Inverse Data Envelopment Analysis Research Articles

An inverse data envelopment analysis model for solving time substitution problems

This paper proposes new inverse data envelopment analysis (DEA) models considering input and output efficiency measures for the time substitution problem. We compare our DEA model with existing models in the literature. We show that existing models in the literature overestimate the required resources, and on the other hand, these are a special case of our models. We show that our models are unit invariant. We also describe another appealing characteristic of our model, that is, efficiency invariant, as a consequence of inverse structure. An illustrative example is provided to explain the proposed model and provide a comparison of our models and existing models in the literature. We also used our models in a real-world application, the selected economic sectors in Iran. The results show some potential improvements during the period of study.

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.

Using inverse DEA and machine learning algorithms to evaluate and predict suppliers’ performance in the apple supply chain

In an era where sustainability is paramount, this study presents a novel analytical framework that uses inverse data envelopment analysis (IDEA) and machine learning to optimize supplier performance in Apple's supply chain. We introduce the application of IDEA to recalibrate operational benchmarks, focusing on substantial CO2 reduction, and couple this with advanced predictive algorithms to proactively steer supplier practices toward Apple's sustainability targets. The study systematically simulates scenarios to achieve 30%–50% CO2 cuts, setting a precedent for environmental strategy integration. Beyond environmental metrics, our approach rigorously evaluates economic indicators such as earnings persistence and market recognition, providing a holistic view of supplier viability. The research employs machine learning, notably random forest and k-Nearest neighbors, to distill unbiased insights from historical data, ensuring precise, objective supplier assessments. Our findings offer a strategic blueprint for corporations and supply chain stakeholders aiming to embed sustainability into their operational ethos, supported by data-centric decision-making. These methodologies and insights contribute valuable perspectives to sustainable supply chain management and predictive analytics discourse. Finally, the study offers guidance on implementing CO2 reduction strategies and evaluating suppliers' economic performance, aligning with Sustainable Development Goals (SDGs) objectives.

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.

Efficiency analysis and CO2 emission reduction strategies in the US forest sector: a data envelopment analysis approach

Industrial economic activities produce pollutants and environmentally sustainable production systems in forestry aim to minimize these undesirable outputs while maintaining high production and economic growth. In this contribution, we assume that in addition to plot-specific inputs and outputs, there are some contextual variables that may be exogenously fixed or may be under the control of the decision-makers. In this sense, we first propose a novel and practical approach to calculate environmental efficiency by reducing undesirable products. Then, we utilize an inverse data envelopment analysis (IDEA) model to effectively manage and reduce CO2 emissions. In doing so, the applied models have been utilized to evaluate the efficiencies of 89 forest plots in the USA. Given our estimations in a real application to the forest plots, the study revealed that the average environmental efficiency score is nearly 0.75 (out of 1). However, there is potential for improvement by adjusting the impacts of contextual factors, which could raise the score to approximately 0.8. Furthermore, the analysis indicates a positive correlation between ownership and environmental efficiency, suggesting that increased ownership leads to higher environmental efficiency. Conversely, temperature exhibits a negative correlation with environmental efficiency. Finally, the results obtained from the IDEA indicate that in order to reduce undesirable outputs by a specific level of 5–10%, it is necessary to decrease other inputs and outputs. This is because, under the assumption of weak disposability, reducing the level of undesirable outputs requires a reduction in certain factors that influence production capacity. In other words, achieving the desired reduction in undesirable outputs inevitably involves diminishing certain aspects of the production process. As the major conclusion, the emergence of IDEA as a powerful tool for sensitivity analysis, along with its flexible nature, offers exciting opportunities for research and practical applications in various fields, including forestry activities. It has the potential to enhance overall environmental efficiency and enable better control over GHG emissions levels.

Inverse DEA based resource allocation method for nonhomogeneous decision-making units

Inverse data envelopment analysis (DEA) method is a useful tool for analyzing the optimization of resource allocation of a set of homogeneous decision-making units (DMUs). However, the assumption of homogeneity for DMUs is not necessarily applied in reality. For example, universities with the same input structure cultivate students with different orientations; power plants consume different resources to generate electricity. Therefore, how to handle nonhomogeneous DMUs in inverse DEA becomes an issue when analyzing the optimization of resource allocation. In this study, an inverse DEA method for nonhomogeneous DMUs under constant returns to scale (CRS) is proposed to handle the aforementioned issue. Furthermore, the inverse DEA method for nonhomogeneous DMUs is extended to the case of variable returns to scale (VRS). The adjustment range of inputs-outputs under VRS is discussed to avoid the problem of infeasibility, and relevant properties of our method are proved. Moreover, the effect of frontier changes on the proposed method is also discussed. Finally, numerical examples are provided to illustrate the effectiveness of our method.

A New Resource Allocation Multiple Criteria Decision-Making Method in a Two-Stage Inverse Data Envelopment Analysis Framework for the Sustainable Development of Chinese Commercial Banks

The resource allocation of commercial banks is a multiple-criteria decision-making issue with complex internal structure, and traditional inverse data envelopment analysis cannot meet its decision-making needs. A two-stage structure with undesirable outputs is constructed to describe the operations of a Chinese commercial bank, and then a new two-stage inverse data envelopment analysis with undesirable outputs is proposed to address its resource allocation multiple criteria decision-making issue. The new method can be used to calculate the minimum input increment required to achieve the goals of desirable and undesirable output under a certain efficiency, and then a specific resource allocation plan can be obtained to promote the sustainable development of commercial banks. Finally, the new method is applied to the resource allocation of 16 Chinese listed commercial banks in 2013, and the application results fully demonstrate the effectiveness of the new method.

A novel model for merger analysis and target setting: A CSW-Inverse DEA approach

The inverse data envelopment analysis (DEA) is an advanced complementary method for efficiency analysis using the classical DEA approach. One of the inverse DEA (InvDEA) method applications is the mergers and acquisitions problem. It can be used for analyzing any under evaluation mergers and acquisitions. The current article is the first attempt to propose a novel inverse structure for the DEA model using the multiplier forms. This eventuates the possibility of incorporating decision maker preferences within the merger analysis.Moreover, compared with the existing models in the literature, the proposed novel models are capable of analyzing multiple merger scenarios simultaneously in a single method based on the common set of weights (CSW) rather than a series of models for studying multiple scenarios of mergers and acquisitions. Practically, this property enables decision-makers to consider and analyze multiple mergers and find possible potentials at the same time. The applicability of the proposed model is investigated by using a real-world dataset in banking.

Inverse Data Envelopment Analysis Model to Improve Efficiency by Increasing Outputs

Inverse Data Envelopment Analysis (IDEA) has gained significant attention among researchers as an analytical tool for assessing efficiency. Estimating input values while ensuring cost efficiency through changes in output quantities is complex and sensitive. In contrast to conventional data envelopment analysis methods, IDEA enables the quantification of input/output variations resulting from output/input reductions or expansions while preserving the measurement efficiency level. This paper aims to introduce a novel approach for estimating input values by incrementally increasing the value of each output of decision-making units (DMUs) during the evaluation process, thereby maintaining or improving cost efficiency. By utilizing IDEA and manipulating the output values of the DMU under evaluation, the input values are estimated while ensuring constant or enhanced cost efficiency. A simple numerical example and a case study from a Turkish automotive company are presented to validate the proposed method. The obtained results demonstrate significant improvements and hold promising prospects, indicating the potential applicability of this approach to other similar problems and research areas.

Target setting using an enhanced inverse DEA approach: application to Spanish universities

This paper proposes a non-oriented, non-radial Inverse Data Envelopment Analysis (InvDEA) approach for target setting. The changes of any input and output dimensions may be fixed. In addition to the corresponding multiobjective optimisation model, the approach includes a prior step that checks the feasibility of the input and output changes that are fixed and revises them if necessary. This Pre-InvDEA model uses Goal Programming (GP) and guarantees the feasibility of those changes. The approach also includes a Post-InvDEA multiobjective optimisation model to optimise the input and output changes given in order to guarantee that the computed target is efficient. The overall target-setting approach is conceived as an interactive process so that the three steps (Pre-InvDEA, InvDEA, and Post-InvDEA) may be run more than once until a satisfactory target is determined. The application of the proposed approach to computing efficient targets for Spanish universities is presented.

Balancing act: Assessing police efficiency amidst staffing shortages through inverse data envelopment analysis

Abstract Police agencies are amid a significant staffing shortage. Scholars and police managers warn about the effects of understaffing on public safety and security. Studies have examined the impacts of events like the Floyd protests had on police resignations. This study uses a linear programming method, Inverse data envelopment analysis (InvDEA), to estimate the efficient allocation of police resources using a simulated agency with 150 sectors. The first decision-making scenario simulated the challenge many agencies currently face with staffing shortages. Reallocating officers and civilians from inefficient to efficient units improved performance by 4.7% without additional officers. Results of the second and third decision-making scenarios indicate a need to reallocate resources by 23% and 19%, respectively. These findings contribute to the scarce literature on police staff allocation. In addition, the methodology employed in this study is helpful for police managers to make accurate operational decisions when combined with changes to the efficiency frontier that reflect the environment in which they operate.

Inverse data envelopment analysis with production trade-offs

As an important resource allocation and production analysis method, the existing inverse data envelopment analysis (Inverse DEA) methods generally ignore the production trade-offs in the production process. However, in some managerial practice, decision makers (DMs) generally have value judgements concerning the importance of inputs and outputs. These value judgements reflect the production trade-offs of DMs for different inputs and outputs and influence the production process. Therefore, this study investigates the inverse DEA method with production trade-offs. By analyzing the effect of production trade-offs on efficient frontier, this study reveals that the existing methods for identifying the limitations of changed range of inputs and outputs in inverse DEA model under variable returns to scale (VRS) are invalid when considering the production trade-offs, and based on this, the new inverse DEA methods with production trade-offs for resource allocation and production analysis are developed. Moreover, the limitations of changed range of inputs and outputs of the proposed methods are identified, thus avoiding the problem of infeasible solutions. In addition, the application scenarios and practical values of the proposed methods are discussed. Finally, two examples are provided to illustrate the rationality and effectiveness of our approaches.

Improving agricultural sustainability through farm mergers: an energy efficiency perspective

ABSTRACT The aim of this paper is to investigate agricultural sustainability as a collective issue involving multiple rather than individual farms. Through the utilization of energy consumption as a proxy, we propose a novel methodology that evaluates the impact of farm consolidations on agricultural sustainability while accounting for resource preferences. Our approach incorporates the ordered weighted averaging (OWA) operator within an inverse data envelopment analysis (IDEA) model to identify post-merger farms that meet preset efficiency targets. We employ a DEA cross-efficiency (DEA-CE) procedure to select merger plans that maximize agricultural sustainability for each preference scenario. By analysing a case study of 43 tomato greenhouse farms in Biskra, northern Algeria, our findings demonstrate that mergers can significantly enhance agricultural sustainability, surpassing the potential of individual farms by a factor of over 15. Additionally, the adoption of the most sustainable merger plan can lead to energy savings of more than 69%. Irrespective of the preference scenario, substantial energy savings in machinery, fertilizers, diesel, and electricity ranging from 22.92% to 73.73% were observed. These results emphasize the strategic role of merger processes in promoting agricultural sustainability and optimizing resource utilization.

Inverse two-stage data envelopment analysis with interval measures for resource planning

Purpose Assessing inputs and outputs is a significant aspect of taking decisions while there are complex and multistage processes in many examinations. Due to the presence of interval performance measures in various real-world studies, the purpose of this study is to address the changes of interval inputs of two-stage processes for the perturbations of interval outputs of two-stage systems, given that the overall efficiency scores are maintained. Design/methodology/approach Actually, an interval inverse two-stage data envelopment analysis (DEA) model is proposed to plan resources. To illustrate, an interval two-stage network DEA model with external interval inputs and outputs and also its inverse problem are suggested to estimate the upper and lower bounds of the entire efficiency and the stages efficiency along with the variations of interval inputs. Findings An example from the literature and a real case study of the banking industry are applied to demonstrate the introduced approach. The results show the proposed approach is suitable to estimate the resources of two-stage systems when interval measures are presented. Originality/value To the best of the authors’ knowledge, there is no study to estimate the fluctuation of imprecise inputs related to network structures for the changes of imprecise outputs while the interval efficiency of network processes is maintained. Accordingly, this paper considers the resource planning problem when there are imprecise and interval measures in two-stage networks.

An Improved Inverse DEA for Assessing Economic Growth and Environmental Sustainability in OPEC Member Nations

Economic growth is essential for nations endowed with natural resources as it reflects how well those resources are utilized in an efficient and sustainable way. For instance, OPEC member nations, which hold a large proportion of the world’s oil and gas reserves, may require a frequent evaluation of economic growth patterns to ensure that the natural resources are best used. For this purpose, this study proposes an inverse data envelopment analysis model for assessing the optimal increase in input resources required for economic growth among OPEC member nations. In this context, economic growth is reflected in the GDP per capita, taking into account possible environmental degradation. Such a model is applied to the selected OPEC member nations, which suggests that in terms of increasing the GDP per capita, only one member was able to achieve the best efficiency (i.e., reaching the efficiency frontier), resulting in a hierarchy or dominance within the sample countries. The analysis results further identify the economic growth potential for each member country. For the case of Indonesia, the analysis suggests that further economic growth may be achieved for Indonesia without additional input resources. This calls for diversification of the nation’s economy or investment in other input resources. In addition, the overall results indicated that each member nation could increase its GDP per capita while experiencing minimal environmental degradation. Our analysis not only benchmarks the growth efficiency of countries, but also identifies opportunities for more efficient and sustainable growth.

Enhanced Efficiency in Fog Computing: A Fuzzy Data-Driven Machine Selection Strategy

With the rapid proliferation of IoT and Cloud networks and the corresponding number of devices, handling incoming requests has become a significant challenge. Task scheduling problems have emerged as a common concern, necessitating the exploration of new methods for request management. This paper proposes a novel approach called the Fuzzy Inverse Markov Data Envelopment Analysis Process (FIMDEAP). Our method combines the strengths of the Fuzzy Inverse Data Envelopment Analysis (FIDEA) and Fuzzy Markov Decision Process (FMDP) techniques to enable the efficient selection of physical and virtual machines while operating in a fuzzy mode. We represent data as triangular fuzzy numbers and employ the alpha-cut method to solve the proposed models. The paper provides a mathematical optimization model for the proposed method and presents a numerical example for illustration. Furthermore, we evaluate the performance of our method in a cloud environment through simulations. The results demonstrate that our approach outperforms existing methods, namely PSO + ACO and FBPSO + FBACO, in terms of key metrics, including energy consumption, execution cost, response time, gain of cost, and makespan.

Unveiling the potential of hotel mergers: A hybrid DEA approach for optimizing sector-wide performance in the hospitality industry

Mergers and acquisitions (M&A) in the hospitality sector involve consolidating assets among hotels through partnerships. While data envelopment analysis (DEA) has been widely used for hotel efficiency analysis, little attention has been paid to hotel M&A. In this paper, a hybrid DEA methodology consisting of two stages is proposed to identify optimal matches among hotels to enhance sector performance. The initial stage employs an inverse Data Envelopment Analysis (IDEA) model to evaluate the maximum gains that could potentially be generated from pairwise consolidations among hotels. A DEA procedure that incorporates a standard DEA model and a greedy heuristic is developed in the second stage to identify the optimal pairs of hotel mergers. The optimal merger strategy for the entire hotel industry is determined from the complete set of hotels under consideration.The pertinence of the proposed methodology is shown through a sample of 58 hotels from the Sultanate of Oman

Will carbon emission trading policy improve the synergistic reduction efficiency of pollution and carbon? Evidence from 216 Chinese cities

AbstractBased on the panel data of 216 Chinese cities from 2008 to 2018, the synergistic reduction efficiency of pollution and carbon (SREPC) was calculated using the super‐efficiency slack‐based measure model. Differences‐in‐differences (DID), propensity score matching (PSM)–DID, and spatial‐DID were adopted to study the impact of the carbon emission trading (CET) policy on SREPC. The study results show that SREPC was not improved overall, with an unbalanced development characteristic of high efficiency in the east and low efficiency in the west. The Meta‐frontier results show that there were indeed significant differences between pilot and non‐pilot cities before and after the implementation of the CET policy. Mechanism tests reveal that CET promoted SREPC by improving energy efficiency and optimizing industrial structures. Spatial analysis shows that CET had spatial spillover effects and decreased SREPC in neighboring cities. These reduction effects occurred in neighboring non‐pilot cities and showed an inverted U‐shaped relationship with increasing geographical distance, particularly significant within 500–600 km. Inverse data envelopment analysis shows that CET can utilize the synergistic reduction potential of pollution and carbon.

Quantifying Webpage Performance: A Comparative Analysis of TCP/IP and QUIC Communication Protocols for Improved Efficiency

Browsing is a prevalent activity on the World Wide Web, and users usually demonstrate significant expectations for expeditious information retrieval and seamless transactions. This article presents a comprehensive performance evaluation of the most frequently accessed webpages in recent years using Data Envelopment Analysis (DEA) adapted to the context (inverse DEA), comparing their performance under two distinct communication protocols: TCP/IP and QUIC. To assess performance disparities, parametric and non-parametric hypothesis tests are employed to investigate the appropriateness of each website’s communication protocols. We provide data on the inputs, outputs, and efficiency scores for 82 out of the world’s top 100 most-accessed websites, describing how experiments and analyses were conducted. The evaluation yields quantitative metrics pertaining to the technical efficiency of the websites and efficient benchmarks for best practices. Nine websites are considered efficient from the point of view of at least one of the communication protocols. Considering TCP/IP, about 80.5% of all units (66 webpages) need to reduce more than 50% of their page load time to be competitive, while this number is 28.05% (23 webpages), considering QUIC communication protocol. In addition, results suggest that TCP/IP protocol has an unfavorable effect on the overall distribution of inefficiencies.

Inverse data envelopment analysis optimization approaches with flexible measures

PurposeThe purpose of this study is to estimate inputs (outputs) and flexible measures when outputs (inputs) are changed provided that the relative efficiency values remain without change.Design/methodology/approachA novel inverse data envelopment analysis (DEA) approach with flexible measures is proposed in this research to assess inputs (outputs) and flexible measures when outputs (inputs) are perturbed on condition that the relative efficiency scores remain unchanged. Furthermore, flexible inverse DEA approaches proposed in this study are used for a numerical example from the literature and an application of Iranian banking industry to clarify and validate them.FindingsThe findings show that including flexible measures into the investigation effects on the changes of performance measures estimated and leads to more reasonable achievements.Originality/valueThe traditional inverse DEA models usually investigate the changes of some determinate input-output factors for the changes of other given input-output indicators assuming that the efficiency values are preserved. However, there are situations that the changes of performance measures should be tackled while some measures, called flexible measures, can play either input or output roles. Accordingly, inverse DEA optimization models with flexible measures are rendered in this paper to address these issues.