Efficiency Scores Of Decision Making Units Research Articles

A simulation-based DEA approach for multiple criterion decision-making problems with uncertain mixed-criteria values

In ex-ante decision scenarios, predicting criterion values accurately is difficult for decision makers (DMs). Inconsiderable work is normally required for measuring criteria by uncertain random values or ordinal values. However, in the classical data envelopment analysis (DEA) model, criterion values are the constants that limit the application of the classical DEA model in ex-ante decision scenarios. This paper presents a simulation-based DEA approach, which captures random and ordinal criterion values by a simple and direct simulation-based approach. The approach includes three steps. In the first step, Monte Carlo simulation methods are used to convert uncertain random values or ordinal values into cardinal data. In the second step, we use traditional DEA methods to compute the efficiency score of decision-making units (DMUs). In the third step, we ranked all DMUs by calculating the DEA-efficient acceptability of each DMU in multiple simulations and then selected the optimal DMU. The proposed approach is illustrated by experimental examples and a case study of a municipal wastewater treatment system.

Cross‐efficiency evaluation of the data envelopment analysis with conflict behaviour and beneficial relationship perspectives

AbstractIn data envelopment analysis, cross‐efficiency evaluation stands out as a valuable tool for ranking the effectiveness of decision‐making units (DMUs). However, existing research commonly assume that DMUs are randomly classified as either collaborators or opponents of the evaluated DMUs. Unfortunately, few studies have considered the presence of conflict behaviour and beneficial relationships among DMUs during cross‐efficiency evaluation. To address this research gap, this study proposes an innovative approach. Firstly, the proposed framework incorporates an interval cross‐efficiency environment to accommodate the inherent uncertainty and fuzziness in the efficiency scores of DMUs. Secondly, two definitions, namely task conflict cross‐efficiency and relationship conflict cross‐efficiency, are introduced by combining the characteristics of the interval cross‐efficiency matrix with conflict behaviour. To measure the strength of the conflict between DMUs, a novel measurement method is proposed, forming the foundation for constructing two cross‐efficiency secondary programming models based on conflict behaviour. Thirdly, the Spearman's rank correlation coefficient is employed to measure the strength of beneficial relationships among DMUs. Subsequently, two cross‐efficiency secondary programming models are developed based on beneficial relationships. To obtain the final scores, the efficiency scores of the four models are integrated using the Shannon entropy method. Finally, two illustrative applications are presented to demonstrate the effectiveness and robustness of the proposed method.

Estimation of technical efficiency of chemical-free farming using data envelopment analysis and machine learning: evidence from India

PurposeThis study aims to examine the technical efficiency of the chemical-free farming system in India using a hybrid combination of data envelopment analysis (DEA) and machine learning (ML) approaches.Design/methodology/approachThe study used a two-stage approach. In the first stage, the efficiency scores of decision-making units’ efficiency (DMUs) are obtained using an input-oriented DEA model under the assumption of a variable return to scale. Based on these scores, the DMUs are classified into efficient and inefficient categories. The 2nd stage of analysis involves the identification of the most important predictors of efficiency using a random forest model and a generalized logistic regression model.FindingsThe results show that by using their resources efficiently, growers can reduce their inputs by 34 percent without affecting the output. Orchard's size, the proportion of land, grower's age, orchard's age and family labor are the most important determinants of efficiency. Besides, growers' main occupation and footfall of intermediaries at the farm gate also demonstrate significant influence on efficiency.Research limitations/implicationsThe study used only one output and a limited set of input variables. Incorporating additional variables or dimensions like fertility of the land, climatic conditions, altitude of the land, output quality (size/taste/appearance) and per acre profitability could yield more robust results. Although pineapple is cultivated in all eight northeastern states, the data for the study has been collected from only two states. The production and marketing practices followed by the growers in the remaining six northeastern states and other parts of the country might be different. As the growers do not maintain farm records, their data might suffer from selective retrieval bias.Practical implicationsGiven the rising demand for organic food, improving the efficiency of chemical-free growers will be a win-win situation for both growers and consumers. The results will aid policymakers in bringing necessary interventions to make chemical-free farming more remunerative for the growers. The business managers can act as a bridge to connect these remote growers with the market by sharing customer feedback and global best practices.Social implicationsAlthough many developments have happened to the DEA technique, the present study used a traditional form of DEA. Therefore, future research should combine ML techniques with more advanced versions like bootstrap and fuzzy DEA. Upcoming research should include more input and output variables to predict the efficiency of the chemical-free farming system. For instance, environmental variables, like climatic conditions, degree of competition, government support and consumers' attitude towards chemical-free food, can be examined along with farm and grower-specific variables. Future studies should also incorporate chemical-free growers from a wider geographic area. Lastly, future studies can also undertake a longitudinal estimation of efficiency and its determinants for the chemical-free farming system.Originality/valueNo prior study has used a hybrid framework to examine the performance of a chemical-free farming system.

FairDEA—Removing disparate impact from efficiency scores

Achieving fairness in algorithmic decision-making tools is an issue constantly gaining in need and popularity. Today, unfair decisions made by such tools can even be subject to legal consequences. We propose a new constraint that integrates fairness into data envelopment analysis (DEA). This allows the calculation of relative efficiency scores of decision-making units (DMUs) with fairness included. The proposed fairness constraint restricts disparate impact to occur in efficiency scores, and enables the creation of a single data envelopment analysis for both privileged and unprivileged groups of DMUs simultaneously. We show that the proposed method - FairDEA - produces an interpretable model that was tested on a synthetic dataset and two real-world examples, namely the ranking between hybrid and conventional car designs, and the Latin American and Caribbean economies. We provide the interpretation of the FairDEA method by comparing it to the basic DEA and the balanced fairness and efficiency method (BFE DEA). Along with calculating the disparate impact of the model, we performed a Wilcoxon rank-sum test to inspect for fairness in rankings. The results show that the FairDEA method achieves similar efficiency scores as other methods, but without disparate impact. Statistical analysis indicates that the differences in ranking between the groups are not statistically different, which means that the ranking is fair. This method contributes both to the development of data envelopment analysis, and the inclusion of fairness in efficiency analysis.

A novel network DEA-R model for evaluating hospital services supply chain performance

AbstractAssessing the efficiency of a supply chain (SC) is of great importance for managers and policy makers. For this aim, we propose a network data envelopment analysis (NDEA) model to reflect the internal structure of networks in efficiency evaluation. For many of the real-world performance evaluation problems, data of inputs and outputs are available, and their ratio conveys important messages to managers. However, conventional data envelopment analysis (DEA) models are no longer able to deal with ratio data. This paper aims to extend the NDEA models with the ratio data (NDEA-R) to evaluate the performance of SCs. Therefore, given the internal structure of a supply chain, relationships among different divisions of an SC are determined under two assumptions of free-links and fixed-links. Applicability of the proposed models is illustrated by evaluating supply chain of 19 hospitals in Iran over 6 months. By performing sensitivity analysis, we find out that the overall efficiency score of decision-making units (DMUs) under the fixed link assumption is greater than or equal to the overall efficiency of DMUs under free link assumption. Our proposed model overcomes the underestimation of efficiency and pseudo-inefficiency scores.

Preserving cost and revenue efficiency through inverse data envelopment analysis models

Data envelopment analysis (DEA) models are applied in commercial firms to evaluate their technical, cost and revenue efficiencies. The new models introduced here are based on inverse DEA for preserving cost/revenue efficiency. The commercial institution management seeks to minimize the input costs for a given level of outputs or maximize the revenue of outputs for a specified level of inputs. It is important to preserve cost/revenue efficiency when data are changed. In this method, we determine the cost efficiency score of decision-making units (DMUs). Then, for each one of them, the outputs are increased and the values of the required increment of inputs are obtained, while the cost efficiency of the unit under evaluation remains unchanged. For practical application, one of these introduced models is applied to a real data set of European and American banks for cost efficiency preservation.

A data envelopment analysis approach for resource allocation with undesirable outputs: an application to home appliance production companies

Traditional data envelopment analysis (DEA) models use all multiple inputs and outputs to estimate efficiency scores of decision-making units (DMUs). Each unit may consist of several subunits in cases such as manufacturing systems, and each subunit may produce both desirable and undesirable outputs. Providing information about the proportion of resources for each subunit could assist managers in making better decisions for increasing the efficiency of production systems. The current study proposes a new approach for resource allocation and efficiency estimation of production units by considering partial impacts among inputs and outputs in the DEA framework. A weak disposable technology is used in these evaluations, and an empirical application of the proposed approach for obtaining performance of home appliances production companies is provided for illustration purposes.

Sustainability Assessment of Supply Chains by Inverse Network Dynamic Data Envelopment Analysis

This paper focuses on assessing sustainability of supply chains. In this paper, at first, we propose network dynamic range adjusted measure (RAM) model. Then, inverse version of network dynamic RAM model is proposed. Our inverse network dynamic data envelopment analysis (DEA) model changes both inputs and outputs of decision making units (DMUs) so that current efficiency scores of DMUs remain unchanged. We change inputs and outputs without any change in efficiency score of DMU under evaluation while inputs and outputs may have large ranges. A case study shows efficacy of our proposed model.

How to assess sustainability of countries via inverse data envelopment analysis?

In this paper, two input-oriented and output-oriented inverse semi-oriented radial measures are presented. Such models are applied to determine resource allocation and investment strategies for assessing sustainability of countries. Our proposed models can deal with both positive and negative data. In our proposed inverse input-oriented data envelopment analysis (DEA) model, optimal inputs are suggested while outputs and efficiency score of decision-making unit (DMU) under evaluation are unchanged. Similarly, in our proposed inverse output-oriented DEA model, optimal outputs are proposed while inputs and efficiency score of DMU under evaluation are kept unchanged. For the first time, we propose two new inverse DEA models to handle resource allocation and investment analysis problems given sustainable development aspects in the presence of negative data. A case study is given for assessing sustainability of countries.

A decision-making methodology for vendor selection problem with uncertain inputs

This paper presents a decision-making scheme for selecting appropriate method for supplier selection under certainly, uncertainly, and stochastic conditions. These models are categorized into three techniques containing deterministic data envelopments analysis (DEA), fuzzy data envelopment analysis (FDEA), and stochastic data envelopment analysis (SDEA). The models are written on the basis of an improved integrated DEA model (i.e. MiniMax model) to find the most efficient vendor. The objective of the model is to minimize the maximum inefficient variables. First, it is supposed that data are crisp and DEA model is developed. Second, it is assumed that data are not crisp and sufficient historical data are not available and fuzzy DEA model is employed. Third, for those cases that data are not crisp but sufficient historical data are available, stochastic DEA is used. Finally, average efficiency scores of decision-making units for each model under different random types of inputs are calculated and the results are analyzed. This is the first study that provides a flexible tool in order to select the most efficient vendors in uncertainty condition.

Outliers/Most Influential Observationsin Variable Returns to Scale Data Envelopment Analysis

Background/Objectives: Outliers are extreme observations which deviate significantly from the normal observations. Their presence distorts the end results of scientific study. In Data Envelopment Analysis (DEA), most influential observations are outliers. Identification of outliers and their deletion is important in DEA problems. Deletion of an extreme observation results in contraction of the production possibility set. Methods/Analysis: This study identifies outliers as these extreme observations whose absence results in significant contraction of the production possibility set. Data Envelopment Analysis is based on solving linear programming problems to assess the efficiency scores of Decision Making Units (DMUs). The present study can estimate efficiency scores of DMUs with and without outliers. Deletion of outliers provides smaller targets to the inefficient DMUs. Findings: For identification of outliers super efficiency, problems can be solved for extremely efficient DMUs, which results in the largest dimension of the contracted Production Possibility Set (PPS). The present study provides many dimensions of the contracted PPset, solving Banker, Charnes and Cooper (BCC 1984) linear programming problems. Sum of these dimensions can be viewed as histogram that closely envelops the contracted Production Possibility Set. Larger is the sum of all dimensions, more influential is the decision making unit. To identify outliers in DEA in this study a statistical test is outlined. Application/Improvements: The methodology outlined can be used for DMUs competing with each other in a competitive environment employing similar inputs to produce similar outputs.

ABC classification using DEA: classification of Iranian universities from students welfare foundation viewpoint

The motivation of this paper is to classify a set of decision making units (DMUs) into three classes A, B, and C using an optimistic-pessimistic approach of data envelopment analysis technique. To this end, the minimum and maximum possible efficiency scores of DMUs are estimated under the assumption that the sum of their scores equals to unity. Then, all DMUs are ranked two times. First, they are ranked according to their minimum scores, and then according to their maximum scores. Finally, the class of each DMU is ascertained according to its ranks in two rankings. We apply the proposed method for classifying the welfare funds of students for the universities in Iran.

Allocating the Fuzzy Resources to Two-Stage Systems

Data envelopment analysis (DEA) is a non-parametric approach for measuring the efficiency of decision making units (DMUs) that use multiple inputs in order to produce multiple outputs. In most real applications, DMUs have a two-stage network process which can be used for management of organizations such as hospitals, insurance companies, banks, and etc. The data are crisp in the standard DEA model whereas there are many problems in the real life that data may be uncertain. Thus, in this paper, we propose a model to estimate the efficiency of DMUs with a two-stage structure and the inputs and outputs of DMUs are fuzzy data. Also, DEA can be used to allocate resources; therefore, we propose a new method to allocate resources for DMUs with a two-stage structure and fuzzy data. The main aim of this allocation is preserving the efficiency score of DMUs. We illustrate the applicability of models by using a numerical example.

Undesirable Outputs’ Presence in Centralized Resource Allocation Model

Data envelopment analysis (DEA) is a common nonparametric technique to measure the relative efficiency scores of the individual homogenous decision making units (DMUs). One aspect of the DEA literature has recently been introduced as a centralized resource allocation (CRA) which aims at optimizing the combined resource consumption by all DMUs in an organization rather than considering the consumption individually through DMUs. Conventional DEA models and CRA model have been basically formulated on desirable inputs and outputs. The objective of this paper is to present new CRA models to assess the overall efficiency of a system consisting of DMUs by using directional distance function when DMUs produce desirable and undesirable outputs. This paper initially reviewed a couple of DEA approaches for measuring the efficiency scores of DMUs when some outputs are undesirable. Then, based upon these theoretical foundations, we develop the CRA model when undesirable outputs are considered in the evaluation. Finally, we apply a short numerical illustration to show how our proposed model can be applied.

Allocating the Fixed Resources and Setting Targets in Integer Data Envelopment Analysis

Data envelopment analysis (DEA) is a non-parametric approach to evaluate a set of decision making units (DMUs) consuming multiple inputs to produce multiple outputs. Formally, DEA use to estimate the efficiency score into the empirical efficient frontier. Also, DEA can be used to allocate resources and set targets for future forecast. The data are continuous in the standard DEA model whereas there are many problems in the real life that data must be integer such as number of employee, machinery, expert and so on. Thus in this paper we propose an approach to allocate fixed resources and set fixed targets with selective integer assumption that is based on an integer data envelopment analysis (IDEA) approach for the first time. The major aim in this approach is preserving the efficiency score of DMUs. We use the concept of benchmarking to reach this aim. The numerical example gets to illustrate the applicability of the proposed method.

Ranking Decision Making Units By Compromise Programming

Data envelopment analysis (DEA) is a very useful management and decision tool. The ranking of decision making units (DMU) has become an important component in the decision process. In this paper we developed a new method for measuring the efficiency score of Decision-Making Units (DMUs) by using compromise programming. The proposed method calculates distance to the ideal for each DMU. The DMU with shorter distance to the ideal has better efficiency. A numerical example is provided to illustrate the application of the proposed DEA model.