conflicting objectives call for an operational

reduction in all inputs (or a uniform rise in all outputs). DEA

assessment framework for a balanced energy supply at thealready has a long history. The standard DEA model wasprefectural level. The main aim of the present chapter is todeveloped by Charnes et al. (1978) for assessing the performance

identify the most efficient and sustainable prefectural strategies inof a given DMUj (j=1,…, J), and can be represented as theJapan, so that other – lower-performing – prefectures canfollowing fractional programming problem:

improve their performance through a comparative benchmarking
exercise. The analytical tool used in the present chapter is based

max
v, u



on Data Envelopment Analysis (DEA), while the prefectures areincluded, viz. an adjusted distance measure for the mostappropriate movement towards the efficiency frontier, and apreference elicitation approach for the incorporation of a decision

s

so

m

mo

s

m

regarded here as agents or Decision Making Units (DMUs). We
present a new type of DEA in which two new elements are

u y
v x

s.t.

u y
v x
s

sj

m

mj

s

1

( j  1,, J )mvm  0 , u s  0 ,(2.1)

maker’s value judgment of input and/or output goals. These

where θ represents an objective function (efficiency score); xmj

integrated elements will be used in a new DEA context, with ais the volume of input m (m=1,…, M) for DMUj (j=1,…,J); ysj isview to the identification of the most efficient DMUs (i.e. thethe output s (s=1,…,s) of DMUj; and vm and us are the weights

Japanese prefectures).

given to input m and output s, respectively.

This study is organized as follows. Section 2 provides a brief
standard introduction to efficiency improvement projection in

The improvement projections  xˆo , yˆo  are usually defined in (2.2)

and (2.3) as follows:

an output increase as a strategy for a DMU. A major advantage ofxˆo    xo  s yˆo  yo  s  .

(2.2)

this model is that there is no need to incorporate the value(2.3)

judgment of a decision maker. Nevertheless, it may also be

These projections indicate that the efficiency of (xo, yo) for

attractive to develop it further to incorporate policy-maker value

DMUo can be improved if the input values are reduced radially-*judgments on political priorities.

by the ratio θ*, and the input excesses s are eliminated. The

We will use the optimal weights us* and vm* from (2.1), andoriginal DEA models presented in the literature have focused on athen describe the efficiency improvement projection model. A

uniform input reduction or a uniform output increase in thevisual presentation of this approach (DFM projection) is given in

efficiency-improvement projections. In principle, an infinite

Figures 3 and 4. In this approach a generalized distance function

number of improvements are required to reach the efficiency

is employed to assist a DMU to improve its efficiency by afrontier, and hence there is a multiplicity of solutions for any

movement towards the efficiency frontier surface. The direction

DMU to enhance its efficiency.

of efficiency improvement depends, of course, on the

The existence of many possible efficiency improvement

input/output data characteristics of the DMU. It is now

solutions has led to a rich literature on the methodologicalappropriate to define projection functions for the minimization of

integration

Lineardistance in weighted spaces. As mentioned, a suitable form ofProgramming) and the DEA models. The first contribution wasof the MOLP(Multiple Objective

multidimensional projection functions that serves to improve

made by Golany (1988), who proposed an interactive MOLP

efficiency is given by an MOQP (Multiple Objective Quadratic

procedure, which aimed to generate a set of efficient points for a

Programming) model which aims to minimize the aggregated

DMU. This model allows a decision maker to select the preferred

input reductions, as well as the aggregated output increases. Thus,

set of output levels, given the input levels. Thanassoulis andthe DFM approach can generate a new contribution to efficiency

Dyson (1992), Joro et al. (1998), Halme et al. (1999), Korhonenenhancement problems in decision analysis by employing aand Siljamäki (2002), Korhonen et al. (2003), Lins et al. (2004),

weighted Euclidean projection function, and, at the same time, it

Washio et al. (2012), and Yang and Morita (2013) have also

may address both input reduction and output increase. We briefly

proposed efficiency improvement solutions.

describe the various steps, based on Suzuki et al. (2010).
First, the distance functions Frx and Fry is specified by means

3. The Distance Friction Minimization (DFM) Approachof (3.1) and (3.2), which are defined by the distances shown in

We now present the principles of a recently developed andFigures 3 and 4. Next, the following MOQP is solved by using (amore appropriate approach. Detailed descriptions and empirical

reduction of distance for xmo) and (an increase of distance for yso)

applications can be found, inter alia, in Suzuki et al. (2010). As

as variables:

mentioned above, the original efficiency improvement solution inmin

Fr x 

the original CCR-input model requires that the input values are
reduced radially by a uniform ratio θ*. The (v*, u*) values

favorable weights for DMUo, in the sense of maximizing the ratio
scale. vm* is the optimal weight for the input item m, and its
magnitude expresses how much in relative terms the item iscontributing to efficiency. Similarly, us* does the same for the
output item s. These values show not only which items contribute


m mo


m

x 2
mo

(3.1)

m

min

Fr y 

obtained as an optimal solution for formula (2.1) result in a set of
optimal weights for DMUo. Hence, (v*, u*) is the set of the most v x  v d  u y  u d 

s so

 y 2
s so

(3.2)

s

s.t.

2 

 v x  d   1  

m

mo

x
mo



(3.3)

m

2 

 u y  d   1  

s

so

y
so



(3.4)

s

x
x
xmo  d mo
 0 , d mo
 0 , d soy  0(3.5)

to the performance of DMUo, but also to what extent they do so.

where xmo is the amount of input item m for any arbitrary

In other words, it is possible to express the distances (orinefficient DMUo; and yso is the amount of output item s for any

alternatively, the potential increases) in improvement projections.

arbitrary inefficient DMUo. The constraint functions (3.3) andSuzuki et al. (2010) proposed a Distance Friction Minimization(3.4) refer to the target values of input reduction and output(DFM) model that is based on a generalized distance function,

augmentation. The proportional distribution of the input andand serves to improve the performance of a DMU by identifying

output contributions in achieving efficiency is established as

the most appropriate movement towards the efficiency frontier

follows. The total efficiency gap to be covered by inputs andsurface. This approach may address both an input reduction andoutputs is (1-θ*). The input and the output side contributeaccording to their initial levels 1 and θ*, implying shares

Parameter (OAP) of the total efficiency gap (1-θ*) in the DFMθ*/(1+θ*) and 1/(1+θ*) in the improvement contribution. Clearly,

model. The value of the OAP ranges from 0 to 1. For example, if

the contributions from both sides equal (1-θ*)[θ*/(1+θ*)], and (1-the OAP is specified to be 1.0, then the PB model can compute anθ*)[1/(1+θ*)].

efficiency-improving projection so that the total efficiency gap (1-Hence, we derive for the input reduction target and the output
augmentation targets the following expressions:

OAP is specified to be 0.7, then the PB model can compute an

Input reduction target:

efficiency-improving projection, so that 70 percent of the total2 v x  d   1  1    1     1   . (3.6)

m

mo

x
mo



1





m

Output augmentation target:2  .

y






u
y

d



1




s s so so1     1   efficiency gap (1-θ*) is allocated to output augmentation, and 30
percent of the total efficiency gap (1-θ*) is allocated to input
reduction. And, if the OAP is specified to be 0.0, then the PB(3.7)

model can compute an efficiency-improving projection so thatthe total efficiency gap (1-θ*) is fully closed by the input

It is now possible to determine each optimal distance dmox* anddsoy*θ*) is fully allocated to output augmentation. If, for instance, thereduction.

by using the MOQP model (3.1)-(3.5). The distanceInstead of the constraint functions (3.3) and (3.4) in the DFM

minimization solution for an inefficient DMUo can be expressed

model, the PB model uses the constraint functions (4.1) and (4.2):

by means of formulas (3.8) and (3.9):

s.t.


x
;
xmo
 xmo  dmo

yso
 yso  d soy  .

(3.8)

 v x

(4.1)

 u y  d     OAP1   .

(4.2)


m





x
 d mo    OAP 1   

m


s

(3.9)

mo

so

y
so





s

A visual presentation of constraint functions (4.1) and (4.2) isgiven in Figure 2.

Fig. 1 Degree of improvement of the DFM and the CCR
projection in weighted input space
By means of the DFM model, it is possible to present a new
efficiency-improvement solution based on the standard CCR
projection. This means an increase in new options for efficiencyimprovement solutions in DEA. The main advantage of the DFM

Fig.2 Illustration of the PB-DFM model with a value 0.7 formodel is that it yields an outcome on the efficient frontier that is

the OAP parameteras close as possible to the DMU’s input and output profile (seeFigure 1). For more details we refer to Suzuki et al. (2010).

First, the PB model starts with an initial specification of a value
for the OAP. This is just a decision maker’s value judgment for
the allocation percentage of an output augmentation in the total

4. A Preference-Based (PB) DFM Model

efficiency gap (1-θ*). Next, the target values, which are allocatedIn this section, we propose a preference-based (hereafter PB)

between input efforts and output efforts based on the OAP, areapproach to the DFM model. The rationale of this approach is thecomputed in Figure 2 using constraint functions (4.1) and (4.2).

following. A DMU may have specific priorities on the cost side

Finally, we are able to compute an input reduction value and an

and on the benefit side of its operation. For example, in various

output increase value based on the DFM model. A visualcases the goal of minimizing all cost items may affect the profit

presentation of this new PB-DFM projection is given in Figures 3

condition. Similarly, extreme output maximization may

and 4. This model will be called a Preference-Based DFM (PB-

jeopardize cost efficiency. Therefore, in many decision-making

DFM) model. We now illustrate the feasibility of the PB-DFM

situations, a balance between input and output targets has to bemodel by means of an application to current Japanese energy

found. Our PB approach specifies an Output Augmentation

policy, as sketched in Section 1.

(O2) Carbon emission in each prefecture (inverse number) (Gigatons/year) (2010). [Data source: Ministry of the Economy,
Trade and Industry in Japan(2010).]In our application, we first applied the CCR-I model, after
which its results were used to determine the CCR-I and DFM
projections. Additionally, we applied the PB-DFM model.
Finally, these results were compared with each other. We now
present the various findings stepwise.
5.2 Efficiency evaluation based on the CCR-I model
The efficiency evaluation results for each of the 47 prefectures
based on the CCR-I model are given in Figure 5. The figure
shows that 8 prefectures (Okinawa, Kochi, Tokushima, Tottori,
Fig. 3 Illustration of the DFM and PB-DFM approach

Nara, Shiga, Yamanashi, and Tokyo) are efficient DMUs. The(Input- vi*xi space)remaining 39 prefectures are inefficient. In particular, Niigata(0.696), Miyagi (0.696), Ehime (0.689), Gifu (0.686), and Aichi(0.678) have low efficiency.
Given the above findings, it seems necessary to make an effort
to improve the efficiency of the energy-environment-economic(EEE) efficiency for inefficient prefectures.

Fig. 4 Illustration of the DFM and PB-DFM approach(Output – ur*yr space)

Fig.5 Efficiency score based on the CCR model

5. An application of PB-DFM Model for Energy-

5.3 Efficiency improvement projection based on the CCR,

Environment-Economic (EEE) Efficiency in JapanDFM and PB-DFM models

5.1 Database and analysis framework

The efficiency improvement projection results based on the

In our empirical work, we use the following input and output

CCR, DFM and PB-DFM models for the 39 inefficient

data on the EEE key variables for a set of 47 prefectures in Japan.

prefectures are presented in Table 1. In the case of the PB-DFM

In our analysis we consider four Inputs (I):model, we apply an OAP parameter with an initially neutral value(I1) Electricity consumption in each prefecture (Giga Watt hours /of 0.7 as in Figure 3. Next, in Section 5.4, we show that theyear) (2010); [Data source: Ministry of the Economy, Trade

outcomes change when the decision maker changes his

and Industry in Japan(2010).]preference parameter OAP.

(I2) Public capital stock in each prefecture (million yen) (2010);[Data source: Government of Japan (2010).](I3) Private-sector capital stock in each prefecture (million yen)(2010); [Data source: Government of Japan (2010).](I4) Labor in each prefecture (employed persons) (2010). [Data

From Table 1, it appears that the empirical ratios of change inthe DFM projection are smaller than those in the CCR projection,as may be expected. In Table 1, this particularly applies to
Hokkaido, Miyagi, Akita, Yamagata, Fukushima, Tochigi,
Gunma, Toyama, Ishikawa, Nagano, Gifu, Shimane, Ehime,

source: Government of Japan (2010).]

Nagasaki, and Kumamoto which are apparently non-slack type

Furthermore, two Outputs (O) are incorporated:(i.e. s-** and s+** are zero) prefectures. The DFM projection(O1) GDP in each prefecture (million yen /year) (2010);

involves both input reduction and output increase, and, clearly,[Data source: Government of Japan (2010).]the DFM projection does not involve a uniform ratio, because thisTable 1 Efficiency-improvement projection results of themodel looks for the optimal input reduction (i.e. the shortest

CCR, DFM and PB-DFM models

distance to the frontier, or Distance Friction Minimization).

CCR

NormalDFM

PB-DFM(OPA=0.7)

Score(θ**) Score(θ**) Score(θ**)

DMU(Input)/(Output)

Score
Data

%

%

%

Hokkaido(I)PCS(I)PSCS(I)Labour(I)EC(O)GDP(O)CE
Aomori(I)PCS(I)PSCS(I)Labour(I)EC(O)GDP(O)CE
Iwate(I)PCS(I)PSCS(I)Labour(I)EC(O)GDP(O)CE
Miyagi(I)PCS(I)PSCS(I)Labour(I)EC(O)GDP(O)CE
Akita(I)PCS(I)PSCS(I)Labour(I)EC(O)GDP(O)CEYamagata(I)PCS(I)PSCS(I)Labour(I)EC(O)GDP(O)CE
Fukushima(I)PCS(I)PSCS(I)Labour(I)EC(O)GDP(O)CE
Ibaraki(I)PCS(I)PSCS(I)Labour(I)EC(O)GDP(O)CE
Tochigi(I)PCS(I)PSCS(I)Labour(I)EC(O)GDP(O)CEGunma(I)PCS(I)PSCS(I)Labour(I)EC(O)GDP(O)CE
Saitama(I)PCS(I)PSCS(I)Labour(I)EC(O)GDP(O)CE
Chiba(I)PCS(I)PSCS(I)Labour(I)EC(O)GDP(O)CE
Kanagawa(I)PCS(I)PSCS(I)Labour(I)EC(O)GDP(O)CE
Niigata(I)PCS(I)PSCS(I)Labour(I)EC(O)GDP(O)CE
Toyama(I)PCS(I)PSCS(I)Labour(I)EC(O)GDP(O)CE
Ishikawa(I)PCS(I)PSCS(I)Labour(I)EC(O)GDP(O)CEFukui(I)PCS(I)PSCS(I)Labour(I)EC(O)GDP(O)CE
Nagano(I)PCS(I)PSCS(I)Labour(I)EC(O)GDP(O)CEGifu(I)PCS(I)PSCS(I)Labour(I)EC(O)GDP(O)CE

0.731
59252111.044889593.7
2374750.043267.4
19846756.0
90.3
0.800
11540768.0
10744292.1
656460.011988.54807989.0
329.9
0.699
12132989.0
11424773.8
689089.010764.2
4314613.0
420.6
0.696
14343319.0
20031378.7
1077902.0
20018.98164598.0
239.2
0.825
10761226.0
9409577.9
527396.0
8568.63931020.0
563.3
0.887
10515916.0
9952882.1
576009.0
8101.64539434.0
584.1
0.742
14886234.0
24138593.0
925459.0
17822.9
7651487.0
288.1
0.738
16704317.0
34530548.8
1391815.0
31373.4
11950133.0
127.2
0.764
10153835.0
23221258.3
979347.021042.1
8312019.0
310.5
0.762
10868867.0
20700298.3
984232.0
19829.8
8284852.0
337.4
0.863
25509372.0
42159163.4
2772667.0
46801.5
21979233.0
122.3
0.769
24613569.0
50974915.1
2348365.0
47067.4
21258377.0
64.7
0.803
35387679.0
78450777.43529244.0
62926.5
33417789.0
74.1
0.696
23150353.0
28199046.1
1182239.0
20985.6
9366380.0
226.0
0.871
9510845.013833473.8
555660.013759.84771179.0
553.1
0.827
9387676.011277881.2
609218.0
9923.94590722.0
687.3
0.993
7581226.0
12891234.4
409695.0
9073.23485807.0
741.1
0.752
17175783.0
20837555.5
1076825.0
18144.69004613.0
302.4
0.686
14563077.0
20113232.7
968187.0
18298.3
7353771.0
286.6

1.000
-76.1%-26.9%-26.9%-56.5%
0.0%
0.0%
1.000
-39.5%-20.0%-20.0%-39.7%
0.0%
0.0%
1.000
-43.8%-30.1%-30.1%-32.4%
0.0%
0.0%
1.000
-49.6%-30.4%-30.4%-54.0%
0.0%
0.0%
1.000
-39.7%-17.5%-17.5%-20.6%
0.0%
0.0%
1.000
-31.4%-11.3%-15.0%-11.3%
0.0%
0.0%
1.000
-48.9%-31.6%-25.8%-25.8%
0.0%
0.0%
1.000
-48.2%-38.2%-26.2%-57.0%
0.0%
0.0%
1.000
-23.6%-30.3%-23.6%-43.7%
0.0%
0.0%
1.000
-28.3%-23.8%-23.8%-42.7%
0.0%
0.0%
1.000
-36.2%-13.7%-29.9%-54.8%
0.0%
0.0%
1.000
-44.0%-29.9%-23.1%-56.8%
0.0%
0.0%
1.000
-39.6%-28.9%-19.7%-50.2%
0.0%
0.0%
1.000
-65.2%-34.4%-30.4%-36.0%
0.0%
0.0%
1.000
-20.9%-12.9%-12.9%-14.8%
0.0%
0.0%
1.000
-20.7%-17.3%-17.3%-24.2%
0.0%
0.0%
1.000
-1.6%
-33.8%
-0.7%
-0.7%
0.0%
0.0%
1.000
-56.3%-24.8%-24.8%-47.5%
0.0%
0.0%
1.000
-53.4%-31.4%-31.4%-46.7%
0.0%
0.0%

1.000
0.0%
-16.0%
0.0%
0.0%
15.6%
0.0%
1.000
-16.4%-11.5%
0.0%-29.0%
12.1%
0.0%
1.000
-8.3%
-18.3%
0.0%-13.7%
20.0%
0.0%
1.000
0.0%
-18.5%
0.0%
0.0%
18.6%
0.0%
1.000
0.0%
-17.3%
0.0%
0.0%
12.0%
0.0%
1.000
0.0%
-7.4%
0.0%
0.0%
7.5%
0.0%
1.000
0.0%
0.0%
-15.1%
0.0%
15.8%
0.0%
1.000
-41.4%-29.5%-15.0%-51.9%
15.3%
0.0%
1.000
0.0%
0.0%
-14.0%
0.0%
14.4%
0.0%
1.000
0.0%
0.0%
-13.8%
0.0%
14.5%
0.0%
1.000
-32.3%-7.3%-25.0%-51.7%
7.4%
0.0%
1.000
-37.0%-21.0%-13.1%-51.6%
13.1%
0.0%
1.000
-33.2%-21.3%-10.9%-45.1%
10.9%
0.0%
1.000
-60.5%-24.2%-17.9%-28.6%
18.6%
0.0%
1.000
0.0%
0.0%
-7.1%
0.0%
8.3%
0.0%
1.000
0.0%
0.0%
-17.0%
0.0%
12.0%
0.0%
1.000
-1.3%
-33.3%
-0.4%
0.0%
0.5%
0.0%
1.000
0.0%
0.0%
-17.1%
0.0%
15.1%
0.0%
1.000
0.0%
0.0%
-19.1%
0.0%
19.9%
0.0%

1.000
0.0%
-8.3%
0.0%
0.0%
25.9%
0.0%
1.000
-21.5%-6.2%
0.0%-28.7%
19.1%
0.0%
1.000
-17.1%-9.3%
0.0%-13.0%
34.1%
0.0%
1.000
-17.1%-9.4%
0.0%-37.4%
31.8%
0.0%
1.000
0.0%
-9.5%
0.0%
0.0%
18.5%
0.0%
1.000
0.0%
-4.2%
0.0%
0.0%
11.2%
0.0%
1.000
0.0%
0.0%
-7.9%
0.0%
26.0%
0.0%
1.000
-37.0%-23.9%-7.8%-48.5%
25.2%
0.0%
1.000
0.0%
0.0%
-7.4%
0.0%
23.4%
0.0%
1.000
-12.6%
0.0%-7.3%-21.3%
23.4%
0.0%
1.000
-30.3%-4.1%-22.5%-50.1%
11.2%
0.0%
1.000
-32.8%-15.5%-6.9%-48.4%
21.1%
0.0%
1.000
-29.6%-16.9%-5.9%-42.1%
17.2%
0.0%
1.000
-57.2%-17.1%-9.1%-23.4%
31.8%
0.0%
1.000
0.0%
0.0%
-4.0%
0.0%
12.5%
0.0%
1.000
0.0%
0.0%
-9.3%
0.0%
18.6%
0.0%
1.000
-1.3%
-33.3%
-0.2%
0.0%
0.7%
0.0%
1.000
0.0%
0.0%
-9.0%
0.0%
24.6%
0.0%
1.000
-38.4%
0.0%-9.7%-17.2%
34.3%
0.0%

CCR

NormalDFM

PB-DFM(OPA=0.7)

Score(θ**) Score(θ**) Score(θ**)

DMU(Input)/(Output)

Score
Data

%

%

%

Aichi
(I)PCS(I)PSCS(I)Labour(I)EC(O)GDP(O)CE
Mie(I)PCS(I)PSCS(I)Labour(I)EC(O)GDP(O)CEKyoto(I)PCS(I)PSCS(I)Labour(I)EC(O)GDP(O)CEOsaka(I)PCS(I)PSCS(I)Labour(I)EC(O)GDP(O)CEHyogo(I)PCS(I)PSCS(I)Labour(I)EC(O)GDP(O)CE
Wakayama(I)PCS(I)PSCS(I)Labour(I)EC(O)GDP(O)CE
Shimane(I)PCS(I)PSCS(I)Labour(I)EC(O)GDP(O)CEOkayama(I)PCS(I)PSCS(I)Labour(I)EC(O)GDP(O)CE
Hiroshima(I)PCS(I)PSCS(I)Labour(I)EC(O)GDP(O)CEYamaguchi(I)PCS(I)PSCS(I)Labour(I)EC(O)GDP(O)CE
Kagawa(I)PCS(I)PSCS(I)Labour(I)EC(O)GDP(O)CE
Ehime(I)PCS(I)PSCS(I)Labour(I)EC(O)GDP(O)CE
Fukuoka(I)PCS(I)PSCS(I)Labour(I)EC(O)GDP(O)CESaga(I)PCS(I)PSCS(I)Labour(I)EC(O)GDP(O)CE
Nagasaki(I)PCS(I)PSCS(I)Labour(I)EC(O)GDP(O)CEKumamoto(I)PCS(I)PSCS(I)Labour(I)EC(O)GDP(O)CEOita(I)PCS(I)PSCS(I)Labour(I)EC(O)GDP(O)CE
Miyazaki(I)PCS(I)PSCS(I)Labour(I)EC(O)GDP(O)CE
Kagoshima(I)PCS(I)PSCS(I)Labour(I)EC(O)GDP(O)CE

0.678
34053192.0
88980912.0
4233682.0
72125.4
33871848.0
56.1
0.819
12381474.0
24437097.0
857656.0
22561.2
7970244.0
209.3
0.868
13670706.0
20590606.9
1128104.0
19393.0
10413400.0
345.7
0.719
39713219.0
87393692.5
4409530.0
69135.537376542.0
93.2
0.745
33135092.0
51620401.8
2330113.0
56340.2
20416330.0
77.0
0.811
7790136.0
10081469.9444554.0
7914.43673439.0
332.5
0.884
9128071.0
6590792.5
355500.0
5726.62460017.0
611.1
0.732
12521509.0
21336338.4
922299.024547.4
7834163.0
93.0
0.726
18511544.0
31623962.2
1383792.0
28102.6
11760690.0
77.0
0.787
10994499.0
20536128.8
676637.0
26494.5
6110901.0
116.5
0.956
6642151.0
10076370.2
476656.0
9161.53846117.0
625.0
0.689
11213303.0
15027200.9703828.017363.1
5282850.0
260.3
0.770
24720822.0
42036117.3
2361425.0
38337.6
19557671.0
96.3
0.873
7583686.0
8175861.9
412993.0
7608.92893241.0
735.7
0.818
11424311.0
11272370.3
670352.08924.34877933.0
527.4
0.767
12256488.0
14091948.1
855097.014261.96088558.0
380.1
0.741
9186693.013207465.1
550330.014607.84582058.0
149.4
0.822
8981528.0
9198735.5
545592.0
9360.73921584.0
517.7
0.799
14382328.0
13067275.9794457.0
12740.95835600.0
405.5

1.000
-36.9%-36.8%-32.2%-56.6%
0.0%
0.0%
1.000
-43.2%-34.6%-18.1%-47.6%
0.0%
0.0%
1.000
-27.4%-13.3%-13.3%-37.3%
0.0%
0.0%
1.000
-39.5%-28.5%-28.1%-49.0%
0.0%
0.0%
1.000
-59.6%-33.1%-25.5%-64.8%
0.0%
0.0%
1.000
-39.0%-24.3%-18.9%-18.9%
0.0%
0.0%
1.000
-40.8%-12.8%-14.0%-11.6%
0.0%
0.0%
1.000
-53.9%-33.8%-26.8%-63.1%
0.0%
0.0%
1.000
-56.6%-35.7%-27.4%-56.7%
0.0%
0.0%
1.000
-55.0%-43.3%-21.3%-69.6%
0.0%
0.0%
1.000
-4.4%
-19.9%-10.8%-30.5%
0.0%
0.0%
1.000
-52.5%-31.1%-31.1%-55.1%
0.0%
0.0%
1.000
-42.6%-23.0%-27.2%-51.3%
0.0%
0.0%
1.000
-12.8%-14.7%-12.7%-12.7%
0.0%
0.0%
1.000
-31.6%-18.2%-23.4%-18.2%
0.0%
0.0%
1.000
-30.7%-23.4%-23.4%-37.9%
0.0%
0.0%
1.000
-52.8%-27.3%-25.9%-49.0%
0.0%
0.0%
1.000
-24.7%-17.8%-17.8%-20.3%
0.0%
0.0%
1.000
-41.5%-20.1%-20.1%-31.0%
0.0%
0.0%

1.000
-25.1%-24.8%-19.2%-48.6%
19.2%
0.0%
1.000
-39.1%-29.0%-9.9%-44.4%
10.4%
0.0%
1.000
-6.6%
-7.3%
0.0%
-29.7%
7.4%
0.0%
1.000
-30.0%-17.0%-16.3%-41.2%
16.4%
0.0%
1.000
-54.0%-23.6%-14.6%-60.0%
14.7%
0.0%
1.000
-32.7%-9.4%-10.6%
0.0%
12.2%
0.0%
1.000
0.0%
0.0%
0.0%
-6.2%
0.0%
10.9%
1.000
-47.8%-24.3%-15.5%-58.6%
15.8%
0.0%
1.000
-50.3%-25.9%-15.9%-50.7%
16.0%
0.0%
1.000
-50.8%-37.3%-11.9%-67.1%
12.3%
0.0%
1.000
-2.3%
-19.3%-10.1%-29.3%
0.0%
3.6%
1.000
0.0%
0.0%
-18.9%
0.0%
20.0%
0.0%
1.000
-36.3%-13.0%-18.1%-45.3%
13.1%
0.0%
1.000
-8.1%
-6.5%
-7.1%
0.0%
10.2%
0.0%
1.000
0.0%
-12.3%
0.0%
0.0%
12.2%
0.0%
1.000
0.0%
-13.7%
0.0%
0.0%
14.3%
0.0%
1.000
-48.0%-18.4%-14.8%-44.6%
15.6%
0.0%
1.000
-3.1%
-10.1%
0.0%-10.1%
11.5%
0.0%
1.000
-19.0%-11.5%
0.0%-18.8%
12.2%
0.0%

1.000
-16.5%-16.0%-9.7%-42.7%
33.3%
0.0%
1.000
-36.8%-26.0%-5.4%-42.6%
16.1%
0.0%
1.000
-11.6%-4.1%
0.0%-29.5%
11.2%
0.0%
1.000
-23.6%-9.3%-8.4%-35.9%
27.4%
0.0%
1.000
-50.5%-17.5%-7.6%-57.0%
24.1%
0.0%
1.000
-31.2%
-6.9%
-5.8%
0.0%
19.1%
0.0%
1.000
0.0%
0.0%
0.0%
-3.5%
0.0%
16.3%
1.000
-43.8%-18.0%-8.0%-55.7%
26.1%
0.0%
1.000
-46.1%-19.4%-8.2%-46.8%
26.7%
0.0%
1.000
-48.3%-33.8%-6.4%-65.6%
19.5%
0.0%
1.000
-1.3%
-19.0%-9.7%-28.8%
0.0%
5.2%
1.000
-38.1%
0.0%-9.6%-31.8%
34.4%
0.0%
1.000
-32.5%-6.9%-12.5%-41.7%
21.0%
0.0%
1.000
-7.3%
-3.9%
-4.0%
0.0%
15.3%
0.0%
1.000
0.0%
-6.7%
0.0%
0.0%
19.0%
0.0%
1.000
-5.0%
-7.2%
0.0%
-23.8%
23.1%
0.0%
1.000
-44.9%-12.7%-7.8%-41.8%
25.7%
0.0%
1.000
-8.0%
-5.5%
0.0%
-9.8%
17.8%
0.0%
1.000
-24.0%-6.2%
0.0%-18.5%
19.2%
0.0%

For instance, the CCR projection shows that Hokkaido should
reduce its Public Capital Stock (PCS) by 76.1 percent, Private
Sector Capital Stock (PSCS) and Labor by 26.9 percent,Electricity Consumption (EC) by 56.5 percent in order to become
efficient.
On the other hand, the DFM results show that a reduction in
Private Sector Capital Stock (PSCS) of 16.0 percent, and anincrease in GDP of 15.6 percent are required for Hokkaido to
become efficient. Furthermore, the PB-DFM results show that a
reduction in the Private Sector Capital Stock (PSCS) of 8.3
percent, and an increase in the GDP of 25.9 percent are required
to become efficient. Apart from the practicality of such a solution,
the models show clearly that a different – and perhaps more
efficient – solution is available than the standard CCR projection
to reach the efficiency frontier.
5.4 Illustration of the results of the PB-DFM model for agiven prefecture
In this subsection, we use Hokkaido and Shimane as an
example of an inefficient reference prefecture, and present anefficiency improvement projection result based on the PB-DFM
model. We assume that the OAP uses steps from 0.0 to 1.0 atintervals of 0.1. Next, the input reduction values and the output
increase values based on the PB-DFM model are calculated in
Figures 6 and 7.
From Figure 6, it can be seen that, if Hokkaido prefecture
implements an efficiency improvement plan with an OAP
amounting to 0.3 (i.e. 30 percent of the total efficiency gap isallocated for output, and 70 percent of the total efficiency gap isallocated for input), then a reduction in Private Sector Capital
Stock (PSCS) of 19.4 percent, and an increase in GDP of 11.1
percent are required to raise efficiency score to 1.000.
Furthermore, if such a plan has an OAP of 0.0 (i.e. 100 percent of
the total efficiency gap is allocated for input), then a reduction in
PSCS of 27.6 percent is required to raise the efficiency score to
1.000.
From Figure 7, it can also be seen that if Shimane prefecture
implements an efficiency improvement plan with an OAP
amounting to 0.4 (i.e. 40 percent of the total efficiency gap isallocated for output, and 60 percent of the total efficiency gap isallocated for input), then a reduction in Electricity Consumption(EC) of 7.0 percent, and an increase in Carbon Emission (CE)(inverse number) of 9.3 percent are required to raise theefficiency score to reach 1.000. Furthermore, the results of a planwith an OAP of 0.0 (i.e. 100 percent of the total efficiency gap isallocated for input), a reduction in EC of 11.6 percent is required

efficiency (to reach the score 1.000), but where the balance ofto raise the efficiency score to 1.000.

input-output improvement can be freely set, in a decentralized
way based on the specific preferences of each prefecture. This
framework might form a basis of a new concept like a ‘Kyoto
Protocol’ for each prefecture in Japan.
References
Agency for Natural Resources and Energy, Ministry of the Economy,
Trade and Industry in Japan, (2010) Statistical report on energy
consumption for each prefecture, and Statistics report on comprehensive
strategy for energy consumption and environment
Cabinet Office, Government of Japan (2010) Economic and Fiscal model

Fig.6 Efficiency improvement projection results based on the
PB-DFM model for Hokkaido prefecture

for Prefectures
Charnes, A., Cooper, W.W. and Rhodes, E. (1978) Measuring the
Efficiency of Decision Making Units. European Journal of Operational
Research, 2: 429-444.
Golany, B. (1988) An Interactive MOLP Procedure for the Extension of
DEA to Effectiveness Analysis. Journal of the Operational ResearchSociety, 39: 725-734.
Halme, M., Joro, T., Korhonen, P., Salo, S. and Wallenius, J. (1999) A
value efficiency approach to incorporating preference information in
Data Envelopment Analysis. Management Science, 45: 103-115.
Joro, T., Korhonen, P. and Wallenius, J. (1998) Structural Comparison of
Data Envelopment Analysis and Multiple Objective Linear
Programming. Management Science 44(7): 962-970.

Fig. 7 Efficiency improvement projection results based on the
PB-DFM model for Shimane prefecture

Korhonen, P. and Siljamäki. A. (2002) On the Use of Value Efficiency
Analysis and Some Further Developments. Journal of Productivity
Analysis 17, (1-2): 49-64

6. Conclusion
In this chapter we have presented a new methodology, the PBDFM model. This model is characterized by two integrated

Korhonen. P., Stenfors, S. and Syrjänen. M. (2003) Multiple objective
approach as an alternative to radial projection in DEA. Journal of
Productivity Analysis 20 (20): 305-321.

features: (i) the use of a general Distance Friction Minimization

Lins, M. P. E., Angulo-Meza, L. and Moreira da Silva, A.C. (2004) A(DFM) model to achieve the most appropriate movement

multi-objective approach to determine alternative targets in data

towards the efficiency frontier surface; and (ii) the incorporationenvelopment analysis. Journal of Operational Research 55: 1090-1101

of preference-based (PB) adjustments in efficiency strategies

Suzuki, S., Nijkamp, P., Rietveld, P. and Pels, E. (2010) A Distanceregarding the input reduction allocation – or the output increase

Friction Minimization Approach in Data Envelopment Analysis: A

allocation – of DMUs in order to balance rigorous efficiency

Comparative Study on Airport Efficiency. European Journal ofdecisions with political priorities.

Operational Research 207: 1104-1115

The results of this methodology may offer a meaningful

Thanassoulis, E., and Dyson, R.G. (1992) Estimating Preferred Target

contribution for the decision making and planning for the

Input-Output Levels Using Data Envelopment Analysis. European

improvement of the energy-environment-economic (EEE)

Journal of Operational Research 56: 80-97

efficiency for each prefecture in Japan. This new model may act

Washio, S., Yamada, S., Tanaka, T. and Tanino, T. (2012) Improvements

as a policy navigation instrument (a ‘dashboard’) that may haveby analyzing the efficient frontier in DEA.

great added value for decision making and planning. For example,

Operational Research 217: 173-184

European Journal ofthis approach – based on interactive preference elicitation – may

Yang, X., Morita, H. (2013) Efficiency improvement from multiple

be useful for EEE strategy, a nation-wide agreement on policy

perspectives: An application to Japanese banking industry. Omega

where all inefficient prefectures would have to improve their41(3): 501-509