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The paper analyzes the relative performance of provincial gas distribution companies with different types of inputs and outputs. A data envelopment analysis (DEA)-based model is developed to construct an equilibrium efficient frontier in the presence of multi-type input/output variables.

A DEA-based model is developed to construct an equilibrium efficient frontier in the presence of multi-type input/output variables.

It has been shown that using this single equilibrium efficient frontier, a trade-off is made between efficient and inefficient companies so as to make all companies as efficient.

The study analyzes the relative performance of provincial gas distribution companies with different types of inputs and outputs. A DEA-based model is developed to construct an equilibrium efficient frontier in the presence of multi-type input/output variables. It has been shown that using this single equilibrium efficient frontier, a trade-off is made between efficient and inefficient companies so as to make all companies as efficient.

The purpose of this paper is to propose a modified model in multi-stage processes when there are intermediate measures between the stages and in this sense, the new efficiency scores are more accurate. Conventional data envelopment analysis (DEA) models disregard the internal structures of peer decision-making units (DMUs) in evaluating their relative efficiency. Such an approach would cause managers to lose important DMU information. Therefore, in multistage processes, traditional DEA models encounter problems when intermediate measures are used for efficiency evaluation.

In this study, two-stage additive integer-valued DEA models were proposed. Three models were proposed for measuring inefficiency slacks in each stage and in the system as a whole.

Three models were proposed for measuring inefficiency slacks in each stage and in the system as a whole.

The advantage of the proposed models for multi-stage systems is that they can accurately determine the stages with the greatest weaknesses/strengths. By introducing an applied case in the Iranian power industry, the paper demonstrated the applications and advantages of the proposed models.

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.

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.

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.

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.

Data envelopment analysis (DEA) is a significant method for measuring the relative efficiency of decision making units (DMUs) that use the least inputs, produce the most desirable outputs and emit the least undesirable outputs in order to maximize their profits. In DEA, detecting an optimal scale size (OSS) is also vital and could be more applicable in economic activities when there are integer and undesirable measures. The purpose of this research is to measure average-profit efficiency (APE) and OSSs with integer data and undesirable outputs.

This study presents an alternative concept of APE using the concepts of most productive scale size (MPSS), profit efficiency and scales, containing desirable and undesirable outputs along with integer and non-integer measures. In fact, the OSS minimizes APE as the optimal scale, which is the ratio of the profit efficiency to the radial average output. Considering the prices of the inputs and desirable outputs, as well as the lack of any specific weight for the undesirable outputs, a two-step model for the numerical calculation of OSS is presented. In addition, the proposed approach is applied to a real data set of Iranian gas companies while there are integer measures and undesirable outputs.

The results show the introduced approach is beneficial to estimate OSSs from the aspect of maximizing profits of firms with undesirable outputs and integer values.

Estimating OSSs is the significant issue for managers, but its investigation in the presence of integer measures and undesirable outputs is presently under-considered.

The purpose of this paper is introducing an alternative model to measure the relative efficiency of observations with undesirable products. Describing the reference set and benchmarking.

In this paper, an alternative definition of weak disposability assumption is introduced to handle undesirable outputs. Actually, two types of undesirable outputs are addressed and a substitute definition of weak disposability is presented.

Using this assumption a linear production technology set along with a performance analysis model is constructed to assess the relative efficiency of the decision-making units. To illustrate the radial application of the proposed approach, a real case on transportation system of USA during 1992-2009 is given.

To date, data envelopment analysis studies have investigated undesirable outputs by the assumption of weak disposability, defined as the proportional contraction of good and bad products, which leads to the null-joint assumption between good and bad outputs. Therefore, the only way to produce no undesirable outputs is producing zero desirable outputs. So the production process should be stopped while it is not economically cost-effective. However, in some processes there are some undesirable outputs, which are decreased with non-same percentages. So these undesirable outputs can be stopped while the good outputs have a strictly positive value. In this situation, the good outputs are not null-joint with this type of bad outputs. In the current paper, a new definition of the weak disposability of outputs was represented while two groups of undesirable outputs were considered. Hence, desirable outputs and the first kind of undesirable outputs were decreased proportionally. However, the reduction value was different for the second kind of undesirable outputs. Hence, the null-joint assumption is removed from the production technology. Then, a new technology was proposed based on five postulates as inclusion of observations, free disposability of desirable outputs and inputs, new weak disposability, convexity and minimum extrapolation.

Merger and acquisitions (M&A) is a process of restructuring two or more companies into one, a process that occurs frequently in many companies. Previous studies on M&A mainly paid attention to the potential gains from a merger, while ignored the problem of how to select the partners to merge. This paper aims to select the best partner from different candidates for a given company to merge.

Each company's historical data are used to identify each company's own production technology. With resources change, each company's new operation is restricted by its own production technology. Then, a 0–1 integer programming is proposed to select the best partner for M&A.

The banking industry involving 27 China's commercial banks is given to verify the applicability of our proposed model. The study shows the best partner selection for each bank company.

On the theoretical side, the study uses each company's own historical data to construct its own production technology to compressively reflect the production change after M&A. On the practical side, the study uses the proposed model to help the 27 commercial banks in China to select their best merger partner.

As returns to scale (RTS) describes the long run connection of the changes of outputs relative to increases in the inputs, the purpose of this study is to answer the following questions: If the proportionate changes exist in the inputs, what is the rate of changes in outputs with respect to the inputs’ variations in the two-stage networks over the long term? How can the authors investigate quantitative RTS in the two-stage networks? In other words, the purpose of this research is to introduce a different approach to estimate the performance, RTS and scale economies (SE) in network structures.

This paper proposes a novel non-radial approach based on data envelopment analysis to analyze the performance and to investigate RTS and SE in two-stage processes.

The findings show that the range adjusted measure (RAM)/RTS approach can identify reference sets for overall systems and each stage. In addition, the models presented in this paper can classify decision-making units and determine the increasing/decreasing trends of RTS.

The majority of previous RTS studies have been examined in black-box structures and have been discussed in a radial framework. Therefore, in this study, RTS and SE in the two-stage networks are dealt with using an extended RAM approach. Actually, the efficiency and RTS for each stage and the overall model are calculated using the proposed technique.