Outputs Of Decision Making Units Research Articles

Uncertain Malmquist productivity index: An application to evaluate healthcare systems during COVID-19 pandemic

Evaluation of healthcare systems, as a key organization providing different health services, is essential. This issue becomes more crucial when occurring crises such as a pandemic. They need to keep track of their success in the face of the crisis to assess the effects of policy changes and their capability to respond to new challenges. The Malmquist Productivity Index (MPI) is measured to analyze the causes of productivity change between two periods of time. The estimation of the traditional MPI requires reliable and detailed information on the inputs and outputs of decision-making units. However, there are a lot of situations where input and/or output may be imprecise. It is not manageable to reliably measure certain measurement indices, such as quality of treatment or system flexibility. For such cases, experts are invited to model their opinion. Uncertainty theory is a mathematical branch rationally dealing with belief degrees. The primary objective of this study is to apply MPI concept in the nonparametric approach of data envelopment analysis to calculate the efficiency of systems over different periods of time under uncertain conditions. Accordingly, we consider the MPI when inputs and outputs are belief degrees of experts. Furthermore, the sensitivity of the model is analyzed to determine the reliability of the results to the variation of variables. Finally, as an illustrative example, we explore longitudinal efficiency of healthcare systems during COVID-19 pandemic. According to the results of our model, the majority of the countries have improved in the second period which can be the result of efforts to improve pandemic preparedness. The decomposition of MPI into efficiency changes and technical changes indicates that the rise in productivity is entirely related to the progressive change of the production frontier related to policymaking. This application attempts to demonstrate how crucial it is to take uncertainties into account when comparing the performance of different systems over periods of time. The developed model enables us to consider the uncertainty existing in COVID-19 pandemic. The proposed model can handle more accurately the uncertainty during the pandemic. Thus, the result could be more reliable, which can benefit decision-makers in regard to performance improvement.

An inverse data envelopment analysis model to consider ratio data and preferences of decision-makers

Abstract Inverse data envelopment analysis (DEA) determines the optimal level of inputs and/or outputs of decision-making units (DMUs) to reach efficiency targets. This paper presents a new inverse DEA model for determining minimum inputs for working capital management. The proposed model is employed in the Indian textile industry to calculate working capital efficiency. Given the working capital efficiency, the decision maker’s preferences will be estimating the change in inputs when outputs increase. Furthermore, unlike the standard inverse DEA model, this article discusses the inverse DEA model when negative ratio data exist. The DEA model requires additional attention when ratio data are present; therefore, a novel inverse DEA ratio model is proposed. The input targets obtained from the proposed model are less than the standard inverse DEA model. Also, the proposed model is a closer estimate of the production probability set for ratio data.

Assessing most productive scale size with fuzzy stochastic data envelopment analysis

Classic data envelopment analysis (DEA) is a linear programming method for evaluating the relative efficiency of decision making units (DMUs) that uses multiple inputs to produce multiple outputs. In the classic DEA model inputs and outputs of DMUs are deterministic, while in the real world, are often fuzzy, random, or fuzzy-random. Many researchers have proposed different approaches to evaluate the relative efficiency with fuzzy and random data in DEA. In many studies, the most productive scale size (mpss) of decision making units has been estimated with fuzzy and random inputs and outputs. Also, the concept of fuzzy random variable is used in the DEA literature to describe events or occurrences in which fuzzy and random changes occur simultaneously. This paper has proposed the fuzzy stochastic DEA model to assess the most productive scale size of DMUs that produce multiple fuzzy random outputs using multiple fuzzy random inputs with respect to the possibility-probability constraints. For solving the fuzzy stochastic DEA model, we obtained a nonlinear deterministic equivalent for the probability constraints using chance constrained programming approaches (CCP). Then, using the possibility theory the possibilities of fuzzy events transformed to the deterministic equivalents with definite data. In the final section, the fuzzy stochastic DEA model, proposed model, has been used to evaluate the most productive scale size of sixteen Iranian hospitals with four fuzzy random inputs and two fuzzy random outputs with symmetrical triangular membership functions.

Uncertain Data Envelopment Analysis for Cross Efficiency Evaluation with Imprecise Data

Self evaluation and peer evaluation in data envelopment analysis (DEA) are effective means to comprehensively reflect the efficiencies of decision-making units (DMUs). However, when some of the inputs and outputs of DMUs cannot be accurately observed, the traditional evaluation methods will lose their applicability. This paper attempts to treat the imprecise inputs and outputs as uncertain variables based on uncertainty theory and hence to propose a new uncertain DEA model for cross-efficiency evaluation via the evaluation of both self efficiency and peer efficiency. Moreover, the equivalent form and the proof of the new model are also presented for accurate calculation. Finally, a numerical example is given to illustrate the evaluation results.

Measurement of Coordinated and Coupled Development and Evaluation of Sustainable Development for Marine Economic-Ecological Complex System

The development of marine economy has stimulated the need for marine natural products and services, as well as the demand and utilization intensity of marine resources. As a result, the coastal regions start to discharge more and more pollutants, posing a serious threat to marine ecoenvironment. Because of the interactions between marine economy and marine ecology, it is of practical significance to study the marine economic-ecological complex system (MEECS). However, the relevant studies have several common defects: the incomplete data statistics system, the limited attention on development law or action mechanism, and the lack of long-term quantitative and empirical analysis. To overcome these defects, this paper tries to measure the coordinated and coupled development (CCD) and evaluate the sustainable development of MEECS. Specifically, an ecology-dominated coordinated development model was proposed for the complex system, and a differential equation model was established to describe the dynamic coordinated development of the complex system. Through data envelopment analysis (DEA), the sustainable development of the complex system was evaluated based on its input-output efficiency. Through experiments, the outputs of decision-making units (DMUs) of our model were obtained, and the development of the subsystems in MEECS was evaluated comprehensively to verify the effectiveness of our algorithm.

Performance management of OECD countries on Covid-19 pandemic: a criticism using data envelopment analysis models

Purpose The Covid-19 pandemic spread rapidly around the world and required strict restriction plans and policies. In most countries around the world, the outbreak of the disease has been serious and has greatly affected the health system and the economy. The factors such as the number of patients with chronic diseases, the number of people over 65 years old, hospital facilities, the number of confirmed Covid-19 cases, the recovering Covid-19 cases and the number of deaths affect the rate of spread of Covid-19. This study aims to evaluate the performances of 21 Organisation for Economic Co-operation and Development (OECD) countries against the Covid-19 outbreak using three data envelopment analysis (DEA) models. Design/methodology/approach In this study, the performance of 21 OECD countries to manage the Covid-19 process has been analysed weekly via DEA which is widely used in various practical problems and provides a general framework for efficiency evaluation problems using the inputs and outputs of decision-making units. Findings The analysis showed that 11 countries out of 21 countries were efficient for selected weeks. According to the DEA results from the 20-week review (09 April 2020–20 August 2020), information about the course of the epidemic prevention and the normalization process for any country can be obtained. Originality/value In this study, due to the problem of the discrimination power of DEA, the cross-efficiency model and the super-efficiency model also used. In addition, the output-oriented model was preferred in this study for Covid-19 management efficiency.

Uncertain Random Data Envelopment Analysis: Efficiency Estimation of Returns to Scale

Evaluating efficiency according to the different states of returns to scale (RTS) is crucial to resource allocation and scientific decision for decision-making units (DMUs), but this kind of evaluation will become very difficult when the DMUs are in an uncertain random environment. In this paper, we attempt to explore the uncertain random data envelopment analysis approach so as to solve the problem that the inputs and outputs of DMUs are uncertain random variables. Chance theory is applied to handling the uncertain random variables, and hence, two evaluating models, one for increasing returns to scale (IRS) and the other for decreasing returns to scale (DRS), are proposed, respectively. Along with converting the two uncertain random models into corresponding equivalent forms, we also provide a numerical example to illustrate the evaluation results of these models.

Ecological Evaluation of Industrial Parks Using a Comprehensive DEA and Inverted-DEA Model

Data envelopment analysis (DEA) and inverted data envelopment analysis (inverted-DEA) are used so that the desirable and undesirable outputs of decision-making units (DMUs) exist simultaneously. We developed a new approach based on the concept of utilizing both DEA and inverted-DEA to enhance the discrimination power of DMUs with undesirable outputs. DMUs are ranked by the Z-score method and classified based on the efficiency scores of DEA and inverted-DEA. Then, the characteristics of the DMUs are analyzed based on the classification result. This paper performs an efficiency evaluation of 21 industrial parks in China in 2017 using this new approach. The overall evaluation results indicate that the proposed new approach increases the discrimination ability in this empirical study.

A unified extension of super-efficiency in additive data envelopment analysis with integer-valued inputs and outputs: an application to a municipal bus system

Conventional data envelopment analysis (DEA) may generate the non-integer targets for integer-valued inputs and outputs of decision-making units (DMUs). To derive the convincing projections, integer-valued DEA has attracted much attention. Given the integrality restriction, Du et al. (Eur J Oper Res 218(1):186–192, 2012) proposed the super-efficiency approach consisting of additive integer-valued and additive super-efficiency integer-valued models for the differentiation of efficient DMUs, thereby raising the discriminatory power. This paper extends their approach to develop a simpler but stricter version, which we refer to as the unified additive super-efficiency model. The newly-developed model has three advantages. First, the slacks of input excess, input saving, output shortage and output surplus can be directly computed in a single program to obtain the efficiencies of inefficient DMUs and super-efficiencies of efficient DMUs. Secondly, it suggests the strongly Pareto-efficient projections for efficient DMUs. Finally, the identified super-efficiencies allow for the property of continuity. A comparison of the proposed model, with Du et al.’s (2012) and standard additive super-efficiency approaches is discussed using a numerical example. In addition, the applicability of the proposed model is illustrated by a data set covering 13 bus companies operating in the municipal bus system of Taichung. Our work not only provides managerial insights into the primary sources of inefficiency and super-efficiency but also contributes to the current understanding of how super-efficiency would be effectively and accurately measured in the presence of integer-valued data.

Preserve the Relative Efficiency Values: An Inverse Data Envelopment Analysis with Imprecise Data

Data envelopment analysis (DEA) measures the relative efficiency of a set of decision-making units (DMUs). With the advent of DEA models, inverse DEA is applied to modify the inputs and outputs of DMUs without affecting their efficiency. InvDEA models are applied when the decision makers need to change the input-outputs of the DMUs to a certain level without affecting their efficiency. InvDEA models are extended when the input-output data are imprecise and available in the intervals form. However, regarding uncertainty, complete information about the input-output data is not available in many real world applications. To address this problem, this study deals with the InvDEA problem in an uncertain environment. Therefore, two multi-objective linear programming (MOLP) models are proposed to estimate the required upper/lower inputs, producing requested outputs and preserving the efficiency scores. The proposed models preserve the upper/lower efficiency scores of all considered DMUs. A numerical example illustrates the proposed methodology.

Cost, Revenue and Profit Efficiency Models in Generalized Fuzzy Data Envelopment Analysis

One of the most important information given by data envelopment analysis models is the cost, revenue and profit efficiency of decision making units (DMUs). Cost efficiency is defined as the ratio of minimum costs to current costs, while revenue efficiency is defined as the ratio of maximum revenue to current revenue of the DMU. This paper presents a framework where data envelopment analysis (DEA) is used to measure cost, revenue and profit efficiency with fuzzy data. In such cases, the classical models cannot be used, because input and output data appear in the form of ranges. When the data are fuzzy, the cost, revenue and profit efficiency measures calculated from the data should be uncertain as well. Fuzzy DEA models emerge as another class of DEA models to account for imprecise inputs and outputs for DMUs. Although several approaches for solving fuzzy DEA models have been developed, numerous deficiencies including the α-cut approaches and types of fuzzy numbers must still be improved. This scheme embraces evaluation method based on vector for proposed fuzzy model. This paper proposes generalized cost, revenue and profit efficiency models in fuzzy data envelopment analysis. The practical application of these models is illustrated by a numerical example.

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.

Input-output Efficiency Set Models of Interval Number DEA

The system relative Effectiveness evaluation under uncertainty factors is the frontier of DEA Theory, research on DEA model with fuzzy elements can help resolve problems of the uncertainty input-output in systematic evaluation. Li and Yan proposed a new to improve the Efficiency Index of Input-output DEA model. However, such model did not consider situation when input-output are uncertain number . In the practice of the economic system evaluation, due to various restrictions, people often use certain methods (such as prediction, simulation, etc.) to obtain the interval estimate of evaluation index based on their own experience and prior knowledge. In current DEA literatures, L-R Interval DEA (IDEA) model based on partial order theories of L-R fuzzy numbers was proposed, and the relationship between fuzzy DEA efficiency Index and deterministic one was discussed by Zhen and Wu . They also discussed the sufficient condition of decision making units (DMUs) in the L-R type DEA model . Zhou et al. discussed the ideas of the Interval CR model (ICR) based on CR (the basic and first DEA model) , and used a simple extension of BCC model to construct a sorting method for interval input-output DMUs [5, , the discussion from Interval DEA from maximum and minimum limit directions in their algorithm is worth learning, but they did not consider the model when all of the inputs and outputs of DMUs are interval numbers. In summary, the reported literature discussed the DEA Efficiency under the most extreme cases, so the corresponding model does not apply to most case in practice. Therefore, this paper proposed a new interval DEA Efficiency Set model to further study the relative effectiveness of DMUs when inputs and outputs are interval numbers.

Determining sources of relative inefficiency in heterogeneous samples: Methodology using Cluster Analysis, DEA and Neural Networks

Data Envelopment Analysis (DEA) is a powerful data analytic tool that is widely used by researchers and practitioners alike to assess relative performance of Decision Making Units (DMU). Commonly, the difference in the scores of relative performance of DMUs in the sample is considered to reflect their differences in the efficiency of conversion of inputs into outputs. In the presence of scale heterogeneity, however, the source of the difference in scores becomes less clear, for it is also possible that the difference in scores is caused by heterogeneity of the levels of inputs and outputs of DMUs in the sample. By augmenting DEA with Cluster Analysis (CA) and Neural Networks (NN), we propose a five-step methodology allowing an investigator to determine whether the difference in the scores of scale heterogeneous DMUs is due to the heterogeneity of the levels of inputs and outputs, or whether it is caused by their efficiency of conversion of inputs into outputs. An illustrative example demonstrates the application of the proposed methodology in action.

Compensation analysis with additive DEA model

PurposeTo develop a method of compensation analysis based on the additive data envelopment analysis model.Design/methodology/approachIt is a common assumption in current target setting literature that outputs of decision making units (DMUs) are generated simultaneously. In practice, outputs of DMUs may be generated consecutively, and targets of posterior outputs may need to be adjusted to keep a DMU efficient when the anterior output cannot reach the previously set output target. The proposed method determines a compensation rate among consecutive outputs, which is applied to keep a DMU efficient when the decrease of an anterior output exceeds its stability region. This compensation analysis is also extended to consecutive inputs.FindingsSufficient and necessary conditions for preserving efficiency upon output compensation are presented.Research limitations/implicationsThe compensation analysis when multiple anterior outputs decrease from their previously set targets is the main limitation, and needs further investigation.Practical implicationsThe paper is a useful method for decision maker to set target consecutively.Originality/valueThe paper defines a new target setting (adjusting) problem, in which targets of posterior outputs may need to be adjusted to keep a DMU efficient if an anterior output of the DMU decreases from its previously set target. Theoretical analyses of the compensation analysis are provided.

Performance evaluation using data envelopment analysis in the presence of time lags

Data Envelopment Analysis (DEA) is a methodology that computes efficiency values for decision making units (DMU) in a given period by comparing the outputs with the inputs. In many applications, inputs and outputs of DMUs are monitored over time. There might be a time lag between the consumption of inputs and the production of outputs. We develop an approach that aims to capture the time lag between the outputs and the inputs in assigning the efficiency values to DMUs. We propose using weight restrictions in conjunction with the model. Our computational results on randomly generated problems demonstrate that the developed approach works well under a large variety of experimental conditions. We also apply our approach on a real data set to evaluate research institutions.

Metal Machinability Evaluation with DEA Method

Data envelopment analysis (DEA) evaluation system of metal materials was established. Evaluated metal materials were regarded as decision making units (DMUs). Property parameters of metal materials were selected as inputs of DMUs, and machining process parameters were selected as outputs of DMUs. Input and output data sequences could be obtained through data processing operations. Mathematics programming model was founded and optimal values of all the evaluated materials were calculated based on the model. Machinabilities of metal materials could be evaluated by comparing the optimal values. Taken 1Cr18Ni9Ti, GCr15, Q235, 45# and LY11 for example, machinabilities of five metal materials were ranked. Research results suggest that DEA method can synthetically consider the relationship between property parameters and machining process parameters. DEA is proved to be a reasonable and available method to evaluate metal material machinability.

Sensitivity Analysis of an Efficient DMU in DEA Model with Variable Returns to Scale (VRS)

In this paper we consider the Variable Returns to Scale (VRS) Data Envelopment Analysis (DEA) model. In a DEA model each Decision Making Unit (DMU) is classified either as efficient or inefficient. Changes in inputs or outputs of any DMU can alter its classification, i.e. an efficient DMU can become inefficient and vice versa. The goal of this paper is to assess changes in inputs and outputs of an extreme efficient DMU that will not alter its efficiency status, thus obtaining the region of efficiency for that DMU. Namely, a DMU will remain efficient if and only if after applying changes this DMU stays in that region. The representation of this region is done using an iterative procedure. In the first step an extended DEA model, whereby a DMU under evaluation is excluded from the reference set, is used. In the iterative part of the procedure, by using the obtained optimal simplex tableau we apply parametric programming, thus moving from one facet to the adjacent one. At the end of the procedure we obtain the complete region of efficiency for a DMU under consideration.

A polynomial-time algorithm for finding ε in DEA models

This paper presents a new algorithm for computing the non-Archimedean ε in DEA models. It is shown that this algorithm is polynomial-time of O( n), where n is the number of decision making units (DMUs). Also it is proved that using only inputs and outputs of DMUs, the non-Archimedean ε can be found such that, the optimal values of all CCR models, which are corresponding to all DMUs, are bounded and an assurance value is obtained.