An equivalent linear programming form of general linear fractional programming: A duality approach

Linear fractional programming has been an important planning tool for the past four decades. The main contribution of this study is to show, under some assumptions, for a linear programming problem, that there are two different dual problems (one linear programming and one linear fractional functional programming) that are equivalent. In other words, we formulate a linear programming problem that is equivalent to the general linear fractional functional programming problem. These equivalent models have some interesting properties which help us to prove the related duality theorems in an easy manner. A traditional data envelopment analysis (DEA) model is taken, as an instance, to illustrate the applicability of the proposed approach.Web of Science914art. no. 158

A dataset of healthcare systems for cross-efficiency evaluation in the presence of flexible measure

This article presents the dataset of the healthcare systems indicators of 120 countries during 2010-2017, which is related to the research article "Cross-efficiency evaluation in the presence of flexible measures with an application to healthcare systems" [1]. The data is collected from the World Bank and selected for the 120 countries. Depending on their role in the performance of the healthcare systems, the indicators are categorized into input (I), output (O) and flexible measure (FM) where the FM measure can play either role of input or output in the healthcare system. The dataset can be used to perform efficiency as well as cross-efficiency analysis of the healthcare systems using methods such as data envelopment analysis (DEA) in the presence of flexible measure.Web of Science25art. no. UNSP 10423

A linear relational DEA model to evaluate two-stage processes with shared inputs

Two-stage data envelopment analysis (DEA) efficiency models identify the efficient frontier of a two-stage production process. In some two-stage processes, the inputs to the first stage are shared by the second stage, known as shared inputs. This paper proposes a new relational linear DEA model for dealing with measuring the efficiency score of two-stage processes with shared inputs under constant returns-to-scale assumption. Two case studies of banking industry and university operations are taken as two examples to illustrate the potential applications of the proposed approach

A comprehensive bibliometric analysis of fractional programming (1965-2020)

Fractional programming (FP) refers to a family of optimization problems whose objective function is a ratio of two functions. FP has been studied extensively in economics, management science, information theory, optic and graph theory, communication, and computer science, etc. This paper presents a bibliometric review of the FP-related publications over the past five decades in order to track research outputs and scholarly trends in the field. The reviews are conducted through the Science Citation Index Expanded (SCI-EXPANDED) database of the Web of Science Core Collection (Clarivate Analytics). Based on the bibliometric analysis of 1811 documents, various theme-related research indicators were described, such as the most prominent authors, the most commonly cited papers, journals, institutions, and countries. Three research directions emerged, including Electrical and Electronic Engineering, Telecommunications, and Applied Mathematics.Web of Science1011art. no. 179

Eco-efficiency considering the issue of heterogeneity among power plants

One of the main objectives in restructuring power industry is enhancing the efficiency of power facilities. However, power generation industry, which plays a key role in the power industry, has a noticeable share in emission amongst all other emission-generating sectors. In this study, we have developed some new Data Envelopment Analysis models to find efficient power plants based on less fuel consumption, combusting less polluting fuel types, and incorporating emission factors in order to measure the ecological efficiency trend. We then applied these models to measuring eco-efficiency during an eight-year period of power industry restructuring in Iran. Results reveal that there has been a significant improvement in eco-efficiency, cost efficiency and allocative efficiency of the power plants during the restructuring period. It is also shown that despite the hydro power plants look eco-efficient; the combined cycle ones have been more allocative efficient than the other power generation technologies used in Iran

An Equivalent Linear Programming Form of General Linear Fractional Programming: A Duality Approach

Linear fractional programming has been an important planning tool for the past four decades. The main contribution of this study is to show, under some assumptions, for a linear programming problem, that there are two different dual problems (one linear programming and one linear fractional functional programming) that are equivalent. In other words, we formulate a linear programming problem that is equivalent to the general linear fractional functional programming problem. These equivalent models have some interesting properties which help us to prove the related duality theorems in an easy manner. A traditional data envelopment analysis (DEA) model is taken, as an instance, to illustrate the applicability of the proposed approach

Notes on classifying inputs and outputs in data envelopment analysis: a comment

Cook and Zhu (2007) introduced an innovative method to deal with flexible measures. Toloo (2009) found a computational problem in their approach and tackled this issue. Amirteimoori and Emrouznejad (2012) claimed that both Cook and Zhu (2007) and Toloo (2009) models overestimate the efficiency. In this response, we prove that their claim is incorrect and there is no overestimate in these approaches.Web of Science235381281

Alternative minimax model for finding the most efficient unit in data envelopment analysis

Data envelopment analysis (DEA) deals with the evaluation of efficiency score of peer decision making units (DMUs) and divides them in two mutually exclusive sets: efficient and inefficient. There are various ranking methods to get more information about the efficient units. Nevertheless, finding the most efficient unit is a scientific challenge and hence has been the subject of numerous studies. Here, the main contribution is an integrated model that is able to determine the most efficient unit under a common condition is developed. The current research formulates a new minimax mixed integer linear programming (MILP) model for fining the most efficient DMU. Three different case studies from different contexts are taken as numerical examples to compare the proposed model with other methods. These numerical examples also illustrate the various potential applications of the suggested model.Web of Science8119418

A technical note on 'erratum to "Finding the most efficient DMUs in DEA: An improved integrated model" [Comput. Indus. Eng. 52 (2007) 71-77]'

You et al. (2013) indicated two errors in Amin and Toloo (2007). The first error was the infeasibility of Amin and Toloo’s (2007) model and the second drawback was the lack of a suitable value for the non-Archimedean epsilon in the proposed approach of Amin and Toloo (2007). This paper deals with the raised issues and proves that the model of Amin and Toloo (2007) is always feasible. In addition, we also formulate a new model for finding a suitable value for the epsilon.Web of Science8326326