Hierarchical Data Envelopment Analysis Research Articles

Developing a sustainable development goals index for OECD countries: An effectiveness-based hierarchical data envelopment analysis

The Sustainable Development Goals (SDGs) consist of a set of multidimensional indicators comprising 17 goals and 169 targets from various perspectives. The use of a composite index is crucial for assessing the overall performance of each country in relation to the SDGs, given the extensive range of indicator measures involved. However, different weight schemes may lead to different results. Therefore, incorporating an objective weight is required to ensure the comparability and accuracy of the index. The main objective of this paper is to construct an SDG index for Organisation for Economic Co-operation and Development (OECD) countries using an effectiveness-based hierarchical data envelopment analysis (H-DEA) model and apply it to assess SDG effectiveness in OECD countries. The results of this study provide countries with more valuable insights based on the weights of the goals (indicators) that are endogenous to the dataset, assisting them in identifying priorities and strategies to improve future SDG performance.

A digital economy development index based on an improved hierarchical data envelopment analysis approach

The digital economy is playing an increasingly important role in the global economy. National and international organizations commonly utilize a composite index composed of multi-dimensional indicators to monitor performance, analyse policies, and communicate in the digital economy. This study introduces a hierarchical framework for constructing a Digital Economy Development Index (DEDI). One of the key challenges is determining the attribute weights to be assigned by aggregating the sub-indicators with hierarchical dimensions for DEDI. The current study shows that an H-DEA model can be transformed into a parametric linear programming problem and develops an improved golden section algorithm to search for approximate optimal solutions. The newly developed method is highly robust and provides an alternative procedure to determine the optimal weights for building a DEDI. We established a hierarchical evaluation framework and utilized a new approach to measure the DEDI of 30 provinces in China from 2015 to 2020. The results show that inter-provincial digital economy development in China shows a sequential weakening from the east, centre, and northeast to the west. The East leads the country's digital economy overall, while there is a clear gradient gap between provinces. The central region needs to create a cluster for the development of digital industries. The Northeast should enhance the competitiveness of the industry across the board. The West must strengthen the construction of innovative talent and new infrastructure for the digital economy. These findings can serve as guidelines for designing China's ongoing digital economy development.

Enhancing logistics performance measurement: an effectiveness-based hierarchical data envelopment analysis approach

The logistics performance index (LPI) is a comprehensive and comparable composite index developed by the World Bank to assess a country’s logistics and trade facilitation environment. However, the existing LPI relies on externally assigned weights. To enhance LPI scores, this study adopts an effectiveness-based hierarchical data envelopment analysis method that internally allocates objective weights based on the dataset. Such endogenous weight information can provide additional valuable insights for countries to prioritize and strategize efforts to enhance their performance in the future. The results of this study indicate that focusing on improving the policy category yields greater benefits than improving the service category in terms of ranking national logistics performance. Furthermore, this study finds that logistics performance is influenced by income levels and geographical area. Income levels impact the regulatory and trade facilitation environment, with varying income levels leading to different priority policy areas. Geographical location also plays a crucial role in regional economic integration and trade facilitation. A favorable geographical location reduces costs and time while enhancing supply chain predictability and reliability. It is hoped that this study serves as a valuable resource for countries in identifying optimization strategies to improve their logistics performance.

An alternative assessment approach to global logistics performance evaluation: Common weight H‐DEA approach

AbstractThe goal of this study is to investigate the objective importance of the categories and sub‐indicators constituting the Logistics Performance Index (LPI) and try to answer which of these LPI's indicators has the most significant importance and to provide a guidance tool for policymakers to devise policies in logistics and transportation. Hence, this study puts forth an integrated multi‐attribute decision‐making technique coalesced with the hierarchical data envelopment analysis and assurance region. For different income groups and regions, this model is employed to reassess the scores and rankings of LPI that are obtained from the World Bank. Displaying a higher objectivity than World Bank's method, the results demonstrate no substantial difference in the rankings obtained under both the proposed and World Bank's methods. Moreover, service delivery performance was found to be more vital to LPI than policy regulations. In terms of global weighting, of the six sub‐indicators, timeliness is the most important. These findings provide a guidance tool for policymakers to devise policies in logistics as well as in transportation. With the common weights that have been utilized, the results may direct toward different priorities in terms of policies, compared to World Bank.

Constructing the performance index of Malaysia’s district health centers using effectiveness-based hierarchical data envelopment analysis

This study aimed to explore the possibility of measuring district health center (DHC) performance using effectiveness-based hierarchical data envelopment analysis (H-DEA). To reflect the overall performance in DHCs, four different scopes of services, namely, disease prevention and control, family health development, health infrastructure and clinical, and governance, were provided by DHCs. The findings show that H-DEA analysis is a possible approach to measure the efficiency of DHCs in Malaysia compared to conventional key performance indicator assessment. This finding hopes to provide guidance to policy makers on DHC service ranking in controlling and distributing the budget pertaining to public health activities at the national level.

Measurement and evaluation of multi-function parallel network hierarchical DEA systems

Many organisations are composed of multiple departments connected either in series or in parallel, which may be further decomposed into a number of functions arranged in a hierarchical structure. Several researchers have successfully used appropriate Data Envelopment Analysis (DEA) modelling techniques to assess complex structures. However, to our knowledge, no-one has yet examined the case of measuring and evaluating a parallel network structure combined with a hierarchical one. This paper discusses the development of a multi-function parallel system with embedded hierarchical network structures. A linear additive decomposition DEA model and a non-linear multiplicative aggregation DEA model are proposed as alternatives to evaluate the operating performance of such a structure. The system, the sub-systems, and the efficiencies of their internal units, as well as their relationships, are identified. The system efficiency of the additive model is shown to be greater than or equal to that of the multiplicative model. To verify the applicability of our proposed models, we consider a hypothetical example of the measurement and evaluation of the performances of several Business Schools across a number of universities. Other envisaged areas of application of our structure could include supporting the evaluation of the supply chain management of a firm, or the determination of the most desirable ship design considering maintenance issues.

An alternative assessment approach to national higher education system evaluation

While the assessment of higher education systems is informative to both policy makers and individuals, it is subjective and performed according to experts’ judgment. The present study proposes a relatively objective approach, hierarchical data envelopment analysis (H-DEA), to rank higher education systems. Unlike the subjective approach, H-DEA utilizes endogenous weight determination, allowing assessors to identify the relative importance of each attribute and subattribute. Utilizing the U21 Ranking of National Higher Education System 2020 data, our analysis indicates that the output attribute is a crucial factor influencing the overall performance of higher education systems, even considering countries’ stage of development and culture. The computed weights of the H-DEA framework show various attributes’ different contributions by group. Resources allocated to the higher education system are important for developing countries, while a high degree of internationalization and a strong link between academia and industry matter for advanced countries. Surprisingly, Asian and Western cultures experience similar performance in their higher education systems, reflecting the Asian higher education system’s development toward the Western style. The performance of countries with non-Asian–non-Western cultures, as expected, lags behind, and putting more resources into these countries’ higher education system is a way to enhance the overall performance.

Developing an innovation capital index of global airlines using a hierarchical data envelopment analysis approach

This study proposes an effectiveness-based hierarchical data envelopment analysis (H-DEA) method to endogenously assign weights with the purpose of aggregating subcategories for an innovation capital index in the global airline industry. The study comprises airlines ranked in the World's Top 100 Airlines in 2018. The effectiveness-based H-DEA results provide evidence that there are opportunities for airlines to improve their innovation capital index, on average, by 48%. Relatively low scores in the internal capital category are identified as the major contributor to the poor innovation capital index, and the optimal scores and weights of the innovation capital index are found to differ by geographical location. Effectiveness-based H-DEA offers an alternative method for determining the optimal weight of an innovation capital index in a multidimensional setting for international comparison. The flexible weight can help each airline to focus on the critical innovation capital categories requiring improvement to create an effective business strategy. To the best of the authors' knowledge, to date, no studies have focussed on innovation capital in the airline industry. This study also provides a detailed discussion on how to assess the innovation capital index in the global airline industry specifically using the effectiveness-based H-DEA method.

Optimal Site Selection for a Solar Power Plant in the Mekong Delta Region of Vietnam

Following the recent development trend in the struggle for cleaning the earth’s environment, solar is the one of most promising area that can partially be used as a replaceable energy from non-renewable fuel sources. As such, it plays a significant role in protecting the environment from global warming. As solar power does not emit harmful gases into the atmosphere, its production, distribution, setup, and operation are vital should the production remain constant. Even solar energy waste emissions are small; when compared to current energy sources, the amount of harmful gases is negligible. This paper presented an integrated approach for site of solar plants by using data envelopment analysis (DEA) and Fuzzy Analytical Network Process (FANP). Furthermore, these integrated methodologies, incorporated with the most relevant parameters of requirements for solar plants, are introduced. First, the paper considers an integrated hierarchical DEA and FANP model for the optimal geographical location of solar plants in Mekong Delta Region, Vietnam. Using the proposed model for implementation would allow the renewable energy policy makers to select and control the optimal location for allocating and constructing a solar energy power plant in Vietnam. This is the preferred strategy for location optimization problems associated with solar plant units in Vietnam and around the world.

Network hierarchical DEA with an application to international shipping industry in Taiwan

Data envelopment analysis (DEA) has been proved to be a powerful approach for measuring the performance of decision making units (DMUs). However, the conventional black-box approach tends to neglect the internal structure of the components and the possibility of having different network structures of DMUs. In reality, DMUs can have complex networks that are in forms of parallel or serial structures and hierarchical processes. For example, in the international shipping industry, the operational tasks can be divided into two stages: supervising the ship dispatch and controlling the work time in the port, which jointly constitute a two-stage operating network structure and each contains its own embedded hierarchical structure. Herein, this study intends to propose a new network hierarchical DEA approach to evaluate the performances of such two-stage structure that embedding the hierarchical structures. Data collected from the Maritime and Port Bureau (MOTC) in Taiwan (2017) is used to validate the reliability and efficiency. The result indicates the effectiveness of the model and provides meaningful implications for the international shipping industry.

The degree of robustness based on hierarchical DEA

Data envelopment analysis (DEA) is a method that is used to evaluate the efficiency values of decision-making units (DMUs), and several methods to evaluate the robustness of efficiency against the changes in specific input or output items has been developed. Although, it is difficult to figure out how robust efficiency values of DMUs are quantitatively considering all input and output items. To overcome this problem, we propose a degree of robustness, τ, based on a hierarchical DEA model. The proposed degree is formulated based on the efficiency value of each combination of input and output items, the number of input and output items of each combination, and parameter p. This parameter p represents the degree of importance on non-characteristic nodes relative to that of the characteristic nodes. The robustness of efficiency considering all input and output items can be evaluated by the proposed degree.

A reassessment of the Global Food Security Index by using a hierarchical data envelopment analysis approach

This study proposes a hierarchical data envelopment analysis (H-DEA) approach to construct a multi-dimensional indicator, and applies it to reassess the 2014 Global Food Security Index created by the Economist Intelligence Unit (EIU) across 110 countries. Instead of using expert opinions to assign weights, the proposed model endogenises the weights, and thus avoids the problems of subjective weighting for international comparisons. The results show that although the ranking is not significantly different from that of the EIU, the optimal scores and weights differ by income levels. Additionally, this work articulates the value of a well-founded performance evaluation method by leveraging experts’ opinions and data-driven techniques through constructing a best-practice frontier with observation-specific weights. It is suggested that food availability should be the top policy priority in low- to medium-income and Sub-Saharan African countries where food deficits are most prevalent. The findings can serve as guidance to improve the design of the ongoing efforts for global food security.

A Hierarchical Methodology for Performance Evaluation Based on Data Envelopment Analysis: The Case of Companies’ Competitiveness in an Economy

In this research, we present a hierarchical Data Envelopment Analysis (DEA) methodology for competitiveness analysis. This methodology takes into account the heterogeneity of the decision making units (DMUs) as well as the diversity of the comparison criteria. We propose to homogenize the DMUs by grouping them hierarchically, which permits a better identification and definition of the criteria in each specific grouping. The methodology proceeds first by the determination of the performances or relative efficiencies, which are in turn aggregated into competitiveness indices in each grouping by the superiority index of [1]; then, the overall competitiveness indices are determined additively along the hierarchical levels. We illustrate the methodology by a competitiveness analysis of several companies belonging to different sectors of activity in an economy, where are suggested ways of improvement for the non-competitive companies within their sectors and within the economy.

Location optimization of wind plants in Iran by an integrated hierarchical Data Envelopment Analysis

Unique features of wind energy have caused increasing demands for such resources in various countries. In order to use wind energy as a natural resource, environmental circumstances and geographical location related to wind intensity must be considered. Different factors may affect on the selection of a suitable location for wind plants. These factors must be considered concurrently for optimum location identification of wind plants. This article presents an integrated approach for location of wind plants by hierarchical Data Envelopment Analysis (DEA). Furthermore, an integrated approach incorporating the most relevant indicators of wind plants is introduced. Moreover, two multivariable methods namely, Principal Component Analysis (PCA) and Numerical Taxonomy (NT) are used to validate the results of DEA model. The prescribed approach is tested for 25 different cities in Iran with 5 different regions within each city. The approach of this study has been validated by the previous studies and actual data of wind plants in Iran. This is the first study that considers an integrated mathematical approach for location optimization of wind plants. Implementation of the proposed approach would enable the energy policy makers to select the best possible location for construction of a wind power plant with lowest possible cost.

Location optimization of solar plants by an integrated hierarchical DEA PCA approach

Unique features of renewable energies such as solar energy has caused increasing demands for such resources. In order to use solar energy as a natural resource, environmental circumstances and geographical location related to solar intensity must be considered. Different factors may affect on the selection of a suitable location for solar plants. These factors must be considered concurrently for optimum location identification of solar plants. This article presents an integrated hierarchical approach for location of solar plants by data envelopment analysis (DEA), principal component analysis (PCA) and numerical taxonomy (NT). Furthermore, an integrated hierarchical DEA approach incorporating the most relevant parameters of solar plants is introduced. Moreover, 2 multivariable methods namely, PCA and NT are used to validate the results of DEA model. The prescribed approach is tested for 25 different cities in Iran with 6 different regions within each city. This is the first study that considers an integrated hierarchical DEA approach for geographical location optimization of solar plants. Implementation of the proposed approach would enable the energy policy makers to select the best-possible location for construction of a solar power plant with lowest possible costs.

Hierarchies and Groups in DEA

Conventional applications of data envelopment analysis (DEA) presume the existence of a set of similar decision making units, wherein each unit is evaluated relative to other members of the set. Often, however, the DMUs fall naturally into groupings, giving rise first to the problem of how to view the groups themselves as DMUs, and second to the issue of how to deal with several different ratings for any given DMU when groupings can be formed in different ways. In the present paper we introduce the concept of hierarchical DEA, where efficiency can be viewed at various levels. We provide a means for adjusting the ratings of DMUs at one level to account for the ratings received by the groups (into which these DMUs fall) at a higher level. We also develop models for aggregating different ratings for a DMU arising from different possible groupings. An application of these models to a set of power plants is given.