Inverse Data Envelopment Analysis Model Research Articles

New insights and theoretical conditions for determining minor and major consolidations in the inverse DEA

Abstract Accepted by: Ali Emrouznejad In the current paper, we propose new conditions for determining major and minor consolidation using the inverse data envelopment analysis models. We categorized the causes of major consolidation into pre and post-effect. Pre-effects may happen due to the omission of pre-merged units and post-effects are associated with the fact that the merged unit may not belong to the production set. The idea is described by numerical examples and graphical illustrations and an empirical analysis in banking also helps us to show the necessity, strength, and applicability of the proposed models for real-world applications.

Improving technical efficiency in data envelopment analysis for efficient firms: A case on Chinese banks

Data Envelopment Analysis (DEA) as a data-oriented benchmarking tool is considered a powerful and promising instrument for performance evaluation in various application areas. In DEA, the set of all decision-making units (DMUs) is divided into efficient and inefficient subsets. Inefficient DMUs are improved by reducing the input and/or increasing the output, and as far as we know, efficient DMUs are abandoned with the conclusion that they are all technically and relatively efficient, and no further analysis has been suggested in the literature. In this article, we first show that there is a gap between the actual efficiency and the efficiency estimated using benchmarking tools such as DEA. This means that there is no guarantee that the efficient DMUs characterized by DEA are really efficient. Thus, there is a gap in improving the technical efficiency of efficient DMUs. In this paper, we attempt to close this gap by introducing a method to improve efficient DMUs. First, we introduce a random variable as a corrector of efficiency evaluation, and then an inverse DEA model (IDEA) is proposed to improve efficient DMUs. To demonstrate the actual applicability of the proposed approach, we present an illustrative empirical application using 106 Chinese bank data from 2021.

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.

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.

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.

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.

Planning for potential increases in disbursements and risk of managed funds conditional on desired short-term performance levels

ABSTRACT As increasing disbursements (such as costs and fees) and risk (such as portfolio risk and leverage risk) may affect managed fund performance, analysts go beyond risk-adjusted return measures for performance appraisal. A methodology that assesses performance in a multidimensional framework is data envelopment analysis (DEA). A variant of DEA is inverse DEA. In this paper, inverse DEA is applied to determine output (investment income and benefit payments) targets for a given fund to perform at a desired efficiency level when increase in disbursements and risk at known levels is envisaged. An output-oriented inverse DEA model assuming variable returns to scale is formulated with theoretical underpinning. The proposed modelling framework ensures that, when an input augmented fund with estimated output targets is included in the observed fund set, the frontier of best performance established with the observed fund set does not change. The inverse DEA model is applied to a sample of Australian superannuation funds to demonstrate how a given fund may obtain pathways to improve its performance under different input-augmentation scenarios. As different pathways suggest feasible output targets, fund managers may find them valuable in forward planning.

Using inverse data envelopment analysis to evaluate potential impact of mergers on energy use optimization - Application in the agricultural production

This paper examines the potential of Mergers & Acquisitions (M&As) as a novel approach to energy use optimization. The investigations are carried out through inverse data envelopment analysis (DEA). Contrary to traditional DEA approaches that restrict the energy savings to individual production units, the proposed methodology looks at the issue from the perspective of possible mergers among these units.The new methodology, which deploys over two stages, is applied to pairwise consolidations among 51 tomato greenhouse (GH) farms from Biskra, Algeria. An inverse DEA model is implemented in the first stage to discern all possibly productive post-merger GH farms, i.e., those mergers that are likely to generate energy gains. In the second stage, a new procedure is devised to find the best matchings among partners of potential mergers and derive the best merger plan out of the whole sample of GH farms.The results of the inverse DEA application revealed that potential gains per energy input can be substantial, reaching proportions as high as 80.78% and above.The derived optimal merger plan exhibited a post-merger energy saving index of 70.23%, that is, 33 times the index of the traditional DEA approach.Practically, these findings leave no doubt that mergers can contribute significantly to energy savings, enough to support new policies for promoting mergers as strategic options towards optimal energy consumption.The application scope of the proposed methodology can be duly extended to other sectors where energy optimization might be a critical issue.

A Study of Forest Carbon Sink Increment from the Perspective of Efficiency Evaluation Based on an Inverse DEA Model

Forest carbon sink efficiency refers to the efficiency of input-output indicators related to carbon sinks. This paper studies carbon sink efficiency from the perspective of resource allocation; guides the optimal allocation of resources; and selects forestry employees, forestry investment amount and afforestation area as input indicators; the forest carbon sink efficiency in China is calculated and analyzed based on a data envelopment analysis model by converting the forest volume into the forest carbon sink through the volume expansion factor method. The grey prediction model is used to estimate the change in the input indicator, and the production possibility set is constructed with the input indicator before and after the change and the current output indicator. The efficiency of the decision units before the change is calculated, and through the comparison of efficiency, the conditions of forest carbon sink increase in 15 provinces are obtained. The optimal allocation of the output indicator is calculated based on the inverse data envelopment analysis model. The largest increase in forestry carbon sink is 169,362 megatons in Guangdong, and the smallest is 619 megatons in Tianjin. Finally, some suggestions for the path of forest carbon sink increment are put forward.

A new inverse DEA model with frontier changes for analyzing the achievement path of CO2 emissions target of China in 2030

China has promised to reduce its CO2 emissions per gross domestic product (GDP) by 60–65% relative to 2005 emissions by 2030, which puts higher requirements for the quality of China's future economic development. Meanwhile, using current methods to scientifically analyze the realization path of CO2 emission reduction while ensuring future economic development remains a challenge. This study develops a new inverse data envelopment analysis (DEA) method to analyze the annual realization path of CO2 emission reduction and economic growth targets in China from 2020 to 2030. This method not only considers undesirable output and frontier changes but also analyzes the realization path of CO2 emission reduction on the premise of ensuring economic growth. Moreover, the proposed method can analyze resource optimization allocation to achieve the corresponding goals, and its contributions to sustainable development are discussed. The results indicate that (1) In terms of CO2 emission reduction, the eastern region will face the largest pressure of CO2 emission reduction, accounting for 52.85% of the total CO2 emission reduction, followed by the central region, accounting for 37.2%, and the western region will face the least pressure, accounting for 9.95%; whereas in terms of the change trend of CO2 emission reduction, the eastern and central regions show opposite CO2 emission reduction trends, while the trend in the western region is relatively stable. (2) At provincial level, CO2 emission reduction shows a polarized distribution. Many provinces, such as Jiangsu, Guangdong, Hunan, and Chongqing, undertake great pressure to reduce CO2 emission. However, some provinces, such as Shandong, Shanxi, and Yunnan, almost have no potential to reduce CO2 emission while maintaining economic growth. (3) The increasement of human and energy resources input in the future is key to achieving CO2 emission reduction and economic development goals. Finally, some useful implications are summarized by analyzing the results to provide powerful decision support for achieving CO2 emission reduction and economic growth targets of China in 2030.

An inverse data envelopment analysis model to consider ratio data and preferences of decision-makers

Abstract Inverse data envelopment analysis (DEA) determines the optimal level of inputs and/or outputs of decision-making units (DMUs) to reach efficiency targets. This paper presents a new inverse DEA model for determining minimum inputs for working capital management. The proposed model is employed in the Indian textile industry to calculate working capital efficiency. Given the working capital efficiency, the decision maker’s preferences will be estimating the change in inputs when outputs increase. Furthermore, unlike the standard inverse DEA model, this article discusses the inverse DEA model when negative ratio data exist. The DEA model requires additional attention when ratio data are present; therefore, a novel inverse DEA ratio model is proposed. The input targets obtained from the proposed model are less than the standard inverse DEA model. Also, the proposed model is a closer estimate of the production probability set for ratio data.

An inverse DEA model for intermediate and output target setting in serially linked general two-stage processes

Abstract In this paper, we formulate an inverse data envelopment analysis (DEA) model for a serially linked two-stage production process operating under constant returns to scale technology. The inverse DEA model determines a set of intermediate and output targets for an input augmented decision-making unit (DMU) to maintain its relative efficiency at a pre-specified level. We solve the inverse DEA model using the constraint method used in multi-objective optimization. The input augmented DMU with intermediate and output targets obtained in the inverse DEA model is a hypothetical DMU. Under our modelling framework, when such a hypothetical DMU established on an inefficient DMU is included in the observed DMU set, the frontier established with observed DMU set remains intact. This is important in practice as the intermediate and output targets of the hypothetical DMU would be feasible. When overall efficiency of the hypothetical DMU is decomposed, individual stages have the same efficiency level as that of the hypothetical DMU. This is important to DMU managers as sub-processes also maintain the desired overall efficiency level. We apply our inverse DEA model to a sample of Australian superannuation funds. We demonstrate that each unique Pareto optimal solution of the inverse DEA model obtained through the constraint method provides a specific set of intermediate and output targets and they may offer trade-off between intermediates and outputs. When fund managers anticipate expansion or growth in their funds, choice of targets allows comparison of different trade-off scenarios and makes informed decisions.

A generalized inverse DEA model for firm restructuring based on value efficiency

Abstract We present a novel general inverse data envelopment analysis model for assessing the restructuring of decision-making units (DMUs) while observing predetermined value efficiency targets, under two distinct scenarios: merger and acquisitions and split. By considering the set of efficient DMUs as the Decision Maker’s set of Most Preferred Solutions, virtual new units with desired targets for value efficiency scores and input and output levels can be computed. The innovations of this paper are threefold. First, a comparison between the proposed value efficiency and previous technical efficiency approaches reveals improvement in the estimation of restructured input/output levels. Second, the proposed approach is capable of handling the decision-maker’s preferences during restructuring. Third, an algorithm to determine the worst case-scenario for restructuring is presented. An applied case study in banking operations is presented to illustrate the validity and applicability of the proposed method.

A new inverse data envelopment analysis approach to achieve China’s road transportation safety objectives

The number of fatalities in road traffic accidents shows a gradual upward trend in recent years, and this has brought great pressure on the realization of China’s safety objectives. Meanwhile, how to make a scientific and feasible path for achieving the safety objective also poses a great challenge to the existing methods. Therefore, the paper introduces the objective constraint to develop a new inverse data envelopment analysis (DEA) model with undesirable outputs for ensuring the realization of safety objective under the current technical level. Subsequently, two safety objectives and two additional objectives are defined for China’s road transportation according to the actual requirements of decision makers, and then their realization paths are determined by using the new inverse DEA model, respectively. By analyzing the connections and differences of different objectives and their realization paths, some useful implications are summarized to promote the realization of the safety objective of China’s road transportation: First, identifying the requirements of decision makers is critical for making the realization path of safety objective; second, reducing desirable outputs, increasing inputs, and improving safety efficiency are the efficient ways to achieve safety objective; third, the influence of technology heterogeneity should be properly considered in the process of making the realization path of safety objective. In general, the paper provides a powerful decision support for achieving the safety objective of China’s road transportation.

Limitation and optimization of inputs and outputs in the inverse data envelopment analysis under variable returns to scale

As an important component of data envelopment analysis (DEA), the inverse DEA method often has no feasible solution under variable returns to scale (VRS). By analyzing the reason of this problem, the limitation of inputs and outputs in the inverse DEA method under VRS is identified. Then the outputs possible set and the inputs possible set are defined for different inverse DEA models; and some models are thus developed to determine the change range of outputs/inputs. Sequentially, by determining the optimal given outputs/inputs, the inverse DEA model under VRS is used to estimate the optimal inputs increment or outputs diminution for the optimal given efficiency, and the problem that the inverse DEA method has no feasible solution is avoided. In addition, the effects of efficiency change and technological change on the optimization of inputs and outputs are further discussed in this paper. Finally, two examples are provided to illustrate the validity and effectiveness of our methods.

Merging Decision-Making Units with Fuzzy Data

This paper studies the problem of target setting for a generated entity from a merger among two or more decision making units. Identification of the inherited input/output levels from merging decision-making units is an important issue. In this study, a novel inverse data envelopment analysis model is introduced for target setting of a merger in the presence of fuzzy data. This model enables the merged unit to recognize the required input/output levels from merging units to achieve a predefined efficiency target. Moreover, a fuzzy linear programming model is presented for estimating the minimum attainable efficiency score through a given merging. Then, the performance of the proposed method is examined through a banking application.

New inverse DEA models for budgeting and planning

Data envelopment analysis (DEA) measures the efficiency score of a set of homogeneous decision-making units (DMUs) based on observed input and output. Considering input-oriented, the inverse DEA models find the required input level for producing a given amount of production in the current efficiency level. This article proposes a new form of the inverse DEA model considering income (for planning) and budget (for finance and budgeting) constraints. In contrast with the classical inverse model, both input and output levels are variable in proposed models to meet income (or budget) constraints. Proposed models help decision-makers (DMs) to find the required value of each input and each output’s income share to meet the income or budget constraint. We apply the proposed model in the efficiency analysis of 58 supermarkets belonging to the same chain. However, these methods are general and can be used in the budgeting and planning process of any production system, including business sectors and firms that provide services.

A model to evaluate the effects of the returns to scale on the inverse data envelopment analysis

The concept of return to scale is the ratio of proportional variations in outputs to proportional variations in inputs. A decision maker by determining the returns to scale of a unit can made a decision to limitation or extension of it. The radial models cannot determine the output changes after applying variations in the input vector. So far, the amount of input changes, output changes and efficiency of decision-making units should be available for estimating returns to scale. So several models need to be solved. This paper describes a single model-mode method that is not required to information of inputs, outputs, or efficiency values. The proposed model provides the conditions for stability or improvement of the returns to scale of the under evaluation decision-maker unit. This model reduces computation volume. This model can find MPSS units, which is the one of important purpose in solving a model, but it usually needs complex computation heretofore. In this article, all MPSS units are introduced by solving one model, so decision maker can use all of them as a target. In this paper, input changes, output changes, efficiency, RTS, BCC-CCR and CCR-BCC efficiency, MPSS units are calculated just by one powerful model. So far, no definitive model has been proposed for evaluating RTS in inverse data envelopment analysis. The purpose of this multistage model is to provide a one linear model to evaluate the rate of change in inputs and outputs, while maintaining efficiency and RTS. Given that none of the inverse data envelopment analysis models have not shown the input and output’s changes with respect to the type of returns, this model can be a starting point for investigating changes in inputs and outputs while maintaining efficiency and RTS. This specific advantage makes this model operational. This information improves managerial decisions and increases the accuracy studies on the system. Estimating outputs (or inputs) and the type of RTS, by using efficiency amount, shows the flexibility of the model. This feature of the model improves inverse data envelopment analysis models.

Assessing sustainability of Islamic countries via data envelopment analysis (DEA)

Given international regulations, countries try to improve their sustainability. The objective of this paper is to assess the sustainability of Islamic countries and to present optimal strategies to promote their sustainability. In developing Islamic countries, increasing level of production requires clean technologies to achieve or promote their level of sustainable development. In this research, given natural disposability and managerial disposability, a new inverse data envelopment analysis model based on range adjusted measure is developed. We assess sustainability of Islamic countries. Then, we suggest how to improve sustainability of the Islamic countries. Our new model determines optimal inputs and outputs given natural disposability and managerial disposability so that the sustainability score of countries is unchanged.