Inverse Data Envelopment Analysis Research Articles

A new inverse DEA cost efficiency model for estimating potential merger gains: a case of Canadian banks

Estimating potential gains from mergers is an important strategic decision-making problem. This paper introduces a new inverse data envelopment analysis (DEA) based on a cost efficiency model for estimating potential gains from mergers. There are restructuring scenarios for firms that want to minimize cost. The existing inverse DEA technical efficiency models are not appropriate for estimating merger gains in these situations. It is also shown that the proposed inverse DEA cost efficiency model can reveal more merger gains than the inverse DEA technical efficiency model. The applicability of the proposed method is shown through an application in Canada’s banking sector to determine the required level of inputs and outputs for a merged bank to achieve target levels of cost and technical efficiencies. The results highlight the potential financial gains to improving both technical and cost efficiencies as efficiency-seeking banks increasingly become large and complex institutions through growth, mergers and acquisitions in a financial environment that is being shaped by reforms and technological innovation.

Developing a novel inverse data envelopment analysis (DEA) model for evaluating after‐sales units

AbstractThis paper proposes a novel model of inverse data envelopment analysis (IDEA) based on the slack‐based measure (SBM) approach. The developed inverse SBM model can maintain relative efficiency of decision making units (DMUs) with new input and output. This model can also measure the input and output volumes when a decision maker (DM) increases efficiency score. The inverse SBM model is a kind of multi‐objective non‐linear programming (MONLP) problem, which is not easy to solve. Therefore, we suggest a linear programming model for solving inverse SBM model. In this model efficiency score of DMU under evaluation remains unchanged. Furthermore, we suggest an optimal combination of inputs and outputs in the production possibility set (PPS). A case study is presented to demonstrate the efficacy of our proposed model.

A Revised Inverse Data Envelopment Analysis Model Based on Radial Models

In recent years, there has been an increasing interest in applying inverse data envelopment analysis (DEA) to a wide range of disciplines, and most applications have adopted radial-based inverse DEA models. However, results given by existing radial based inverse DEA models can be unreliable as they neglect slacks while evaluating decision-making units’ (DMUs) overall efficiency level, whereas classic radial DEA models measure the efficiency level through not only radial efficiency index but also slacks. This paper points out these disadvantages with a counterexample, where current inverse DEA models give results that outputs shall increase when inputs decrease. We show that these unreasonable results are the consequence of existing inverse DEA models’ failure in preserving DMU’s efficiency level. To rectify this problem, we propose a revised model for the situation where the investigated DMU has no slacks. Compared to existing radial inverse DEA models, our revised model can preserve radial efficiency index as well as eliminating all slacks, thus fulfilling the requirement of efficiency level invariant. Numerical examples are provided to illustrate the validity and limitations of the revised model.

An inverse semi-oriented radial data envelopment analysis measure for dealing with negative data

Abstract The conventional inverse data envelopment analysis (DEA) model is only applicable to positive data, while negative data are commonly present in most real-world applications. This paper proposes a novel inverse DEA model that can handle negative data. The conventional inverse DEA model is a special case of our model as our model is more general in terms of returns-to-scale properties. The proposed model is used to evaluate the efficiency of the Chinese commercial banks after the global financial crisis, where negative outputs existed. We show that our model is feasible in the presence of negative data and generates empirical findings that are consistent with reality.

A model for sector restructuring through genetic algorithm and inverse DEA

The aim of this study is to devise a sector restructuring model in which all the decision making units (DMUs) satisfy a predefined global efficiency level. The proposal makes several realistic assumptions regarding the merging of DMUs under specific circumstances. The model computes the global efficiency target by giving preference to merging DMUs over saving inputs, hence considering that the affected stakeholders may be resistant to restructuring, and this resistance may have overall negative effects on the image and reputation of the companies and organizations. In addition, the number of constituents in the new entities can be limited by the decision maker after the restructuring process, so that the model also considers a constraint on cardinality. The proposal combines the inverse data envelopment analysis (InvDEA), which computes the merger’s input savings, and the genetic algorithm (GA), which solves the combinatorial problem of identifying the merging units. The proposal is illustrated by two examples from banking and higher education.

Inverse DEA in two-stage systems based on allocative efficiency

Inputs and outputs of Decision Making Units (DMUs) are estimated by the Inverse Data Envelopment Analysis (InvDEA) models, while their relative efficiency scores remain unchanged. But, in some cases, cost/price information of the inputs and outputs are available. This paper employs the input and output cost/price information, including the generalized InvDEA concept in two-stage structures. To this end, it proposes a four-stage method to deal with the InvDEA concept, for estimating the inputs and outputs of the DMUs with a two-stage network structure method, while the allocative efficiency scores of all the units remain stable. Eventually, an empirical example is rendered to illustrate the competence of the method which is presented.

Mergers and acquisitions matching for performance improvement: a DEA-based approach

This article proposes a new data envelopment analysis (DEA)-based approach to deal with mergers and acquisitions (M&As) matching. To derive reliable matching degrees between bidder and target firms, we consider both technical efficiency and scale efficiency. Specifically, an inverse DEA model is developed for measuring the technical efficiency, while a conventional DEA model is employed to identify the return of scale of the merged decision-making units (DMUs). Then, an optimization model is formulated to generate matching results to improve DMUs’ performance. An empirical study of M&As matching Turkish energy firms is examined to illustrate the proposed approach. This study shows that both technical efficiency and scale efficiency have impacts on M&As matching practices.

Evaluating after-sales service units by developing inverse network data envelopment analysis model

PurposeThe purpose of this paper is to develop an inverse network data envelopment analysis (INDEA) model to solve resource allocation problems.Design/methodology/approachThe authors estimate inputs’ variations based on outputs so that the efficiencies of decision-making unit under evaluation (DMUo) and other decision-making units (DMUs) are constant.FindingsThe new INDEA model is developed to allocate resources such that inputs are not increased while efficiency scores of all DMUs remain constant. Furthermore, the authors obtain new combinations of inputs and outputs, together with a growth in efficiency score of DMUo such that efficiency scores of other DMUs are not changed. A case study is provided.Originality/valueThis paper proposes INDEA model to estimate inputs (outputs) without changing efficiency scores of DMUs.

A ranking system based on inverse data envelopment analysis

Abstract Inverse (DEA) is an approach to estimate the expected input/output variation levels when the efficiency score reminds unchanged. Essentially, finding most efficient decision-making units (DMUs) or ranking units is an important problem in DEA. A new ranking system for ordering extreme efficient units based on inverse DEA is introduced in this article. In the adopted method, here the amount of required increment of inputs by increasing the outputs of the unit under evaluation is obtained through the proposed models. By obtaining these variations, this proposed methodology enables the researcher to rank the efficient DMUs in an appropriate manner. Through the analytical theorem, it is proved that suggested models here are feasible. These newly introduced models are validated through a data set of commercial banks and a numerical example.

A generalized DEA model for inputs (outputs) estimation under inter-temporal dependence

This paper extended the inverse Data Envelopment Analysis (DEA) to the framework of dynamic DEA. The following question is studied under inter-temporal dependence assumption: among a set of decision making units (DMUs), to what extent should the input (output) levels of the DMU change if the efficiency index of a DMU remains unchanged, yet the output (input) levels change? This question is answered using (periodic weak) Pareto solutions of multiple-objective linear programming (MOLP) problems in the framework of dynamic DEA. In this study, unlike other proposed methods, the simultaneous increase and decrease of the various input (output) levels are considered under inter-temporal dependence. In addition, a numerical example with real data is provided to illustrate the objective of this research.

Inverse Dynamic Data Envelopment Analysis for Evaluating Faculties of University with Quasi-Fixed Inputs

Like other organizations, universities must evaluate their performance to identify areas for improvement. Although the different aspects of a university are considered for evaluation, the research section is deemed to be the most important and is where the necessity of the performance evaluation is most salient. In this study, the relative efficiency of the sub-units of several faculties of the university has been investigated through dynamic data envelopment analysis (DDEA) and inverse DDEA (IDDEA). The capability of traditional DEA to differentiate between efficient and non-efficient units decreases as the ratio of the number of inputs and outputs to the number of decision-making units increases. To remove this limitation by adding intermediate constraints between stages, a dynamic form of the method was applied in this research. The paper provides distinctions between the faculties as well as sensitivity analysis of the inputs/outputs of each faculty. The proposed IDDEA is implemented to scrutinize the changes in the input and output levels. The proposed approach is output-oriented to account for the homogeneity of faculties and their subordination under a specific unified management policy. A case study of Urmia University is used to demonstrate the proposed approach.

Performance Evaluation and Investment Analysis for Container Port Sustainable Development in China: An Inverse DEA Approach

Container ports play an important role in international maritime trade. However, the rapid growth of the port and terminal industry has caused many environmental pollution problems. This paper intends to develop an inverse data envelopment analysis (IDEA) model for measuring container ports’ efficiency and analyzing their resource consumption by considering undesirable outputs. Statistical data from 16 main ports are empirically examined using the proposed method in accordance with the 13th Five-Year Plan in China. The results indicate that the proposed IDEA is a feasible approach for performance evaluation, and provides policymakers with insights into resource optimization of container ports. A comparative study with another DEA model is also discussed.

Preserving cost and revenue efficiency through inverse data envelopment analysis models

Data envelopment analysis (DEA) models are applied in commercial firms to evaluate their technical, cost and revenue efficiencies. The new models introduced here are based on inverse DEA for preserving cost/revenue efficiency. The commercial institution management seeks to minimize the input costs for a given level of outputs or maximize the revenue of outputs for a specified level of inputs. It is important to preserve cost/revenue efficiency when data are changed. In this method, we determine the cost efficiency score of decision-making units (DMUs). Then, for each one of them, the outputs are increased and the values of the required increment of inputs are obtained, while the cost efficiency of the unit under evaluation remains unchanged. For practical application, one of these introduced models is applied to a real data set of European and American banks for cost efficiency preservation.

WITHDRAWN: A combined genetic algorithm and inverse data envelopment analysis model for target setting in mergers

WITHDRAWN: A combined genetic algorithm and inverse data envelopment analysis model for target setting in mergers

Resource planning of Chinese commercial banking systems using two-stage inverse data envelopment analysis with undesirable outputs.

This paper develops two-stage inverse data envelopment analysis models with undesirable outputs to formulate resource plans for 16 Chinese listed commercial banks whose outputs are increased and overall efficiency is kept unchanged in the short term. We use these models to meet three different output targets, namely, increasing both the desirable and undesirable outputs by the same percentage, increasing these outputs by different percentages, and increasing only the desirable outputs while keeping the undesirable outputs unchanged. We find that operation cost and interest expense are more flexible than labor in the adjustment process and that deposits have no obvious law of change. The findings of this work provide some suggestions for bank managers.

Features of the efficiency frontier and its application in Inverse DEA without solving a model

The inverse data envelopment analysis is an inverse optimization problem, which can be used as an appropriate planning tool for management decisions. The typical DEA mainly focuses on post-operative evaluation of an organizational performance. Sometimes economic conditions such as economic prohibitions on exports or imports are imposed on a system. These prohibitions prevent decision-making units from best performance (efficiency one). In this case, if the system has the best performance (with a less than one efficiency score) then it will be considered as an efficient system. So, the efficiency frontier change’s problem must be studied. So by making change in definition of the best efficiency amount of a system, it still has the best performance. In these situations, the inefficient units can select a real pattern instead of reaching an unrealistic pattern that is presented in ideal terms to achieve the best conditions (the best efficiency value is one). So a long-term management plan can be developed. the efficiency frontier change will be expressed inputs and outputs as a coefficient of efficiency. The frontier change looks at the changes in inputs and outputs to reach the new frontier. One of the purposes of the data envelopment analysis is the investigation of input’s and output’s amounts by changing the amount of efficiency. So far, many models must be solved to calculating these changes. Efficiency frontier problem can replace a simple mathematical model with these models. All of these advantages can improve calculating input and output’s changes and RTS will be unchanged and decision maker can estimate unit’s RTS without solving any model. So a unit will be stayed MPSS by reducing inputs. In other frontier change methods some hyperplanes and extreme units had been deleting but our method transforms them on new frontier. So all extreme units and RTS can estimate easily. The efficiency frontier changes can delete some inefficient units so system’s cost will be reduced. For this purpose, in this paper, the change in the efficiency frontier, its properties and its effect on the inverse data envelopment analysis is examined.

Determining Minor and Major Consolidations in Network Inverse Data Envelopment Analysis

Using scientific methods is necessary for merging Decision-Making Units (DMUs), in organizations. Tools such as Data Envelopment Analysis (DEA) and network DEA (NDEA) are quite useful for merging units in two-stage network processes. In this paper, a two-stage network inverse DEA (InvDEA) process is proposed for merging university units and bank branches based on linear programming models. Prioritizing inputs and outputs and finding intermediate vectors in multi-stage networks is in general very crucial. Therefore, the two-stage network inverse DEA model is proposed for the purposes of this study. Finally, we have provided some applications of the proposed model in merging DMUs by prioritization of vectors using Shannon’s entropy, namely the mergers of 5 universities, 24 insurance companies, and 20 commercial banks.

Environmental efficiency of small-scale tea processors in Kenya: an inverse data envelopment analysis (DEA) approach

Vision 2030, Kenya’s development blueprint for the period 2008–2030, envisions transforming the country into middle-income status where citizens enjoy a high quality of life. The blueprint has three pillars: economic, political and social. The thread that binds the three pillars is the natural environment, which supplies both renewable and non-renewable resources. Unfortunately, development in the other sectors may easily compromise the conditions of the natural environment and put the supply of clean water, food and fiber in jeopardy. For example, processing of agricultural products may increase gains from agriculture and lead to rapid expansion of the sector. If this is not carefully done, it may be characterized by wastage of resources, cutting down of forests to provide fuel and more land for cultivation, disposal of raw wastes into water bodies and over-exploitation of the soils. Using the example of small-scale tea processors in the country, this study sought to understand the environmental efficiency of the small-scale agro-processors. Small-scale tea processors were chosen because they have been implementing environmental efficiency-enhancing techniques in their production, yet no study had endeavored to test whether their initiatives were yielding positive results. The study adopted the innovative inverse data envelopment analysis approach on panel data to generate environmental efficiency scores, in the first step. In the second step, it analyzed the predictors of environmental efficiency using Tobit regression. Overall, the results showed that small-scale tea processors in Kenya were still environmentally inefficient, recording a mean efficiency index of only 49%, despite previous initiatives to improve efficiency. Thus, the processors could reduce 51% of the environmentally detrimental inputs without compromising output. Environmental inefficiency could be attributed to pursuit for higher profits and higher cost of investible funds. This shows that investment in environmental conservation is expensive and eats into the profits of the processors. Therefore, the small-scale processors may lack the incentives, in the short term, to invest in environment-friendly technologies. This may be compounded by the high cost of finance to be invested in such initiatives. Policy implication is that government should intervene in terms of tax concessions for firms that invest in environmental conservation, subsidies on technologies that guarantee environmental efficiency and access to cheaper funds for purchase and maintenance of environment-friendly technologies.

Preserve the Relative Efficiency Values: An Inverse Data Envelopment Analysis with Imprecise Data

Data envelopment analysis (DEA) measures the relative efficiency of a set of decision-making units (DMUs). With the advent of DEA models, inverse DEA is applied to modify the inputs and outputs of DMUs without affecting their efficiency. InvDEA models are applied when the decision makers need to change the input-outputs of the DMUs to a certain level without affecting their efficiency. InvDEA models are extended when the input-output data are imprecise and available in the intervals form. However, regarding uncertainty, complete information about the input-output data is not available in many real world applications. To address this problem, this study deals with the InvDEA problem in an uncertain environment. Therefore, two multi-objective linear programming (MOLP) models are proposed to estimate the required upper/lower inputs, producing requested outputs and preserving the efficiency scores. The proposed models preserve the upper/lower efficiency scores of all considered DMUs. A numerical example illustrates the proposed methodology.

Flexible target setting in mergers using inverse data envelopment analysis

In a merger, one important issue is the estimation of the levels of inputs and outputs required from each merging decision-making unit (DMU) so that the merged entity can realise a desired efficiency target. This paper uses the potential of inverse data envelopment analysis (InvDEA) to build a flexible target setting of the inputs and outputs. This study expands the application of the InvDEA methodology in a merger by introducing a flexible target setting that allows the decision maker to favour specific input in the target setting. We use a dataset of 30 universities to illustrate the practical scope of the proposed flexible target setting method, which can obviously be employed in any other merging context.