Decision Making Units Research Articles

Hotel Performance in the Guangdong-Hong Kong-Macau Greater Bay Area: A Non-Homogeneous Perspective

Improving upon previous studies on hotel performance evaluation in terms of efficiency, which usually treat different hotels as homogeneous in their product provision, this study examines the performance of 53 hotels in the Guangdong-Hong Kong-Macau Greater Bay Area (GBA) during 2015 to 2019, by employing data envelopment analysis with a non-homogeneous decision making units (DMUs) model. The results show that the hotels in GBA were inefficient, and those with high product diversification are generally closer to achieving optimal efficiency levels, particularly those providing rooms, food and beverage, meeting services, and spa services, while those providing only rooms had the worst performance. Among the GBA cities included in this study, the non-homogeneous efficiency scores of the hotels in Guangzhou outperformed those of hotels in the other cities, and the overall hotel efficiency score of the core cities was better than that of the key node cities.

Performance Measurement: Machine Learning as a Complement to DEA for Continuous Efficiency Estimation

Data Envelopment Analysis (DEA) is a well-established non-parametric technique for performance measurement to access the efficiency of Decision-Making Units (DMUs). However, its inability to predict the efficiency values of new DMUs without re-conducting the analysis on the entire dataset has led to the integration of Machine Learning (ML) in previous studies to address this limitation. Yet, such integration often lacks a thorough evaluation of ML's adaptability in replacing current DEA process. This paper presents the results of an empirical study that employed eight ML models, two DEA variants, and a dataset of S&P500 companies. The findings demonstrated ML’s remarkable precision in predicting efficiency values derived from a single DEA run and comparable performance in predicting the efficiency of new DMUs, thus eliminating the need for repeated DEA. This discovery highlights ML’s robustness as a complementary tool for DEA in continuous efficiency estimation, rendering the practice of re-conducting DEA unnecessary. Notably, boosting models within the Ensemble Learning category consistently outperformed other models, highlighting their effectiveness in the context of DEA efficiency prediction. Particularly, CatBoost demonstrated its superiority as the top-performing model, followed by LightGBM in the second position in most cases. When extended to five enlarged datasets, it shows that the model exhibits superior R² values in the CRS scenario.

Strategic alliances and partnerships based on the semi-additive production technology in DEA

Strategic alliances and partnerships based on mergers and acquisitions can be used to improve the performance of decision-making units (DMUs). In this paper, we present different types of strategic alliance cooperation and partnership between DMUs and their corresponding aggregation DMUs. We propose two different strategies, we were able to carry out the process of strategic alliances and partnerships in semi-additive production technology. In the first strategy, two partner DMUs can compensate for the lack of resources in some of their input components by using excess input resources in some of each other's input components. Thus these DMUs can improve their efficiency score among all DMUs. The modeling of strategic alliances and partnerships in the first strategy was based on data envelopment analysis (DEA) models. In the second strategy, the two DMUs selected as partners adjust their input and output levels with the help of each other in such a way that these two DMUs achieve a target efficiency level predetermined by the DM. The modeling of strategic alliances and partnerships in the second strategy was based on inverse DEA models. We also apply the proposed approach to show importance strategic alliances and partnerships in banking. In the following, we compared the results of the models in carrying out the partnership process in two different technologies. The results showed that in semi-additive production technology, we can achieve potential gains for banks.

Marginal abatement cost of CO2: A convex quantile non-radial directional distance function regression method considering noise and inefficiency

By purchasing emission reduction equipment or reducing production scale, it is possible to effectively decrease CO2. Therefore, understanding the marginal abatement cost (MAC) associated with these methods is crucial for making decisions. However, previous studies using the directional distance function (DDF) approach often mis-specified production functions and neglected data noise. They also assumed decision-making units (DMUs) to be on the production frontier and used proportional changes in inputs and outputs as abatement paths. This paper addresses these limitations by developing the convex quantile non-radial directional distance function (CQR-NDDF) method, which estimates the MAC of CO2 and determines optimal abatement paths for DMUs without assuming a specific production function, employing linear programming techniques. Applying this method to 30 provinces in mainland China from 2011 to 2019, the study finds that China's CO2 MAC increased from 182 to 247 yuan/ton. The lowest-cost abatement path varies by province and time. The club convergence and ordered probit model are employed to conclude that the second industry and urbanization increase the MAC of CO2, while factors such as foreign direct investment, openness level, and human capital decrease the MAC. Moreover, the CQR-NDDF method yields significantly lower MAC estimates than the NDDF method. In conclusion, this paper provides new insights into China's CO2 MAC, emphasizing the importance of considering inefficiency and data noise in MAC estimation. We anticipate that utilizing CO2 MAC as a benchmark for carbon trading market prices could lead to an increase in prices within China's carbon trading market.

Comprehensive intuitionistic fuzzy network data envelopment analysis incorporating undesirable outputs and shared resources

The economic growth rate is intricately linked to the efficiency and effectiveness of the banking industry. A widely applicable mathematical technique for such assessments is Data Envelopment Analysis (DEA), which evaluates the relative efficiency of Decision-Making Units (DMUs) by comparing their inputs and outputs. Traditional DEA treats DMUs as black boxes, neglecting internal processes that contribute to inefficiencies in individual DMUs. Additionally, it assumes precise values for inputs and outputs that do not apply to real-world problems. This study introduces a comprehensive network series of two-stage DEA, incorporating shared inputs and intermediate measures, undesirable outputs, external inputs and outputs, initial inputs, and terminal outputs. The network two-stage DEA is extended to intuitionistic fuzzy circumstances to address uncertainty. In this extension, a non-linear intuitionistic fuzzy number, namely a parabolic intuitionistic fuzzy number, represents higher-order imprecise datasets. An illustrative example validates the proposed methodology, and comparisons with existing methods are conducted. Moreover, the methodology is applied to assess the efficiency of Indian public sector banks, demonstrating its applicability and showcasing the efficacy of the procedures and algorithms used. Decision-makers can make better choices using optimal efficiency values to gain insights into inputs, intermediate measures, and outputs.•The research study focused on a network two-stage DEA model, incorporating undesirable outputs and shared resources in the presence of uncertainty.•The methodology involves solving the network two-stage DEA model using parabolic intuitionistic fuzzy numbers.•The experimental analysis involves assessing the efficiency of Indian public sector banks.

Allocating the fixed cost as a complementary input in two-stage system: A DEA approach

The existing research on fixed cost allocation (FCA) in two-stage system data envelopment analysis (DEA) models typically regards the fixed cost as an additional input for each decision-making unit (DMU). However, these models overlook the prevalent real-world scenario where fixed costs act as complementary inputs in actual production processes. This study proposes a general two-stage network DEA model that incorporates the fixed cost as a complementary input to optimize the allocation scheme. First, we construct a functional relationship between the efficiency scores of DMUs and their allocated fixed costsusing a modified super-efficiency DEA model, which effectively classifies DMUs and solves infeasible solutions within the variable returns to scale (VRS) framework. Then, we propose a fair and unique allocation model based on fairness and efficiency maximization principles. Specifically, we allocate fixed costs based on the operational scale for inelastic DMUs while equitably increasing the efficiency scores for elastic DMUs. Finally, a numerical example and an empirical study on subsidy allocation among 30 provinces demonstrate the rationality and acceptability of our approach.

An Improved Slack Based Measure Model for Evaluating Green Innovation Efficiency Based on Asymmetric Data

Nowadays, one of the main challenges facing green innovation management is how to enhance the performance of innovation processes by utilizing asymmetric input and output data. Therefore, this paper develops an improved SBM model analysis framework for evaluating the green innovation efficiency of asymmetric input and output data. The framework is applied to assess the technical (TE), managerial (PTE), and scale (SE) efficiencies of new energy companies under three input variables (R&D personnel input, R&D capital input, and comprehensive energy consumption input), two desirable output variables (green technology output and economic output), and one undesirable output variable (greenhouse gas emissions). Then, environmental factors and random factors are eliminated from the obtained input slack variables based on the SFA model, placing decision-making units in a homogeneous environment. The results demonstrate that TE, PTE, and SE are improved after eliminating environmental factors and random factors. Subsequently, based on the entropy method, this paper classifies companies’ green innovation patterns into four categories and provides targeted solutions. The purpose of this paper is to provide an evaluation method for new energy companies to understand green innovation efficiency and assist decision makers in identifying the most optimal resource allocation approach. The proposed improved SBM model contributes to the literature and to industry practice by (1) providing a reliable evaluation of green innovation efficiency under asymmetric input and output data; (2) determining effective improvement actions based on a slack analysis of environmental variables and random variables that lead to improved process performance; and (3) making fuzzy innovation performance efficient to facilitate understanding and managing innovation resource allocation quality.

An optimistic-pessimistic game cross-efficiency method based on a Gibbs entropy model for ranking decision making units

The game cross-efficiency method, a commonly utilized approach for ranking decision-making units in tie-breaking scenarios, is based on secondary goals. However, in certain data envelopment analysis ranking problems, the classical game cross-efficiency method may fail to differentiate all decision-making units effectively. To address this limitation, it is prudent to explore the development of a new method that can enhance the ranking performance of the classical game cross-efficiency approach. In this study, we propose a novel Gibbs entropy linear programming model that integrates both optimistic and pessimistic perspectives of the classical game cross-efficiency method for data envelopment analysis ranking problems. To validate the reliability and utility of our proposed method, we present three examples: the six nursing homes problem, numerical example 2, and an application involving twenty Thai provinces with cash crop data. The reliability of the proposed method is assessed using Spearman’s correlation coefficient (rs) on the numerical examples. The results demonstrate that the rs values for both the proposed method and the classical game crossefficiency method, specifically for the six nursing homes problem, numerical example 2, and the application involving twenty Thai provinces, are determined to be rs=0.998, 0.998, and 0.986 respectively.

Impact of research and development expenses on the profitability of assets: The case of textile and clothing industry in Portugal

The study aims to examine the financial efficiency of the textile and clothing industries in Portugal using official statistical data. The main objective is to assess the relationship between spending on research and development and return on assets. The study analyzes the performance of various subsectors of the textile and clothing industries, presenting the relationship between investments in research and development and the operating return on assets over various economic periods. The study adopted data envelopment analysis, classifying decision-making units based on average efficiency levels. The results highlight sectors of manufacture of textiles for technical and industrial use, manufacture of other textiles, production of outerwear, and manufacture of workwear as the most efficient. In contrast, sectors of manufacture of clothing and accessories, manufacture of knitwear, and leather clothing show lower levels of efficiency. From 2003 to 2022, the textile industry exhibited the highest levels of financial efficiency, with an above-average ratio between spending on research and development and return on assets. However, sectors of knitwear manufacturing and textile finishing have maintained a more or less constant level of financial efficiency. The analysis highlights the need for targeted interventions to increase the financial efficiency of different subsectors within the textile and clothing industries. It is evident that there are varying levels of financial efficiency across these sectors, and the need for benchmarking periods can help identify areas for improvement and set achievable goals. AcknowledgmentThis article is financed by Instituto Politécnico de Setúbal [Polytechnic Institute of Setúbal].

Evaluation of intercity road passenger transportation using a novel double-frontier game-regret-cross-efficiency

The Cross-Efficiency (CE) method, based on Data Envelopment Analysis (DEA), is a commonly used approach to measure the efficiency of Decision-Making Units (DMUs). Various secondary goal models can yield different efficiency results. The recently developed Game CE (GCE) method aims to address this issue and achieve convergence efficiencies. However, the conventional GCE was developed under the unrealistic assumption that Decision Makers (DMs) are perfectly rational, as it relies on the arithmetic mean aggregation method. Additionally, the GCE evaluates DMUs based on efficient reference points, disregarding the pessimistic perspective. The study introduces a new aggregation method called Regret-Consensus Aggregation (RCA) that captures the subjective preferences of DMs. GCE-RCA scores are obtained by incorporating RCA into the GCE. A new method called Game Cross In-Efficiency (GCIE) with RCA (GCIE-RCA) has been developed to incorporate anti-efficient reference points into the evaluation process. A Double-Frontier GCE based on the RCA (DFGCE-RCA) is developed from two perspectives. The DFGCE-RCA is implemented to evaluate the performance of the Iranian Inter-City Road Passenger Transportation (IC-RPT) system based on six key performance indicators. DFGCE-RCA has several advantages in addition to those of GCE. Firstly, considering two perspectives provides more comprehensive results. Additionally, it can capture the subjective perspectives of DMs. Lastly; it enables the aggregation process to reach a consensus.

A Flexible Cross-Efficiency Model with Partial Preference for Efficiency Evaluation of Clean Transportation Energy

The rapid development of the transportation industry benefits from the consumption of energy, but the excessive dependence on petroleum fuels makes it a major source of air pollution. In order to achieve green and high-quality development of the transportation industry, many countries are committed to scientifically evaluating the utilization efficiency of clean energy, which has attracted wide attention from the whole society. Significantly, without considering the diversity and complexity of pollutants, indicators used in previous studies were unable to cover all pollutants when establishing the evaluation index system. Meanwhile, as an efficient tool, data envelopment analysis (DEA) is extensively used when it comes to efficiency evaluation. However, the absolute preference of existing benevolent and aggressive cross-efficiency models limits its application scenarios. To address the challenges above, an improved flexible cross-efficiency DEA model is proposed considering both same and different benevolence coefficients of decision-making units (DMUs) on the basis of pointing out the inadequacy of the previous model. The concepts of consensus coefficient and group preference are introduced in the aggregation of cross-efficiency. Besides, based on the theory of undesirable output, the consumption of nonclean energy is taken into account as the input indicator to characterize the degree of pollution. The results show that the obtained cross-efficiency value and efficiency ranking of clean transportation energy change sensitively under various benevolent coefficients. There is an important practical significance to consider the independent preference information of DMUs for the evaluation and ranking of cross-efficiency.

Technical Efficiency of Mexico's Public Health System in the Delivery of Obstetric Care, during 2012-2018.

The objective of this study was to evaluate the technical efficiency of Mexico's public health system in the delivery of obstetric care from 2012 to 2018. A multi-stage quantitative study of the public health institutions responsible for 95% of the system's obstetric services was conducted using data envelopment analysis. The efficiency of state-level productive units (decision-making units, or DMUs) was calculated and juxtaposed with the DMUs' maximum (0.82) and minimum (0.22) scores. Using the outcomes of the initial stage, the average technical efficiency of each institution at the national level was estimated and compared. The results were also utilized to estimate and compare the average efficiency of each state-level health system based on economic characteristics (state GDP per capita). Outputs included prenatal visits and deliveries, while inputs comprised gynecologists, exam rooms, and delivery rooms. Institutional efficiency ranged from 0.16 to 0.82, with an average of 0.417. The Ministry of Health (0.82) and the Mexican Social Security Institute (0.747) exhibited the highest efficiency scores, while the remaining institutions (Institute for Social Security and Services for State Workers [ISSSTE]; Mexican Petroleum [PEMEX]; the Secretary of National Defense [SEDENA]; and the Navy [SEMAR]) scored below the health system average. Of the 153 DMUs, 20% surpassed the maximum (0.82) and 40.6% fell below the minimum (0.22). These findings indicate that 80% of DMUs have unused operational capacity that could be utilized to enhance technical efficiency. No relationship was found between efficiency and the GDP of Mexico's 32 politico-administrative divisions. The efficiency gap between institutions (0.66) shows that while some DMUs are saturated (exhibiting high efficiency scores), the majority have unused operational capacity. Leveraging this untapped capacity could address the needs of vulnerable populations facing restricted access due to health system fragmentation.

Ranking DMUs by using interval efficiencies in data envelopment analysis

Efficiency is a relative measure that allows assessment across different ranges. Evaluating the performance of decision-making units (DMUs) from an optimistic perspective yields the best relative efficiency (optimistic efficiency), which establishes an efficiency frontier. Conversely, evaluating from a pessimistic perspective produces the worst relative efficiency (pessimistic efficiency) and creates an inefficiency frontier. This study examines the efficiency of DMUs in two scenarios and proposes models for adjustment coefficient. The pessimistic and optimistic efficiencies are adjusted to the lower and upper bounds of the DMUs based on the adjustment coefficient, enabling determination of efficiency intervals for all DMUs, as well as evaluation and ranking. A Hurwicz criterion-based approach is introduced and applied to compare and rank the interval efficiencies of DMUs. Two numerical examples are examined using the proposed DEA adjustment coefficient models to demonstrate its potential application and validity.

Multicast Routing Based on Data Envelopment Analysis and Markovian Decision Processes for Multimodal Transportation

In the context of Iraq’s evolving transportation landscape and the strategic implications of the Belt and Road Initiative, this study pioneers a comprehensive framework for optimizing multimodal transportation systems. The study implemented a decision-making framework for multimodal transportation, combining data envelopment analysis (DEA) efficiency scores and a Markov decision process (MDP) to optimize transportation strategies. The DEA scores captured decision-making unit (DMU) performance in various aspects, while the MDP rewards facilitated strategic mode selection, promoting efficiency, cost-effectiveness, and environmental considerations. Although our method incurs a total cost approximately 29% higher than MRMQoS, it delivers a nearly 26% reduction in delay compared to MCSTM. Despite MRMQoS yielding an 8.3% higher profit than our approach, our proposed scheme exhibits an 11.7% higher profit compared to MCSTM. In terms of computational time, our method achieves an average CPU time positioned between MCSTM and MRMQoS, with MCSTM showing about 1.6% better CPU time than our approach, while our method displays a 9.5% improvement in computational time compared to MRMQoS. Additionally, concerning CO2 emissions, the proposed model consistently outperforms other models across various network sizes. The percentage decrease in CO2 emissions achieved by the proposed model is 7.26% and 31.25% when compared against MRMQoS and MCSTM for a network size of 25, respectively.

IMPROVING THE EVALUATION AND PREDICTION OF PREVENTION AND TREATMENT EFFICIENCY DURING PUBLIC HEALTH EMERGENCIES BY USING THE SBM-BPNN ALGORITHM

Crisis response is the key to reducing the impact and damage of public health emergencies. Previous studies only focused on specific measures for emergency response, but the effectiveness of these measures has seldom been discussed. How about the effective of the crisis response on public health emergencies? What will happen to the effectiveness of crisis response after the transformation of public health emergency measures? To address these questions, a novel research framework was constructed by combining slacks-based measure (SBM) and back propagation neural network (BPNN) algorithms. At Stage I, an efficiency evaluation was conducted on SBM with undesirable outputs to evaluate the prevention and treatment efficiency during public health emergencies, and stochastic frontier analysis was performed to mitigate the influence of environmental factors and statistical noise. At Stage II, the adjusted efficiency was predicted with the BPNN model. The decision-making units were effectively improved by incorporating slack variables, thus enabling the prediction and optimization of optimal cases given the epidemic resources. An empirical analysis of the response of 43 G20 member countries to the COVID-19 pandemic showed that the novel framework could evaluate prevention and treatment efficiency across regions and predict the efficiency and optimal case outputs following shifts in epidemic preventive measures. After evaluation, the mean squared error of the BPNN efficiency prediction model was only 0.0014, whereas that of the BPNN optimal output prediction model was 0.126. Therefore, this novel framework is suitable for evaluating and predicting the effectiveness of crisis response on public health emergencies, which provides necessary assistance for crisis decision-making by the government and emergency management organizations., Keywords: Public health emergencies, COVID-19 pandemic, Crisis response efficiency, Evaluation, Prediction.

An Inverse BCC Model for Evaluating and Ordering Decision-Making Units under Fuzziness

An Inverse BCC Model for Evaluating and Ordering Decision-Making Units under Fuzziness

Merging decision-making units in the simultaneous presence of desirable and undesirable factors

This paper is devoted to applying the inverse Data Envelopment Analysis (InvDEA) in the simultaneous presence of desirable and undesirable factors. One of the most common ways to improve units’ performance in the business environment is through activity synergies called units’ merging. The present study models how to identify the inherited input/output from the units participating in the merger process to achieve the desired efficiency goal. The proposed models are established based on the InvDEA approach and multiple-objective programming tools. Sufficient conditions to estimate desirable and undesirable data are obtained using Pareto solutions to multi-objective programming problems. The theory extended in the study is explained by an application in the banking sector.

A Novel Data Envelopment Analysis Framework for Performance Evaluation of European Road Transport Systems

The role of transportation is becoming increasingly important in the world economy, and road transport in particular plays a very important role in all types of transportation. For this reason, it is extremely important to monitor its performance regularly. Very often, this is done using Data Envelopment Analysis (DEA) performance evaluation models, and consequently, there are numerous articles in the literature on DEA evaluation of road transport systems. In this study, we first summarise these articles and classify them according to different characteristics (environmental, safety, economic, energy). Finally, we use them as a basis for developing a novel DEA framework, which is used for the evaluation of the efficiency and ranking of road transport systems that also takes into account undesirable outputs, i.e. environmental and safety outputs. As a case study, we evaluate 28 European countries from technical, safety and environmental aspects. The CCR and SBM models are used to evaluate the efficiency of these countries for the last two years of published data. The results show that Denmark ranks first and Cyprus last for both years. It was also found that safety efficiency is generally rated lower than other criteria. Finally, the results and reasons for the efficiency and inefficiency of specific decision-making units, i.e. countries, are discussed.

A Slacks-Based Measure Model for Computing Game Cross-Efficiency

This paper introduces an improved slack-based game cross-efficiency measurement model that enhances the existing cross-efficiency framework and integrates it with the Data Envelopment Analysis (DEA) game cross-efficiency. The model ensures the fairness of its results through the implementation of a more stringent selection of frontier face weights. It accounts for the competitive relationships among Decision Making Units (DMUs), achieving a Nash equilibrium solution through continuous iterations. Furthermore, the model accounts for undesirable outputs and various strategic orientations, enhancing its applicability. The model’s effectiveness is validated through comparative analyses of diverse case studies. Additionally, the model’s practical utility is demonstrated through the analysis of industrial data from various Chinese provinces between 2010 and 2019. Analysis results show that the proposed model measures production efficiency with greater precision and comparability than alternative models.

Allocating Benefits Due to Shared Resources Using Shapley Value and Nucleolus in Dynamic Network Data Envelopment Analysis

Shared resources are common among supply chain partners and also occur in multiple linked stages of an internal network. The sharing of these resources impacts the organization’s profits. This study is focused on the potential benefits of resource sharing on a three-stage network system and on the profit improvement allocation. Previous treatments concentrate on defining optimal proportions to allocate resources and disregard the impacts of allocations to promote cooperation and are limited to static evaluations. Data Envelopment Analysis performs the decision-making units (DMUs) efficiency measurement. Methodological advances have resulted in models that analyze their internal structure and temporal impacts on efficiency. We propose an integrated cooperative game and dynamic network DEA that considers known quantities of resources used in each stage and the time effects to optimize the system’s profit. Each DMU stage is a player, and we investigate performance before and after resource sharing. Using Shapley value and Nucleolus, it is possible to allocate the benefits obtained based on the marginal contributions of each stage, providing incentives to motivate and maintain cooperation. A numerical example is used to illustrate the method. The results confirm the identification of inefficient DMUs and that sharing resources allows for profit increase for all of them.