Inverse ratio-based data envelopment analysis models for input and output estimation

Inverse ratio-based data envelopment analysis models for input and output estimation in the presence of negative data

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.

Inverse chance-constrained dynamic data envelopment analysis under natural and managerial disposability: Concerning renewable energy efficiency and potentials

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

Many production systems have acquisition and merge operations to increase productivity. This paper proposes a novel method to anticipate whether a merger in a market is generating a major or a minor consolidation, using Inverse data envelopment analysis (InvDEA) model. A merger between two or more decision making units (DMUs) producing a single merged DMU that affects the efficiency frontier, defined by the pre-consolidation market conditions, is called a major consolidation. The corresponding alternative case is called a minor consolidation. A necessary and sufficient condition to distinguish the two types of consolidations is proven and two numerical illustrations in banking and supply chain management are discussed. The crucial importance of anticipating the magnitude of a consolidation in a market is outlined.

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.

An inverse DEA model for inputs/outputs estimate

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.

PurposeTo manage cash flow in supply chains, the purpose of this paper is to propose inverse data envelopment analysis (DEA) model.Design/methodology/approachThis paper develops an inverse range directional measure (RDM) model to deal with positive and negative values. The proposed model is developed to estimate input and output variations such that not only efficiency score of decision making unit (DMU) remains unchanged, but also efficiency score of other DMUs do not change.FindingsGiven that auto making industry deals with huge variety and volumes of parts, cash flow management is so important. In this paper, inverse RDM models are developed to manage cash flow in supply chains. For the first time, the authors propose inverse DEA models to deal with negative data. By applying the inverse DEA models, managers distinguish efficient DMUs from inefficient ones and devise appropriate strategies to increase efficiency score. Given results of inverse integrated RDM model, other combinations of cash flow strategies are proposed. The suggested strategies can be taken into account as novel strategies in cash flow management. Interesting point is that such strategies do not lead to changes in efficiency scores.Originality/valueIn this paper, inverse input and output-oriented RDM model is developed in presence of negative data. These models are applied in resource allocation and investment analysis problems. Also, inverse integrated RDM model is developed.

This study suggests a novel application of Inverse Data Envelopment Analysis (InvDEA) in strategic decision making about mergers and acquisitions in banking. The conventional DEA assesses the efficiency of banks based on the information gathered about the quantities of inputs used to realize the observed level of outputs produced. The decision maker of a banking unit willing to merge/acquire another banking unit needs to decide about the inputs and/or outputs level if an efficiency target for the new banking unit is set. In this paper, a new InvDEA-based approach is developed to suggest the required level of the inputs and outputs for the merged bank to reach a predetermined efficiency target. This study illustrates the novelty of the proposed approach through the case of a bank considering merging with or acquiring one of its competitors to synergize and realize higher level of efficiency. A real data set of 42 banking units in Gulf Corporation Council countries is used to show the practicality of the proposed approach.

In sheet metal-forming processes, the final product can deviate from the target shape as a result of springback. Several approaches have been proposed for analysis of springback and compensating for its error. In this paper, a new approach for springback analysis is presented based on inverse modelling. The springback occurs at the last step of the process and the final geometry of the workpiece can be obtained at the end of direct process modelling. By applying inverse springback analysis, iterative die design becomes possible from the end of the process. Applying bending theory in an inverse algorithm, compensation of springback error is performed in the V-bending process. Convergence of the inverse approach is compared with the direct approach. The inverse springback analysis is developed for three-dimensional analysis of sheet metal forming by applying the explicit—implicit finite element method. Inverse springback modelling of asymmetric and large springback processes is feasible by this new algorithm. The capability and accuracy of this method are investigated for various symmetric and asymmetric processes by comparing results of the method by three-dimensional finite element analysis and V-bending experimental results.

Introduction. The aim of this study is to provide group-specific regression equations for age estimation of immature human skeletal remains younger than 12 years of age from the diaphyseal length of the six long bones. Further, to compare inverse and classical calibration models for age estimation and the suitability of previously published regression methods for archaeological and present-day populations in relation to the analyzed sample. Materials and methods. The studied sample consists of 128 non-adult individuals from Gonur Depe – the major BMAC site in Turkmenistan (2300–1500 BCE). Regression formulae were obtained for each of the six long bones, separately for entire sample (0–12 years of age) and for two subsamples below and above 2 years of age. For each equation the coefficient of determination (R2) and F-statistics were calculated. Residuals were tested for normality of distribution, autocorrelation, homoscedasticity, and the equality of mean to zero (one-sample t-test). Comparison between inverse and classical calibration was provided using paired samples t-test. To assess the applicability of other regression formulae to the studied sample both the mean residuals (MR) and mean of the absolute value of the residuals (MAR) were calculated, as an estimate of bias and accuracy respectively. Results. All regression models showed a strong statistical significance and high R2 value. The slope coefficients of the regression lines of diaphyseal length upon age are greater for the upper limb bones both in the entire sample and two subsamples separately. The lower limb bones are characterized by lower growth rates. In contrast to the inverse calibration, for the classical model the mean standard errors (MSE) were smaller for the upper limb bones rather than for the lower limb bones. For the lower limb bones the standard error of the estimate (SE) was generally smaller in inverse formulae. Comparison of both models for the femur however shows their equal performance. For the exception of proposed and classical calibration formulae all inverse models for femur diaphyseal length show consistent differences from zero in relation to the studied sample. Discussion. The inverse and classical calibration models as a technique for age estimation using diaphyseal long bone lengths are both equally applicable in the studied sample. It is recommended to use the equations for the lower limb bones in the inverse model and for the upper limb bones in the classical model. The Gonur Depe population is characterized by relatively higher growth rates of the upper limb bones and distal limb segments relative to the proximal ones. Most of the previously published inverse calibration models are not recommended for uncritically use due to the high risk of obtaining biased estimates on samples that are different chronologically and/or territorially.

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.

This paper presents an efficient inverse analysis technique for the identification of an unknown boundary condition in a finite element method (FEM) on a small memory capacity machine such as a personal computer. The author has previously presented the FEM of inverse analysis introducing an inverse compliance matrix that uses an influence function into the stiffness matrix for the unknown boundary. Since the stiffness matrix of the FEM becomes singular, following two calculation processes are adopted: (1) a calculation process which obtains an approximate solution by decreasing the effect of the inverse compliance in the stiffness, and (2) an iterative calculation process computing a correct solution from the approximation using (1). First, a penalty function method is used to decrease the rank of a singular stiffness matrix in (1). Then, the number for computing LDU decomposed matrix becomes twice in comparison with fourth times in the previous paper. Next, an efficient calculation method is presented using an attack technique based on both accelerative moving lower and upper bounds in (2). Moreover, a zooming identification method is developed, owing to an improvement of node displacements on and near the edges. Therefore, this technique makes it possible to establish an efficient inverse analysis for the identification of the unknown boundary. Finally, the validity of the inverse analysis technique is confirmed from the numerical solution of a three-dimensional inverse finite element analysis model, as an example of an elastic structure with reinforced members under tension, carried out on a small memory capacity machine.

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