A novel best worst method robust data envelopment analysis:Incorporating decision makers’ preferences in an uncertain environment

Data Envelopment Analysis (DEA) has been widely applied in measuring the efficiency of Decision-Making Units (DMUs). The conventional DEA has three major drawbacks: a) it does not consider Decision Makers’ (DMs) preferences in the evaluation process, b) DMUs in this model are flexible in weighting the criteria to reach the maximum possible efficiency, and c) it ignores the uncertainty in data. However, in many real-world applications, data are uncertain as well as imprecise and managers want to impose their opinions in decision-making procedure. To address these problems, this paper develops a novel multi-objective Best Worst Method (BWM)-Robust DEA (RDEA) for incorporating DMs’ preferences into DEA model in an uncertain environment. The proposed model tries to provide a new efficiency score which is more reliable and compatible with real problems by taking the advantages of the BWM to apply experts’ opinions and RDEA to model the uncertainty This bi-objective BWM-RDEA model is solved utilizing amin-max technique and so as to illustrate its usefulness, this model is implemented for assessing Iranian airlines

Performance evaluation in education under uncertainty: A robust optimization approach

Analysing and enhancing education system performance is of importance to local authorities and policy makers because education improves the human capital, which, in turn, leads to economic growth. This study draws on the secondary data to assess the education performance using data envelopment analysis (DEA). However, the reliability of the efficiency measures calculated by DEA is jeopardized if the inputs and outputs are erroneous, which is likely to occur through secondary data collected by government agencies. This study attends to uncertainty through the lens of robust optimization, which fits into a DEA application. We propose a robust enhanced Russell measure model to consider the extent of inherent uncertainty in the light of uncertain characteristics. We also present a case study in education to demonstrate the applicability and efficacy of the proposed models in practice

Robustness of Farrell cost efficiency measurement under data perturbations: Evidence from a US manufacturing application

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Measuring economic and cost efficiency receives ever-increasing attention of the executives and managers of small-and medium-sized enterprises (SMEs) to minimise the total production costs. The conventional Farrell cost efficiency (CE) as a key determinant requires the precise information on inputs, outputs and input prices, while in praxis uncertainty is inherent and inevitable in data and its negligence conceivably results in a dire approximation for CE measures. This paper is concerned with Farrell CE in situations of both endogenous and exogenous uncertainty. The source of uncertainty allows us to define two different scenarios; (i) in situations of endogenous uncertainty in input and output data where the uncertainty is affected by the decision maker, and (ii) in situations of uncertain prices for inputs where the uncertainty is exogenously given. In the first scenario, the theory of robust optimisation is adopted to develop the robust data envelopment analysis (DEA) models with the aim of grappling uncertainties in input and output data when measuring technical and cost efficiencies. The second scenario aims to accommodate uncertainties on price information by developing a pair of robust DEA models based upon robust optimisation estimating the upper and lower bounds for CE measures. This unprecedented study helps us to provide a generalised framework for economic efficiency with uncertainties in which conventional properties of Farrell measures are fulfilled. In addition to comparing the developed approach in this paper with other existing approaches through a simple numerical example, the usefulness and applicability of the suggested framework are minutely studied in an empirical application in the context of allocation problems

Robust worst-practice interval DEA with non-discretionary factors

Traditionally, data envelopment analysis (DEA) evaluates the performance of decision-making units (DMUs) with the most favorable weights on the best practice frontier. In this regard, less emphasis is placed on non-performing or distressed DMUs. To identify the worst performers in risk-taking industries, the worst-practice frontier (WPF) DEA model has been proposed. However, the model does not assume evaluation in the condition that the environment is uncertain. In this paper, we examine the WPF-DEA from basics and further propose novel robust WPF-DEA models in the presence of interval data uncertainty and non-discretionary factors. The proposed approach is based on robust optimization where uncertain input and output data are constrained in an uncertainty set. We first discuss the applicability of worst-practice DEA models to a broad range of application domains and then consider the selection of worst-performing suppliers in supply chain decision analysis where some factors are unknown and not under varied discretion of management. Using the Monte-Carlo simulation, we compute the conformity of rankings in the interval efficiency as well as determine the price of robustness for selecting the worst-performing suppliers.Web of Science182art. no. 11525

Robust productivity growth and efficiency measurement with undesirable outputs: evidence from the oil industry

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.This paper aims to contribute to the contemporary and imperative research on the performance and productivity growth of the oil industry. Among cutting edge methods, frontier analysis is a successful approach that has been widely used to assess the efficiency and productivity of entities with multiple resources and multiple outputs. This study first develops a unique framework based upon data envelopment analysis (DEA) to measure efficiency and productivity in the way that it tackles the uncertainty in data and undesirable outputs and, in turn, provides useful information to decision-makers. An adaptive robust optimisation (RO) is utilised to combat those uncertain data whose distributions are unknown and consider the nexus between the level of conservatism and decision makers’ risk preference. The key advantage of the proposed robust DEA approach is that the results remain relatively unchanged when uncertain conditions exist in the problem. An empirical study on the oil refinery is presented in situations of data uncertainty along with considering CO2 emissions as the undesirable output to conduct environmental efficiency and productivity analysis of the 25 countries over the period 2000-2018. The empirical results obtained from the proposed approach give some imperative implications. First, results show that the price of robustness does not affect identically for varying technologies when assessing productivity in a global oil market, and USA's oil industry is observed as the highest productivity growth in all cases confirming its efforts for the rapid rise in oil extraction and production at low costs. There may be practical lessons for other nations to learn from the American oil industry to improve productivity. Findings also support a considerable regress during the 2008 Global Financial Crisis in the oil industry compared to the rest of the periods in question, and due to monetary and fiscal stimulus, there is a sharp productivity growth from 2009 to 2011. The other implication that can be drawn is that the GDP growth rate and technology innovation can more effectively improve the productivity of the oil industry across the globe

Assessing Performance of Organizations Under Uncertainty: An Application in Higher Education

Data envelopment analysis (DEA) is an established approach to measure the efficiency of a group of firms. Amongst many existing DEA models, enhanced Russell measure (ERM) has received some attention and it minimises the ratio of average input reduction to average output increase. In the original ERM, observations are assumed to be precise but in reality, it is always true. This paper presents a class of robust optimisation models to deal with uncertainty with a high degree of robustness in the ERM models. In addition, this study leverages the Monte-Carlo simulation to give an appropriate range for the budget of uncertainty approving the highest level of conformity for the ranking of units. An application on the Master of Business Administration (MBA) programmes is presented

Robust non-radial data envelopment analysis models under data uncertainty

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Russell measure (RM) and enhanced Russell measure (ERM) are popular non-radial measures for efficiency assessment of decision-making units (DMUs) in data envelopment analysis (DEA). Input and output data of both original RM and ERM are assumed to be deterministic. However, this assumption may not be valid in some situations because of data uncertainty arising from measurement errors, data staleness, and multiple repeated measurements. Interval DEA (IDEA) has been proposed to measure the interval efficiencies from the optimistic and pessimistic viewpoints while the robustness of the assessment is questionable. This paper draws on a class of robust optimisation models to surmount uncertainty with a high degree of robustness in the RM and ERM models. The contribution of this paper is fivefold; (1) we develop new robust non-radial DEA models to measure the robust efficiency of DMUs under data uncertainty, which are adjustable based upon conservatism levels, (2) we use Monte-Carlo simulation in an attempt to identify an appropriate range for the budget of uncertainty in terms of the highest conformity of ranking results, (3) we introduce the concept of the price of robustness to scrutinise the effectiveness and robustness of the proposed models, (4) we compare the developed robust models in this paper with other existing approaches, both radial and non-radial models, and (5) we explore an application to assess the efficiency of the Master of Business Administration (MBA) programmes where data uncertainties influence the quality and reliability of results

Robust non-radial data envelopment analysis models under data uncertainty

Russell measure (RM) and enhanced Russell measure (ERM) are popular non-radial measures for efficiency assessment of decision-making units (DMUs) in data envelopment analysis (DEA). Input and output data of both original RM and ERM are assumed to be deterministic. However, this assumption may not be valid in some situations because of data uncertainty arising from measurement errors, data staleness, and multiple repeated measurements. Interval DEA (IDEA) has been proposed to measure the interval efficiencies from the optimistic and pessimistic viewpoints while the robustness of the assessment is questionable. This paper draws on a class of robust optimisation models to surmount uncertainty with a high degree of robustness in the RM and ERM models. The contribution of this paper is fivefold; (1) we develop new robust non-radial DEA models to measure the robust efficiency of DMUs under data uncertainty, which are adjustable based upon conservatism levels, (2) we use Monte-Carlo simulation in an attempt to identify an appropriate range for the budget of uncertainty in terms of the highest conformity of ranking results, (3) we introduce the concept of the price of robustness to scrutinise the effectiveness and robustness of the proposed models, (4) we compare the developed robust models in this paper with other existing approaches, both radial and non-radial models, and (5) we explore an application to assess the efficiency of the Master of Business Administration (MBA) programmes where data uncertainties in-fluence the quality and reliability of results.Web of Science207art. no. 11802