Modelling generalized firms' restructuring using inverse DEA

The key consideration for firms’ restructuring is improving their operational efficiencies. Market conditions often offer opportunities or generate threats that can be handled by restructuring scenarios through consolidation, to create synergy, or through split, to create reverse synergy. A generalized restructuring refers to a move in a business market where a homogeneous set of firms, a set of pre-restructuring decision making units (DMUs), proceed with a restructuring to produce a new set of post-restructuring entities in the same market to realize efficiency targets. This paper aims to develop a novel inverse Data Envelopment Analysis based methodology, called GInvDEA (Generalized Inverse DEA), for modeling the generalized restructuring. Moreover, the paper suggests a linear programming model that allows determining the lowest performance levels, measured by efficiency that can be achieved through a given generalized restructuring. An application in banking operations illustrates the theory developed in the paper

Using slacks-based model to solve inverse DEA with integer intervals for input estimation

This paper deals with an inverse data envelopment analysis (DEA) based on the non-radial slacks-based model in the presence of uncertainty employing both integer and continuous interval data. To this matter, suitable technology and formulation for the DEA are proposed using arithmetic and partial orders for interval numbers. The inverse DEA is discussed from the following question: if the output of DMUo increases from Y-o to /beta(o), such the new DMU is given by (alpha(o)& lowast;, /3) belongs to the technology, and its inefficiency score is not less than t-percent, how much should the inputs of the DMU increase? A new model of inverse DEA is offered to respond to the previous question, whose interval Pareto solutions are characterized using the Pareto solution of a related multiple-objective nonlinear programming (MONLP). Necessary and sufficient conditions for input estimation are proposed when output is increased. A functional example is presented on data to illustrate the new model and methodology, with continuous and integer interval variables

A spatiotemporal Data Envelopment Analysis (S-T DEA) approach:the need to assess evolving units

One of the major challenges in measuring efficiency in terms of resources and outcomes is the assessment of the evolution of units over time. Although Data Envelopment Analysis (DEA) has been applied for time series datasets, DEA models, by construction, form the reference set for inefficient units (lambda values) based on their distance from the efficient frontier, that is, in a spatial manner. However, when dealing with temporal datasets, the proximity in time between units should also be taken into account, since it reflects the structural resemblance among time periods of a unit that evolves. In this paper, we propose a two-stage spatiotemporal DEA approach, which captures both the spatial and temporal dimension through a multi-objective programming model. In the first stage, DEA is solved iteratively extracting for each unit only previous DMUs as peers in its reference set. In the second stage, the lambda values derived from the first stage are fed to a Multiobjective Mixed Integer Linear Programming model, which filters peers in the reference set based on weights assigned to the spatial and temporal dimension. The approach is demonstrated on a real-world example drawn from software development

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

An Investment Analysis for China\u27s Sustainable Development Based on Inverse Data Envelopment Analysis

In the face of environmental degradation, sustainable development has become a common goal across the globe. Making a scientifically based investment scheme is of great significance to promote the sustainable development of China\u27s economy. However, there is scarce research related to such an investment scheme of sustainable development. This paper proposes a new inverse data envelopment analysis method with undesirable outputs to make several scientifically based investment schemes from different perspectives, namely, the natural, regulation, and optimal perspectives. By this method, decision makers can scientifically forecast the specific amount of investment based on their actual sustainable development objectives, which is conducive for reducing the blindness of investment in the future. In addition, a new ideal perspective is defined to guide a definite direction for improving the level of sustainable development. Combined with the gray forecasting model GM(1,1), the methods proposed by this paper were then applied to analyze the investment problem for China\u27s sustainable development during the 2015–2024 period. The results show that: the unbalanced distribution of labor investment and the excessive investment in capital and energy are serious barriers to China\u27s sustainable development in the short term; and in the long term, the demand for investment in labor and capital will continue to increase along with a lower demand for energy investment, and that appropriately strengthening environmental regulations will not affect the overall demand for investment. Meanwhile, improvement directions for improving China\u27s sustainable development are discussed, and the results show that most of developing and undeveloped regions in China have great potential for improvement. Finally, some suggestions are proposed in order to create better conditions for China\u27s sustainable development

A novel inverse DEA model with application to allocate the CO2 emissions quota to different regions in Chinese manufacturing industries

This paper aims to address the problem of allocating the CO2 emissions quota set by government goal in Chinese manufacturing industries to different Chinese regions. The CO2 emission reduction is conducted in a three-stage phases. The first stage is to obtain the total amount CO2 emission reduction from the Chinese government goal as our total CO2 emission quota to reduce. The second stage is to allocate the reduction quota to different two-digit level manufacturing industries in China. The third stage is to further allocate the reduction quota for each industry into different provinces. A new inverse data envelopment analysis (InvDEA) model is developed to achieve our goal to allocate CO2 emission quota under several assumptions. At last we obtain the empirical results based on the real data from Chinese manufacturing industries

Merging of units based on inverse data envelopment analysis

Inverse data envelopment analysis (InvDEA) is a remarkable and popular management tool. This paper deals with one application of this tool. In fact, the problem of the combination of the units is investigated in the presence of negative data. The problem of combining units refers to the fact that a set of units create a new unit based on synergy to improve their performance. We use multiple objective programming for this purpose and suggest new models based on predetermined conditions for the new unit. The proposed models estimate inputs and outputs simultaneously. Importance advantages of the proposed models are i) We can follow multiple goals in the problem of combining units because multiple objective programming is applied. ii) Models can simultaneously estimate the inputs and outputs of the combined unit. iii) Unlike the existing methods in the InvDEA-based merging literature, the negative data do not need to be transferred to positive data. Finally, a numerical example is used to explain and validate the model proposed in this paper

Interval and fuzzy optimization. Applications to data envelopment analysis

Enhancing concern in the efficiency assessment of a set of peer entities termed Decision Making Units (DMUs) in many fields from industry to healthcare has led to the development of efficiency assessment models and tools. Data Envelopment Analysis (DEA) is one of the most important methodologies to measure efficiency assessment through the comparison of a group of DMUs. It permits the use of multiple inputs/outputs without any functional form. It is vastly applied to production theory in Economics and benchmarking in Operations Research. In conventional DEA models, the observed inputs and outputs possess precise and realvalued data. However, in the real world, some problems consider imprecise and integer data. For example, the number of defect-free lamps, the fleet size, the number of hospital beds or the number of staff can be represented in some cases as imprecise and integer data. This thesis considers several novel approaches for measuring the efficiency assessment of DMUs where the inputs and outputs are interval and fuzzy data. First, an axiomatic derivation of the fuzzy production possibility set is presented and a fuzzy enhanced Russell graph measure is formulated using a fuzzy arithmetic approach. The proposed approach uses polygonal fuzzy sets and LU-fuzzy partial orders and provides crisp efficiency measures (and associated efficiency ranking) as well as fuzzy efficient targets. The second approach is a new integer interval DEA, with the extension of the corresponding arithmetic and LU-partial orders to integer intervals. Also, a new fuzzy integer DEA approach for efficiency assessment is presented. The proposed approach considers a hybrid scenario involving trapezoidal fuzzy integer numbers and trapezoidal fuzzy numbers. Fuzzy integer arithmetic and partial orders are introduced. Then, using appropriate axioms, a fuzzy integer DEA technology can be derived. Finally, an inverse DEA based on the non-radial slacks-based model in the presence of uncertainty, employing both integer and continuous interval data is presented

Time-series cross-sectional environmental performance and disclosure relationship:specific evidence from a less-developed country

This paper relies on ‘vulnerability and exploitability’ framework to submit new insights into legitimacy theory and voluntary disclosure theory using specific empirical evidence from the Nigerian oil and gas industry. The study connects the voluntary and legitimizing disclosure behaviors, regarding carbon emission due to gas flaring, of dominant companies in the Nigerian upstream petroleum sector to the vulnerability and exploitability of Nigeria as a less developed country. The hypothesized relations between gas flaring-related environmental performance and two forms of its disclosure (volume and substance) are estimated and tested using Prais-Winsten regression with Panel Corrected Standard Errors (PCSE). While the paper uses Data Envelopment Analysis (DEA) to measure gas flaring-related carbon performance, the two forms of gas flaring-related disclosures are measured using content analysis. We document significant positive and negative association between gas flaring-related carbon emission performance, on one hand, and the volumetric disclosure and disclosure substance on the other hand. These results imply that while the positive relation confirms the vulnerable nature of Nigeria as a less developed country, the negative relation is linked to the country’s exploitability. It is also empirically established that environmental performance is one of the key factors responsible for the undulating trend in the volume of environmental disclosures by large corporations operating in less-developed countries

Stochastic Nonparametric Envelopment of Data: Combining Virtues of SFA and DEA in a Unified Framework

The literature of productive efficiency analysis is divided into two main branches: the parametric Stochastic Frontier Analysis (SFA) and nonparametric Data Envelopment Analysis (DEA). This paper attempts to combine the virtues of both approaches in a unified framework. We follow the SFA literature and introduce a stochastic component decomposed into idiosyncratic error and technical inefficiency components imposing the standard SFA assumptions. In contrast to the SFA, we do not make any prior assumptions about the functional form of the deterministic production function. In this respect, we follow the nonparametric route of DEA that only imposes free disposability, convexity, and some specification of returns to scale. From the postulated class of production functions, the proposed method identifies the production function with the best empirical fit to the data. The resulting function will always take a piece-wise linear form analogous to the DEA frontiers. We discuss the practical implementation of the method and illustrate its potential by means empirical examples.Productivity Analysis,