A multi-division efficiency evaluation of U.S. electric power companies using a weighted slacks-based measure

Socio-Economic Planning Sciences 43 (2009) 201–208

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Socio-Economic Planning Sciences journal homepage: www.elsevier.com/locate/seps

A multi-division efficiency evaluation of U.S. electric power companies using a weighted slacks-based measure Miki Tsutsui*, Mika Goto Central Research Institute of Electric Power Industry 2-11-1, Iwado kita, Komae-shi, Tokyo 201-8511, Japan

a r t i c l e i n f o

a b s t r a c t

Article history: Available online 18 June 2008

Prior to the 1990s, the electric power industry was highly regulated across the world. Under a liberalization policy to open markets and to grow competition commenced in the early 1990s, efficient management has become a necessity for companies in this industry. The current study examines the divisional efficiencies of multi-functional, vertically integrated companies seeking to optimize their overall management efficiency. For this purpose, divisional cost data are used as input into a slacks-based measure (SBM) model. This provides divisional efficiency indices based on slacks, as well as one for the larger firm-level management function. Further, given the important role of cost structure, we introduce a modified SBM, named the weighted SBM (WSBM), which directly incorporates division-specific weights into the objective function. Results reveal that the power generation divisions of the companies studied have significant influence on the overall cost, whereas the impact of the other four divisions – transmission, distribution, sales and general administrative – is limited.  2008 Elsevier Ltd. All rights reserved.

Keywords: Weighted slacks-based measure Divisional efficiency Vertical integration Electric power company

1. Introduction Liberalization of the electric power industry commenced in the early 1990s in several countries in Europe, with many countries and regions worldwide having followed suit in recent years [1,2]. In the European Union (EU), the amending Directive concerning common rules for the internal market in electricity was enforced in 2003 [3]. According to the Directive, all EU member countries were required to open their electricity markets to all customers, including households, by July 2007. Customers could subsequently choose their electricity suppliers freely thus leading to competition for customers. Unlike the EU countries, the U.S. retail market was opened on an individual state basis despite the policy being federally implemented [4,5]. Although retail competition

* Corresponding author. Fax: þ81 3 3480 3491. E-mail addresses: [email protected] (M. Tsutsui), mika@criepi. denken.or.jp (M. Goto). 0038-0121/$ – see front matter  2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.seps.2008.05.002

was introduced in nearly half the states, the others had no plans to introduce the policy. One of the main purposes for deregulation of the U.S. electric power industry was to reduce price. Indeed, it has been pointed out that states with higher electricity prices tended to introduce retail competition at an earlier stage [6]. Several functions are involved in supplying electricity to customers, e.g. generation, transmission, distribution and retail sales. Liberalization of electric power industry allows new entrants into the power generation markets and retail electric supply markets, and allows competition with incumbent players. While the generation and sales businesses are exposed to the competition in the liberalization process, network businesses such as transmission and distribution remain regulated as exemplified by the rate of return (ROR) regulation [1,2] and the performance-based regulation (PBR) on networks [4,7]. Under the new business environment, efficient management becomes essential for electric power companies that have been regulated for a prolonged period of time. The key suppliers in many countries have been vertically integrated

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and comprise several divisions with different functions as described earlier within each company.1 In particular, these companies are required to improve the efficiency of each division and to pursue the optimization of the overall management. Given this situation, efficiency analyses can provide important information not only for the electric power companies to help them survive in a competitive environment but also for the governmental regulatory agencies. Considerable number of studies examined the efficiency measurement performed by the divisions of electric power companies, for example, efficiency analysis specifically for the transmission or distribution division [8–14]. However, these analyses aimed to optimize the efficiency of individual divisions but not that of the overall management. When we evaluate management efficiency of a vertically integrated company, individual measurement of divisional efficiency is not enough for firm-level evaluation, because it is only ‘‘local’’ efficiency for this type of company. From the viewpoint of firm-level optimization rather than local divisional optimization, it is essential for analysts to utilize a consistent framework to measure the firm-level efficiency exhibited by each division. There exist few studies on vertically integrated companies from this perspective. Thus, the purpose of this study is to measure the efficiency index of multi-functional and vertically integrated electric power companies in order for them to consistently optimize the overall management efficiency based on closely linked divisional efficiencies. For this purpose, we employ the slacks-based measure (SBM) model introduced by Tone [15], which is the representative method of ‘‘non-radial’’ data envelopment analysis (DEA) model. This is suitable for our purpose, because it can provide overall efficiency based on divisional efficiencies.2 If, instead of the SBM, we employ the traditional Charnes-Cooper Rhodes (CCR) model [16] for this purpose, divisional efficiency scores are identical for all divisions since it is a ‘‘radial’’ model. However, the efficiencies of divisions are not uniform. Actually, the business conditions are different between divisions, i.e. the generation and sales divisions are in competitive conditions, while the transmission and distribution divisions are regulated [1,2]. Under these situations, it is impractical to assume the radial and identical divisional efficiency scores for all divisions. In other words, radial models such as the CCR lose useful and important information of divisional efficiencies. Thus, the SBM model is more suitable than the traditional radial models for our purpose. However, the original SBM model employs the equal weight for all divisions [15] regardless of the relative importance of divisions. Therefore, this study introduces a modified SBM, named the weighted SBM (WSBM), which directly incorporates division-specific weights into the objective function of the SBM. Using the WSBM model with

1 Another type of electric power company is a function-specific one, i.e. a generation company. 2 In the general case, the SBM provides overall efficiency based on ‘‘input factor inefficiencies’’ [15]. However, in this study, we apply the cost data of each division as an input to the SBM model. This treatment enables us to interpret ‘‘input factor inefficiency’’ to ‘‘divisional inefficiency’’.

the divisional cost shares as weights, overall management efficiency index can be consistently evaluated not only from the cross-firm perspective but also from the cross-divisional viewpoints in an integrated optimization model. This study is organized as follows. Section 2 reviews the previous studies that examined the performance of electric power companies and indicates novelty of our study. Section 3 provides explanation of the SBM and introduces the WSBM model for measuring the overall management efficiency based on the divisional efficiencies. In Section 4, these models are applied to 90 electric power companies in the U.S. during the 1990s. Section 5 concludes this study and mentions future directions of study. 2. Literature review Studies on the management efficiency of electric power companies were published primarily after the 1990s [10,11]. The methods employed can be classified into parametric and non-parametric frameworks [17]. The two groups have different characteristics in the sense that the former utilizes econometric estimations and the latter mathematical programming methods in operations research. However, the commonality is that the productive efficiency is evaluated by the degree of deviation or distance of the observed data from the efficiency frontier, which represents the ‘‘best practice’’ production technology and serves as a norm for efficiency evaluation. The most popular method based on the non-parametric technique is data envelopment analysis (DEA), which was put forth in Ref. [16]. The stochastic frontier analysis (SFA) is another popular method of efficiency measurement that applies the parametric estimation of the efficient frontier. The SFA was originally developed in Refs. [18–20]. Most of the previous studies have focused on the efficiency of specific functions (or specific divisions of the vertically integrated companies), particularly network functions (transmission and distribution), which remained under regulation even after liberalization. Hjalmarsson and Veiderpass [12] examined the productivity growth in electricity retail distribution in Sweden using the Malmquist index measured by DEA. Førsund and Kittelsen [13] also employed DEA to analyze the Malmquist efficiency of Norwegian distribution companies. Pollitt [14] employed DEA and SFA, to measure the productive efficiency of companies and demonstrated empirical results in electric utilities using an international sample from more than 10 countries. This study examined the productive efficiencies of specific functions of electric utilities, e.g. power plants, transmission and distribution systems, respectively. Hattori [8] and Hattori et al. [9] also compared the efficiency performance of vertically integrated electric power companies between Japan and the U.S. [8] and Japan and the U.K. [9], focusing only on their distribution divisions. Compared to the function-specific analyses mentioned above, studies on vertically integrated companies are scarce. Goto and Tsutsui [21] examined the firm-level efficiency of vertically integrated companies using DEA; their study focused on major power companies in Japan and the U.S. This study decomposed the overall inefficiency

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into technical, scale, and allocative inefficiency, and compared the results between the two countries but did not take into account of the internal divisions of the companies. Delmas and Tokat [22] also examined the efficiency of vertically integrated companies in the U.S. and revealed the relationship between efficiency scores and the proportion of supplied electricity that was generated by their own power plants. This study considered divisional inputs as generation, transmission, distribution, sales and administrative expenses. However, it employed a radial model, focused only on an integrated score, and hence could not deal with the divisional efficiencies. As we surveyed, the objects of previous studies were mainly measuring efficiencies of specific functions. With regard to the division-specific analyses for the vertically integrated companies, these studies aimed local optimization at the divisional level. Although it is important to evaluate division-wise efficiency for improving the overall management efficiency of these companies, much more importance should be given to the optimization of the overall management efficiency. In a multi-functional, vertically integrated company, inseparable links exist between the generation, transmission, distribution, and sales divisions. If a company shows exceptional efficient performance only in a certain division, the efficiency in the other divisions might be sacrificed. For instance, even if the generation division alone performs exceptionally well, the other divisions, e.g. transmission and distribution, might perform worse than those of the other companies. In its entirety, this company cannot be evaluated as being efficient from the viewpoint of firm-level management. Thus, in order to evaluate such companies, it is necessary to focus on the optimization of the overall management efficiency and on closely linked divisional efficiencies for optimizing entirely. Several studies proposed methods to evaluate overall efficiency based on the divisional efficiencies. Sexton and Lewis [23] and Lewis and Sexton [24] focused on divisional efficiencies and the overall efficiency of Major League Baseball teams, using two-stage DEA and network DEA models. These models proved to be very useful in evaluating the efficiency of multi-divisional decision making units (DMUs). However, their models were based on a radial model to measure the efficiency of each division and hence lost useful information about the divisional inefficiency, since a radial model puts slacks out of account [15]. Further, divisional efficiencies in their study were measured on the basis of different efficiency frontiers in multistage models. This might achieve local optimization but not overall optimization. In the current study, we examine the performance of vertically integrated electric power companies using a non-radial SBM model. It is suitable for our study because non-uniform divisional efficiencies can be measured for optimizing the total management efficiency. 3. Models

203

utilizes the SBM model3 introduced by Tone [15]. This model is characterized by several desirable features such as non-radial efficiency measures for individual inputs and the integrated scalar efficiency measure for total operation based on slacks. While radial models such as the CCR ignore slacks for evaluation of the efficiency score, thus making the reduction rate the same for all inputs, the SBM takes into account the slacks that are not considered in the radial models and provides various efficiency scores for all inputs. Although there are still a limited amount of application studies of the SBM, these have been increasing in recent years, for example see Refs. [27–30]. Throughout this paper, we consider n DMUs, each having m inputs for producing g outputs. For DMUo ðo ¼ 1; .; nÞ, we denote, respectively, the input and output vectors as xo ˛Rm and yo ˛Rg . The input and output matrices are defined as X ¼ ðx1 ; .; xn Þ˛Rmn and Y ¼ ðy1 ; .; yn Þ˛Rgn . The general SBM model is indicated as follows:

½SBM

Pm s L i i[1 r [ min P sxLio g h 1D1g h[1 yho s:t: xo [ X lDsL yo [ Y lLsD l ‡ 0; sL ‡ 0; sD ‡ 0; 1 1Lm

(1)

where s ˛Rm and sþ ˛Rg are slack vectors for the input and output, which indicate input excess and output shortfall. s i l n and sþ h are slack variables for input i and output h. ˛R is the non-negative intensity vector to form a frontier, and the optimal solution of r* is the SBM efficiency score for DMUo. We can transform this fractional program into an equivalent linear program using the Charnes-Cooper transformation (see Tone [15, p. 500]). In this study, in order to compare the results with those of the input-oriented CCR model (CCR-I), we employ the input-oriented SBM model (SBM-I) as follows:

½SBMLI

Pm

sL i x ito Pt s:t: xto [ k[ 1 Xk lk DsL P yto [ tk[ 1 Yk lk LsD lk ‡ 0 ðk [ 1;.; tÞ; sL ‡ 0; sD ‡ 0: 

r [ min 1Lm1

i[1

(2)

Eq. (2) is also an expanded model of Eq. (1) for time series data. The subscript t indicates data in period t, and Xk and Yk (k ¼ 1,.t) are input and output matrices of all DMUs up to period t. For example, in the 2nd period (t ¼ 2), the set of DMUs is composed of both periods 1 and 2 DMUs, and we evaluate DMUs in the period 2 with respect to periods 1 and 2 DMUs. Summing up Xklk and Yklk in this way and using them instead of Xl and Yl, the efficiency frontier of this model comprises data from the cumulative input and output data up to period t. It is interesting to note that a portion of the objective function, i.e. the optimal value of s i =xito , indicates the ratio

3.1. The SBM model For measuring the divisional management efficiency in an integrated model with overall consistency, this study

3 The SBM model is substantially equivalent to the enhanced Russell graph measure (ERGM) introduced by Pastor et al. [25]. See also Cooper et al. [26].

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of input excess to actual input. It can be regarded as the input inefficiency index of DMUo for input i at period t, and can be referred to as the slack ratio (SR) index. 

SRito [

sL ito : Slack ratio index; xito

(3)



 where s ito is an optimal solution of input slack si of DMUo at period t in Eq. (2). Therefore, it can be said that r* is the overall integrated scalar efficiency index composed by the average of the input inefficiency indices. In the case of CCR-I, the input inefficiency index is measured as 1  q* for all inputs, where q* indicates the CCR efficiency score. Hence, we have no discrimination regarding the importance of input items. Contrary to the case of CCR-I, the input inefficiency indices (SR) measured by the SBM-I model can differ severally division by division.

3.2. The WSBM model It should be noted that r* in Eq. (2) is constituted by the arithmetic average of SR (slack ratio) of each input. It implies that Eq. (2) assumes a uniform weight (1/m) to all input factors. However, their relative importance is not always uniform. In fact, it may be more common to assume non-uniform weight for input factors. Thus, this study focuses on the weighted average of SR and introduces a modified SBM model, namely, the WSBM model.4 This model directly incorporates the non-uniform weight to input factors in the objective function instead of the uniform weight (1/m) for SR. The WSBM model can be applied to any case wherein the weights for inputs or outputs are known or can be supplied exogenously. The WSBM model that takes into account the weights of both input and output can be defined as follows:

3.3. Incorporating cost data into the WSBM In order to examine the divisional efficiencies, this study utilizes divisional cost data as inputs instead of physical input data. Specifically, the first input is the cost from the generation division and the second is the cost from the transmission division, and so forth. Accordingly, we can interpret an ‘‘input inefficiency’’ index in the SBM model as a ‘‘divisional cost inefficiency’’ index. Thus, by applying cost data to the SBM (or WSBM), we can evaluate the cost efficiency for the overall management. In reality, each division utilizes several physical inputs such as capital and labor. However, if we utilize all of these inputs for all divisions, the discriminating power of DEA results could get lost because of too many numbers of inputs. In this sense, cost data are beneficial to achieve our purposes because it can be regarded as a proxy of several physical inputs in each division. Furthermore, using divisional cost data would also be advantageous because the relationship between divisions can be clearly defined by their cost shares. Since xito is P cost data of input i for DMUo at period t, the sum ð xito Þ ini

dicates the total cost at period t. Thus, the cost share for this input (CSito) is calculated as

xito CSito [ Pm f [1

½WSBM

Pm

sL i xio m [ min P sL 1D gh [ 1 rho h yho s:t: xo [ X lDsL yo [ Y lLsD l ‡ 0; sL ‡ 0; sD ‡ 0; 1L



where v and u are the unknown weight vectors (multipliers) for input and output, respectively, and h* (¼m*) is the efficiency score for DMUo. It should be noted that vixio and uhyho are not less than wio and hrho, respectively. This implies that input and output with large weights strongly affect the efficiency score.

i[1

wio

(4)

: Cost shar information:



(5)

(6)

P where CSito satisfies the condition m i ¼ 1 CSito ¼ 1. By multiplying the SR index (3) with the cost share CS (6), we can obtain an index that is termed the slack share (SS); this indicates the impact of the inefficiency of each division on the total cost.

SSito [ SRito CSito [

where wio and rho are, respectively, the weights for input i and output h of DMUo given exogenously, and satisfy the Pg Pm normalizations i ¼ 1 wio ¼ 1 and h ¼ 1 rho ¼ 1. m* is the WSBM efficiency score. The dual model of Eq. (4) is described as follows5:

½D—WSBM  h [ max h s:t: hDvxo Luyo [ 1 LvXDuY £ 0 wio vi ‡ ði [ 1; .mÞ xio rho uh ‡ h ; ðh [ 1; .; gÞ yho

xfto



sL xito sL ito Pm [ Pm ito xito f [ 1 xfto f [ 1 xflo

: Slack share index:

(7)

In other words, SS index is the SR index weighted by the cost share. For a valid comparison of divisional efficiencies, it is necessary to properly define the relative importance of each division. Since the SS index is calculated based on the cost share of each division, it enables us to compare the efficiency indices between them. In this study, we use the input-oriented WSBM (WSBM-I) model with a time series and the cost share (CSito) for the input weight wito as follows:

½WSBM—I

4

Ruggiero and Bretschneider [31] introduced the weighted Russell measure, where they explained only an input-oriented model. If it is extended to the non-oriented enhanced Russell graph measure [26], it will be substantially equal to the WSBM model. 5 The dual model (5) will be equivalent to the profit maximization problem, which has a meaningful economic implication. See [26, p104].

 Pm  sL i i[1 CSito xito Pt s:t: xto [ k[1 Xk lk DsL P yto [ tk[1 Yk lk LsL lk ‡ 0 ðk[1;.;tÞ; s L ‡ 0; sD ‡ 0: 

m [min 1L

(8)

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Table 1 Major statistics of datasets. 1990

1999

Whole sample

Generation ($1000) Transmission ($1000) Distribution ($1000) Sales ($1000) Administration ($1000) Electric power sales (GWh)

Max

Average

SD

689,598 29,249 92,172 44,602 109,012 18,237

766,211 31,479 107,863 51,663 120,910 18,144

Min

2,866,171 109,565 404,735 151,650 390,784 77,645

Whole sample

2831 104 325 93 623 46

Average

SD

773,900 36,812 109,659 55,072 123,724 24,531

793,027 42,339 126,792 64,813 145,942 23,448

Max

Min

2,876,952 131,648 538,316 303,555 573,749 102,988

3064 88 375 171 534 43

Average: whole sample average for each year; SD: standard deviation of whole sample for each year; max: average data of the company with the highest electric power sales for each year; min: average data of the company with the lowest electric power sales for each year; and GWh: Giga Watt hour.

This model provides the efficiency index m* based on the divisional inefficiencies, consistently reflecting their relative importance through the cost share. The dual model of Eq. (8) is formulated as

½D—WSBM—I P P  h [ max 1L mi[ 1 vi xito D gh [ 1 uh yhto s:t: LvXk DuYk £ 0 ðk [ 1; .; tÞ vi xito ‡ CSito ði [ 1; .; mÞ uh ‡ 0: ðh [ 1; .; gÞ

(9)

It is seen from the term vixito in the objective function and the constraint vixito  CSito that a large cost share exerts strong influence on vixito and hence efficiency score h* (¼m*). 4. Application to vertically integrated electric power companies In this section, we examine the efficiency scores calculated by the CCR-I, SBM-I, and WSBM-I models, using the data of the U.S. electric power companies.

state. Output data represent the electric power sales to final customers (GWh: Giga Watt hour). These data were obtained from the ‘‘FERC Form 1’’ provided by the Federal Energy Regulatory Commission (FERC) in the U.S. [32]. The major statistics of the datasets are described in Table 1. As illustrated in Table 1, there is a wide gap between large and small companies because there are various and different sized electric power companies in the U.S. This table clearly indicates that companies spend a considerable amount of money on the generation division. Fig. 1 describes the summary of the cost structure of the sample. The middle bar graph describes the average of all companies during the study period. It is evident that the generation division displays a larger share than the other divisions. The bar graph on the right-hand side represents a company with the largest generation share, and that on the left-hand side represents a company with the smallest generation share. According to these graphs, a common trend is observed in the cost structure, that is, the share of the generation division is relatively large, whereas those of the transmission and sales divisions are relatively small.

4.1. Data We chose 90 vertically integrated electric power companies in the U.S. and collected cost data for five divisions, i.e. generation, transmission, distribution, sales, and general administrative, from 1990 to 1999. In the typical technical efficiency model of DEA, physical inputs such as capital and labor are utilized as input data [14]. As mentioned in Section 3.3, instead of these data, we apply divisional cost data to the technical efficiency model as inputs in this study. The input data for each division represents the total sum of operation & maintenance (O&M) expenses and depreciation expenses. In addition, the cost of the generation division includes purchased power expenses because it can be regarded as the cost of an alternative energy source to generation plants. An electric power company can choose the manner in which the supplied energy is procured by either generating power at its own power plants or by purchasing power from other companies. With regard to the sales division, O&M expenses constitute the only cost because this division does not have any fixed capital. All cost data were deflated by the gross state product deflator of each

4.2. Empirical results Fig. 2 illustrates the result of the average efficiency scores of all companies calculated by the CCR-I, SBM-I, and WSBM-I models. The efficiency score of the CCR-I model (q*) is greater than those of the SBM-I (r*) and the WSBM-I (m*) during the study period. It exhibited the known relationship derived from the following inequalities established by Tone ([15, p.502]).6 



m  SL 1X i £q; m i [ 1 xi 

r £qL

(10)



where S i is the input slack of the CCR-I model. Contrary to the case q*, no explicit relationship was found between the scores r* and m*.

6 Tone [15] proved the relationship of efficiency scores between the CCR and the non-oriented SBM model. Eq. (10) for the input oriented SBM model can be conducted in the same manner.

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G

T

100%

CCR-I

A 9.3%

4.9% 4.5%

9.7%

5.5%

SBM-I

0.5 3.4% 2.8%

0.4

3.6%

15.3% 60%

S

12.2%

20.8% 80%

D

0.3 5.9%

40%

0.2

78.9%

69.6% 53.5%

0.1

20% 0 0%

Smallest

Average

G

T

D

S

A

Largest

Fig. 1. The cost structure. *G: generation division; T: transmission division; D: distribution division; S: sales division; A: general administration division; average: whole sample average; smallest: the company with the smallest generation cost share; and largest: the company with the largest generation cost share.

As can be seen from Fig. 2, all the scores are broadly flat during the study period. If we would observe drastic changes in scores during the study period, it might suggest that a structural change has occurred in this industry. In such case, we should be careful in averaging the results over the whole period. However, in our study, we can assume that the electric power industry effected no large structural change during this period, even if the deregulation of this industry advanced in the 1990s. Therefore, we adopt the results in terms of average for all companies and for all years in the following figures. Fig. 3 describes the results of the SR index for five divisions for the CCR-I and SBM-I. In order to ensure consistency with the SR index of the SBM-I (SRSBM), the results of the CCRI model are exhibited as 1  q*, which implies the CCR ‘‘inefficiency’’ index denoted by SRCCR. Since the efficiency index q*obtained from the CCR-I model is ‘‘radial,’’ the inefficiency level of all divisions is equivalent, as observed in Fig. 3. Compared to the results of the CCR-I, it can be observed that the SBM-I produces a larger SR index on average in four divisions except for the generation division. It is

Fig. 3. Slack Ratio (SR) Index of CCR-I and SBM-I. *G: generation division; T: transmission division; D: distribution division; S: sales division; and A: general administration division. Note: SR is an ‘‘inefficiency’’ index for each division. Therefore, as the index score increases, the ‘‘efficiency’’ level decreases.

noteworthy that SRs in the transmission and sales divisions are larger than those in the CCR-I model, whereas there is only a 1% difference in the SR of the generation division between the two models. In contrast to the scalar indices q* and r* that maintain the relationship as in Eq. (10), we found no explicit relationship between the magnitude of the SR indices of the CCR-I and SBM-I. In some cases, the SRCCR is greater than the SRSBM, and vice versa. In the generation division, nearly half of the companies exhibit SRCCR > SRSBM, and the remaining half exhibit the opposite, i.e. SRCCR < SRSBM, which results in, on an average, a negligible difference between them. Compared to this, a lot of companies exhibit SRCCR < SRSBM in the other four divisions and the gap is greater than that of the generation division, which results in significant differences between the SRCCR and SRSBM scores for the other four divisions in Fig. 3. Focusing on the results of the SBM-I, the inefficiency in the generation division is the lowest, which implies that this division is more efficient than the others and has

CCR-I

SBM-I

0.25 1 0.2 0.8 0.15 0.6 0.1

0.4

0.05

0.2 0

0 y90

y91

y92

y93

y94

y95

y96

y97

y98

y99

Fig. 2. The result of efficiency scores of the three models. q*: the average efficiency score of the input-oriented CCR-I model for entire companies; r*: the average efficiency score of the input-oriented SBM-I model for entire companies; and m*: the average efficiency score of the input-oriented WSBM-I model for entire companies.

G

T

D

S

A

Fig. 4. Slack Share (SS) Index of CCR-I and SBM-I. *G: generation division; T: transmission division; D: distribution division; S: sales division; and A: general administration division. Note: SS index indicates the impact of each division on the overall cost of DMU. The impact increases with an increase in the index score.

M. Tsutsui, M. Goto / Socio-Economic Planning Sciences 43 (2009) 201–208

WSBM-I

SBM-I 0.5 0.4 0.3 0.2 0.1 0

G

T

D

S

A

Fig. 5. Slack Ratio (SR) Index of SBM-I and WSBM-I. *G: generation division; T: transmission division; D: distribution division; S: sales division; and A: general administration division. Note: SR is an ‘‘inefficiency’’ index for each division. Therefore, as the index score increases, the ‘‘efficiency’’ level decreases.

limited scope for improvement in its efficiency. However, as a result of the SS index shown in Fig. 4, the impact on the overall cost of this division is outstanding, which reflects its significantly larger cost share. Even if its divisional inefficiency (SR) is the lowest under the uniform weight, it has the most significant impact on the total cost. This indicates that improving the efficiency of the generation division is effective for reducing the overall cost of a company. These results also indicate that cost share information is important when evaluating the overall cost efficiency, as demonstrated by the SS results. It can be said that the WSBM model is suitable for the framework of our study because it directly incorporates the cost share information in the objective function. Figs. 5 and 6 depict the results of the SR and the SS indices by comparing the SBM-I and the WSBM-I cases. The results of the WSBM-I, which incorporate the actual and different cost shares for divisions, show that the SR and SBM-I

WSBM-I

0.25

0.2

0.15

0.1

0.05

0

G

T

D

S

A

Fig. 6. Slack Share (SS) Index of SBM-I and WSBM-I. *G: generation division; T: transmission division; D: distribution division; S: sales division; and A: general administration division. Note: SS index indicates the impact of each division on the overall cost of DMU. The impact increases with an increase in the index score.

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the SS indices for the generation division are larger than those of the SBM-I. The WSBM-I indices for the administration division also increase because of its second largest cost share. The remaining three divisions with small shares indicate opposite results, that is, SBM-I > WSBM-I. In particular, the SR of the transmission division is much smaller than that of the SBM-I model reflecting its smaller cost share. While the inefficiency (SR) of the transmission division under the uniform weight is the largest, as illustrated in Fig. 5, it is the lowest under the non-uniform weight. Furthermore, the impact on the overall cost of this division is drastically reduced, as illustrated in Fig. 6. In other words, even if this division would become efficient, it could save only an insignificant amount of the overall cost. 5. Conclusions For vertically integrated companies, it is important to evaluate the overall management efficiency based on closely linked divisional efficiencies rather than independently measured division-specific efficiencies. In this study, the WSBM model was applied to the vertically integrated electric power companies in the U.S. in order to evaluate their divisional efficiencies by optimizing the overall management efficiency. This model provides us with a scalar integrated efficiency score (m*) which consists of a weighted average of divisional inefficiencies (SR). The advantage of the WSBM over the original SBM model exists in the fact that the WSBM imposes different weights for reflecting differences in importance existing among divisions, such as cost share, while the original SBM employs a uniform weight for all divisions. The results revealed that the generation division exerted a significant influence on the overall cost because of its largest cost share, in spite of the fact that its efficiency was higher than those of the other four divisions. On the other hand, the impacts of the other four divisions on the overall cost were very limited. These results implied that even a slight improvement in the efficiency of the generation division would contribute to improve the overall management efficiency. Although this result discloses considerable inefficiencies in other divisions, the most effective way to reduce the overall cost is to focus on the generation division. In this sense, the introduction of competition into the power generation market is proved to be reasonable. To cope with competition, the generation division will make an effort to improve its efficiency. Meanwhile, the transmission and distribution systems are still under regulation. In the U.S. electric power industry, the performance-based regulation (PBR) on network functions has gained popularity. According to the results of our study, even that improving the efficiency of the transmission and distribution divisions is meaningful to reduce network charges, it has a marginal contribution toward reducing its overall cost. As a further extension of this study, we would like to consider the streamlined relationship among vertically integrated divisions by using the network DEA models [23,24,33]. This would have a significant influence on the efficiency of each division. Furthermore, it is essential to

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separate uncontrollable factors from inefficiency scores measured by DEA and reveal the ‘‘pure’’ inefficiency of DMUs. The cost data used in this study are the sum of O&M and depreciation expenses, which may include a non-reducible cost to companies. Also, several regulations on generation plants exist, particularly those such as environmental quality standards. If we take into account these uncontrollable factors, the cost share of the generation division may be dropped. Additionally, it is necessary to eliminate the effects of uncontrollable differences in business circumstances among DMUs [34,35]. These are important issues to be resolved in the future studies. Acknowledgements The authors wish to acknowledge the useful comments and suggestions of the two anonymous referees. The authors are also grateful for the assistances provided by Prof. K. Tone and the Editor-in-Chief, Dr. B.R. Parker. References [1] Joskow PL. Introduction to electricity sector liberalization: lessons learned from cross-country studies. In: Sioshansi FP, Pfaffenberger W, editors. Electricity market reform: an international perspective. Oxford: Elsevier; 2006. p. 1–32. [2] OECD/IEA. Lessons from liberalised electricity markets. Paris: OECD/ IEA; 2005. [3] European Commission. DIRECTIVE 2003/54/EC OF THE EUROPEAN PARLIAMENT AND OF THE COUNCIL of 26 June 2003 concerning common rules for the internal market in electricity and repealing Directive 96/92/EC. Brussels: EC; 2003. Official Journal L 176. [4] OECD/IEA. Energy policies of IEA countries – the United States of America – 2002 Review. Paris: OECD/IEA; 2002. [5] Rose K, Meeusen K. 2006 Performance review of electric power markets. Virginia: State Corporation Commission; 2006. [6] Hattori T, Graniere RJ. An empirical analysis of the transition to retail competition in the U.S. electricity industry. CRIEPI Report Y01003. Tokyo: CRIEPI; 2001. [7] Hemphill RC, Meitzen ME, Schoech PE. Incentive regulation in network industries: experience and prospects in the U.S. telecommunications, electricity, and natural gas industries. Review of Network Economics 2003;2:316–37. [8] Hattori T. Relative performance of U.S. and Japanese electricity distribution: an application of stochastic frontier analysis. Journal of Productivity Analysis 2002;18:269–84. [9] Hattori T, Jamasb T, Pollitt M. Electricity distribution in the UK and Japan: a comparative efficiency analysis 1985–1998. Energy Journal 2005;26(2):23–47. [10] Jamasb T, Pollitt M. Benchmarking and regulation: international electricity experience. Utilities Policy 2001;9:107–30. [11] Qassim RY, Corso G, Lucena LS, Thome ZD. Application of data envelopment analysis in the performance evaluation of electricity distribution: a review. International Journal of Business Performance Management 2005;7(1):60–70. [12] Hjalmarsson L, Veiderpass A. Productivity in Swedish electricity retail distribution. Scandinavian Journal of Economics 1992;94: S193–205. [13] Førsund F, Kittelsen S. Productivity development of Norwegian electricity distribution utilities. Resource and Energy Economics 1998; 20:207–24. [14] Pollitt M. Ownership and performance in electric utilities. Oxford: Oxford University Press; 1995. [15] Tone K. A slacks-based measure of efficiency in data envelopment analysis. European Journal of Operational Research 2001;130: 498–509.

[16] Charnes A, Cooper WW, Rhodes E. Measuring the efficiency of decision making units. European Journal of Operational Research 1978; 2:429–44. [17] Fried HO, Lovell CAK, Schmidt SS. The measurement of productive efficiency. New York: Oxford University Press; 1993. [18] Aigner DJ, Lovell CAK, Schmidt P. Formulation and estimation of stochastic frontier production function models. Journal of Econometrics 1977;6(1):21–37. [19] Meeusen W, van den Broeck J. Efficiency estimation from CobbDouglas production functions with composed error. International Economic Review 1977;18(2):435–44. [20] Battese GE, Corra GS. Estimation of a production frontier model: with application to the pastoral zone off eastern Australia. Australian Journal of Agricultural Economics 1977;21(3):169–79. [21] Goto M, Tsutsui M. Comparison of productive and cost efficiencies among Japanese and US electric utilities. Omega 1998;26:177–94. [22] Delmas M, Tokat Y. Deregulation, governance structures, and efficiency: the U.S. electric utility sector. Strategic Management Journal 2005;26:441–60. [23] Sexton TR, Lewis HF. Two-Stage DEA: an application to major league baseball. Journal of Productivity Analysis 2003;19:227–49. [24] Lewis HF, Sexton TR. Network DEA: efficiency analysis of organizations with complex internal structure. 2004;31:1365–1410. [25] Pastor JT, Ruiz JL, Sirvent I. An enhanced DEA Russell graph efficiency measure. European Journal of Operational Research 1999; 115:596–607. [26] Cooper WW, Seiford LM, Tone K. Data envelopment analysis – a comprehensive text with models applications references and DEA-solver software. 2nd ed. New York: Springer; 2006. [27] Harn FR. Measuring performance – a multiple-stage approach. WIFO working papers No.228. The Austrian Institute for Economic Research; 2004. [28] Morita H, Hirokawa K, Zhu J. A slack-based measure of efficiency in context-dependent data envelopment analysis. OMEGA 2005;33:357–62. [29] Saen RF. Developing a nondiscretionary model of slacks-based measure in data envelopment analysis. Applied Mathematics and Computation 2005;169:1440–7. [30] Drake L, Hall MJ, Simper R. The impact of macroeconomic and regulatory factors on bank efficiency: a non-parametric analysis of Hong Kong’s banking system. Journal of Banking & Finance 2006;30:1443–66. [31] Ruggiero J, Bretschneider S. The weighted Russell measure of technical efficiency. European Journal of Operational Research 1998; 108:438–51. [32] FERC. FORM No.1: annual report of major electric utility. Federal Energy Regulatory Commission, 1990–1999 (each year). [33] Fa¨re R, Grosskopf S, Network DEA. Socio-Economic Planning Sciences 2000;34:35–49. [34] Fried HO, Schmidt SS, Yaisawarng S. Incorporating the operating environment into a nonparametric measure of technical efficiency. Journal of Productivity Analysis 1999;12:249–67. [35] Fried HO, Lovell CAK, Schmidt SS, Yaisawarng S. Accounting for environmental effects and statistical noise in data envelopment analysis. Journal of Productivity Analysis 2002;17:157–74. Miki Tsutsui is a researcher in the Socio-economic Research Center, Central Research Institute of Electric Power Industry in Japan and has been engaged in productivity and efficiency analysis for the electric power industry. She is also involved in research on Network and Dynamic DEA models. She holds a Ph.D. in operations research from the National Graduate Institute for Policy Studies, Tokyo, Japan. Her research has been published in Omega, Energy Policy, Energy Economics and Socio-economic Planning Sciences. She is a member of the Operation Research Society of Japan. Mika Goto is a research economist in the Socio-economic Research Center, Central Research Institute of Electric Power Industry, Tokyo, Japan. She received the Ph.D. degree (economics) in 2003 from the Nagoya University on efficiency analysis of electric power utilities. Her research interests include efficiency analysis and cost structure of firms with applied econometrics and operations research approach. Her paper has appeared in such journals as Omega, European Journal of Operational Research, Economics Letters and International Journal of Industrial Organization.