Document Type : Research Paper

Authors

• Maryeh Nematizadeh ¹
• Alireza Amirteimoori ²
• Sohrab Kordrostami ³
• Leila Khoshandam ⁴

¹ PhD student, Applied Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran

² Professor, Department of Applied Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran

³ Professor, Department of Applied Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran

⁴ Assistant Professor, Department of Applied Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran

Abstract

The electricity industry plays a pivotal role in a country's economic growth and development. Therefore, it is imperative to assess its performance and identify the strengths and weaknesses of its different sectors, such as production, transmission, and distribution, to enhance economic growth in diverse areas. Given the significance of the transmission sector, this research focuses on analyzing and evaluating the performance of 16 regional electricity companies in Iran from 1390 to 1398, with the aim of comprehending the impact of contextual variables on efficiency. To achieve this, the study will utilize two techniques - Data Envelopment Analysis (DEA) and Ordinary Least Squares (OLS) - to determine the efficiency score and estimate the effect of contextual variables on efficiency, respectively. In the first stage, the DEA technique is employed to calculate the technical efficiency of each company, considering their specific inputs and outputs. In the second stage, the logarithm of the efficiency scores obtained is regressed on contextual variables to establish their effect on efficiency. The residual derived from the regression is referred to as managerial ability. Finally, the companies are ranked based on their modified efficiency after removing the impact of contextual variables.
Introduction
The electricity industry comprises three key sectors: production, transmission, and distribution. It stands as one of the most crucial economic infrastructures in the country, exerting significant influence on industrial, agricultural, service, and other sectors. Undoubtedly, the growth of the electricity industry drives the nation's economic development and progress, contributing to the prosperity and comfort of its citizens (Tavassoli et al., 2020). Consequently, analyzing and examining the growth trajectory of each sector across different years becomes pivotal in mitigating adverse effects and fostering progress within this domain.
In recent years, numerous researchers have conducted studies in this field. Some have independently evaluated each production, transmission, and distribution sector, while others have adopted a comprehensive approach by considering the integrated three-stage network structure. The research background highlights that the transmission sector has received less attention from researchers than other sectors. This is noteworthy because, following electricity production, the transmission process and energy accessibility to consumers are paramount. The absence of proper energy transfer can result in consumer dissatisfaction, financial losses, and stagnation within the competitive economic market. Therefore, identifying the strengths and weaknesses of the transmission sector's performance and comparing regional electricity transmission companies can effectively help enhance the performance level of each.
One technique that has captured researchers' attention for evaluating the electricity industry's performance is the data envelopment analysis (DEA) technique. DEA is a non-parametric method used to assess the performance of homogeneous units, considering multiple inputs and outputs. It was initially introduced in 1978 by Charnes et al. The initial model was built upon the assumption of constant returns to scale. Subsequently, Banker et al. (1984) extended it by presenting a model under the assumption of returns to a variable scale.
Importantly, traditional DEA models evaluate a system's performance based on specific inputs and outputs consumed and produced by the unit. However, various factors, such as contextual variables, managerial ability, and skill, can significantly influence performance and productivity. A crucial point to consider is that managerial abilities are not always overtly visible. This lack of direct visibility can impede accurate measurement. Hence, recognizing these variables among the existing indicators and assessing their influence on the performance and efficiency of each unit holds particular significance. This procedure enhances the precision of evaluation and opens avenues for delivering enhanced solutions aimed at improving the system's overall performance.
Methodology
The objective of this study is to analyze and evaluate the performance of Iran's regional electricity transmission sector while considering contextual variables and establishing a ranking methodology based on managerial ability. This perspective enables the identification of strengths and weaknesses in the system's structure from various angles and offers appropriate solutions for enhancement. To accomplish this, the first step involves identifying all variables within the transmission section, encompassing inputs, outputs, and contextual factors. Subsequently, we determine the technical efficiency of each regional power transmission company, taking into account specific inputs and outputs, using meta-frontier technology. The concept of meta-frontier in DEA measures the gap or distance between decision-making units (DMUs) across different boundaries. This approach assumes a unified boundary for all subgroups, enabling efficiency estimation based on a single boundary (Battese, 2004; O'Donnell, 2008). Its primary advantage lies in resolving the challenge of evaluating efficiency at varying levels. As a result, meta-frontier technology enhances the precision of evaluating regional power companies over multiple periods. After assessing the efficiency of each regional electricity transmission company, we employ the linear regression method to estimate the impact of contextual variables on efficiency, subsequently yielding a measure of managerial ability. Ultimately, we introduce a method for ranking each company based on managerial ability. The advantage of the proposed method is that, in addition to reviewing and analyzing the technical efficiency of each of the companies in the regional electricity transmission sector during different periods, it will be possible to evaluate the managerial ability of each of the companies. Such a perspective allows for companies to be compared from different dimensions. Moreover, providing a new ranking criterion based on managerial ability also facilitates a better and more accurate comparison.
Results
In this study, the performance of Iran's regional power companies was analyzed and evaluated from two systems and management perspectives during the years 1390-1398. Additionally, a new rating criterion based on managerial ability was presented to compare the performance of companies during 9 time periods. In this regard, firstly, the technical efficiency of 16 regional electricity companies during 9 time periods was calculated based on the inputs of the number of employees and receiving energy from neighboring companies and the outputs of sending energy to neighboring companies and delivering energy to distribution companies, using meta-frontier technology and the DEA approach. Then, the effect of contextual variables, such as line length, transformer capacity, and loss magnitude, on the efficiency score of each company was estimated using the ordinary least squares method (OLS). Furthermore, the managerial ability of each company was determined during different periods. Ultimately, a ranking criterion was established based on the results of technical efficiency after removing the effect of contextual variables.
Conclusion
The results of efficiency measurements over 9 time periods indicate that the highest and lowest average efficiencies were observed in the years 1390 and 1398, respectively. Furthermore, it's evident that, in general, the performance of Iran's 16 regional electricity companies exhibited a consistent upward trend from 1390 to 1398. Among the 16 evaluated companies, the Guilan regional electricity company consistently achieved the highest level of efficiency across all 9 time periods, reflecting its strong performance. Conversely, the Fars regional electricity company consistently had the lowest efficiency, indicating its weaker performance compared to other companies. When analyzing the companies' performance by year, it's noteworthy that the Tehran regional electricity company secured the highest rank in 1390, 1391, and 1394, while the Fars regional electricity company held the top spot in the remaining years. In contrast, the Sistan regional electricity company consistently displayed the lowest performance throughout all periods. The assessment of management performance over the 9 time periods indicates that the Kerman regional electricity company demonstrated superior performance from 1390 to 1393, whereas the Guilan regional electricity company excelled from 1394 to 1398, outperforming other companies. Conversely, the Gharb regional electricity company exhibited weaker performance compared to its counterparts. Additionally, the results of the regression analysis highlight a positive relationship between the efficiency score and two variables: line length and transformer capacity. Conversely, the relationship with loss magnitude is observed to be inversely correlated.

Keywords

• Data Envelopment Analysis
• Ordinary Least Squares
• Contextual variable
• Managerial ability
• Ranking