Stochastic Data Envelopment Analysis Model Research Articles

A hybrid stochastic data envelopment analysis and decision tree for performance prediction in retail industry

Assessing the retail industry's efficiency is pivotal for economic growth and corporate productivity. This study employs a novel approach, utilizing a regression-based Stochastic Data Envelopment Analysis (SDEA) model, Balanced Scorecard (BSC), and Decision Tree. The integration of these methods is a pioneering effort in the retail sector. This is a data-driven decision-making framework, aiding managers in predicting efficient and inefficient Decision-Making Units (DMUs). Results from a case study in 44 retail store chains in Iran indicate that the accuracy of the SDEA model is 99%. The Decision Tree highlights low branch efficiency due to a low customer count, a unique finding in comparison to prior studies.

Efficiency assessment of public sector management and culture-led urban regeneration using the enhanced Russell-based directional distance function with stochastic data

Generic data envelopment analysis (DEA) models are based on deterministic input and output. However, input and output vectors are often interrupted by random factors, such as measurement errors and data noise, in real economic situations. This study proposes a new chance-constrained network DEA model based on the modified directional distance function (DDF) and enhanced Russell measure (ERM) model for assessing government management and culture-led urban regeneration. In addition to exploring the randomness of data, this study integrates the advantages of both ERM and DDF and considers the inefficiency level from a non-oriented viewpoint, the direction vector, and each input and output simultaneously. Each input and output of the two production stages can use non-radials to measure efficiency. Results show that the urban-rural gap has gradually widened since 2015. To validate the legitimacy of the model, this study utilizes the bootstrapping method to verify the results of the stochastic network DEA model and the conventional two-stage network DEA approach. This study also considers different alpha values as basis for comparison to confirm whether the results obtained differ by uncertainty level.

A stochastic approach for evaluating production planning efficiency under uncertainty

<span lang="EN-US">Planning production is an essential component of the decision-making process, which has a direct bearing on the effectiveness of production systems. This study’s objective is to investigate the efficiency performance of decision-making units (DMU) in relation to production planning issues. However, the production system in a manufacturing environment is frequently subject to uncertain situations, such as demand and labor, and this can have an effect not only on production but also on profit. The robust stochastic data envelopment analysis model was proposed in this study with maximizing the number of outputs as the objective function thus means of handling uncertainty in input and output in production planning problems. This model, which is based on stochastic data envelopment analysis and a method of robust optimization, was proposed with the intention of providing an efficient plan of production for each DMU of stage production. The model is applied to small and medium-sized businesses (SMEs), with inputs consisting of the cost of labor, the number of customers, and the quantity of raw materials, and the output consisting of profit and revenue. It has been demonstrated through implementation that the proposed model is both efficient and effective.</span>

Marginal rates of technical changes and impact in stochastic data envelopment analysis: An application in power industry

Marginal rates of technical changes and marginal impact are useful tools to calculate the trade-offs between production factors in a production process. In the data envelopment analysis (DEA) framework, the calculation of these trade-offs (marginal rates of technical substitution, marginal rates of transformation, marginal productivity and marginal costs) using the existing deterministic approaches may be sensitive to uncertainty and variability of the input and output data. Therefore, in this contribution, we introduce a stochastic DEA model based on chance-constrained programming to develop a measure of the marginal rates of firms facing data uncertainty. In this contribution, chance-constrained programming is used to develop a procedure to calculate these trade-offs. Our proposed stochastic procedure is applied to sample data on 31 power plants. The empirical results on marginal rates obtained from our proposed stochastic programs revealed that the results are different at various tolerance levels of chance constraints.

A novel stochastic semi-parametric frontier-based three-stage DEA window model to evaluate China's industrial green economic efficiency

Traditional three-stage data envelopment analysis (DEA) models do not consider the problem of functional form and multicollinearity. This study develops a new stochastic semi-parametric frontier-based three-stage DEA model. The frontier incorporates the effects of both external environmental factors and statistical noise on efficiency. We adopt the StoNED (stochastic non-smooth envelopment of data) approach and use the quasi-likelihood estimation method to estimate the parameters of inefficiency term and stochastic noise. We conduct Monte Carlo experiments to examine the performance of the new frontier under different circumstances. Our results show that the new frontier provides a more realistic and accuracy estimator for efficiency measures. An empirical analysis is used to evaluate green economic efficiency (GEE) in China. We empirically compare different models and the results show that external environmental factors cause significant differences. We provide each provincial average GEE evaluated by the improved QLE-StoNED model, which are outperforms compared with other recently developed estimators. And a gradient difference emerges in the GEE among the eastern, central and western areas of China. The results also offer practical implications for the harmonious development of industrial production and a green economy in China.

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.

Improving weak efficiency frontier in a variable returns to scale stochastic data envelopment analysis model

The conventional stochastic data envelopment analysis (SDEA) model suffers from biased efficiency scores for units located at the weak efficient frontier or compared to the weak frontier. This study modifies the weak efficient hyperplane(s) while maintaining the general production function by restricting the gradients of weak efficient hyperplanes in the original model using facet analysis. Empirical analysis on environmental efficiency of sustainable development goals validates the results of the modification. Results of the modified model compared to the conventional model show change in efficiency scores of weak efficient units and those compared to the weak part of the frontier while the efficiency scores of the strong efficient frontier remain the same. Furthermore, the proposed model shows greater discriminatory power compared to the conventional model, hence, providing a reliable benchmark and improvement strategy post efficiency analysis.

Estimation of portfolio efficiency via stochastic DEA

Traditional data envelopment analysis (DEA) and diversification DEA are two common data-driven evaluation approaches, which have been widely used in the estimation of portfolio efficiency. The above two DEA approaches usually use the risk and expected return indicators to build the input-output process of portfolios. However, this input-output process derived from the risk and expected return is inconsistent with the actual investment process, since the real input should be the initial wealth, and the output should be the terminal wealth. To address this problem, we propose a novel input-output process based on the initial and terminal wealth of portfolios. We transform the terminal wealth into the rate of return and construct a stochastic attainable set by using portfolio returns. We provide three deterministic estimation approaches to deal with the stochastic attainable set, and then obtain three deterministic attainable sets. We further propose three stochastic DEA models to estimate the portfolio efficiency by using the above three deterministic attainable sets. Finally, we provide an empirical analysis to assess the portfolio efficiency of 50 open-ended funds in China. The results show that there are some differences in the portfolio efficiency and its ranking between the proposed DEA models and the existing DEA models, which further verify the rationality of the proposed DEA models.

A stochastic data envelopment analysis approach for multi-criteria ABC inventory classification

ABSTRACT One of the common methods for classifying inventory items is ABC classification approach. In many cases, the data might be stochastic. In the current study, using stochastic data envelopment analysis model, we present a new approach to categorize inventory items given stochastic data and nature of criteria. Then, a new stochastic mixed integer programming model is proposed to forecast classes of the new inventory items. The proposed stochastic mixed integer programming model does not impose subjective judgment on the classification of inventory items and can be used for multi-group classification. The developed approach can classify inventory items and forecast the class of new items with both qualitative and quantitative criteria. The applicability of developed stochastic data envelopment analysis and stochastic mixed integer programming models is demonstrated by a case study.

A Modified Russell Measure for Estimating Efficiency Changes in the Presence of the Undesirable Outputs and Stochastic Data

Although data envelopment analysis (DEA) assumes deterministic data, a great volume of data might be stochastic. The global Malmquist productivity index (GMPI) is a highly effective instrument for productivity analysis in DEA. This paper extends GMPI in the presence of stochastic data. Our new stochastic DEA model is a chance-constrained programming model, which is converted to a deterministic programming problem with a linear objective function and quadratic constraints. For efficiency evaluation purposes, in this paper, the weak disposability principle is used to model Russell’s measure in the presence of undesirable outputs. The main contribution of this paper is to develop a global Russell model with stochastic data. A case study is presented to illustrate the applicability of the proposed models.

Developing new data envelopment analysis models to evaluate the efficiency in Ontario Universities

Data Envelopment Analysis (DEA) is a popular operations research technique for determining the relative efficiency of organizations. The main goal of this study is to develop a unique stochastic DEA model to evaluate the efficiency of Ontario universities in Canada based on two inputs (i.e., Expenditures and Number of Academic Staff) and four outputs (i.e., Tri-council Grants, Student's Satisfaction Level, Enrolment (number of students), and Number of Publications). The satisfaction level is a unique parameter that has not previously been applied in this field. This study focuses on the stochastic model because of its ability to handle uncertainty in the parameters of the optimization model. Real data are utilized and applied in this research. Three types of universities are investigated including medical/doctoral universities, comprehensive universities, and primarily undergraduate universities. According to the results, there is some room for improvement of the efficiency in Ontario universities. Furthermore, the results of this study show that the selection of inputs and outputs plays a crucial role in determining the ranks of universities using DEA. The results also are discussed with details for each category. For instance, increasing the number of publications is a prominent factor to rise the efficiency scores of undergraduate universities.

Efficiency evaluation with cross-efficiency in the presence of undesirable outputs in stochastic environment

Data envelopment analysis (DEA) is a useful tool for efficiency evaluation of decision making units (DMUs). The classical DEA models deal with exact data while in real world problems we concern with uncertain data such as fuzzy, stochastic and etc. In this paper, using input oriented CCR model (ICCR) in the presence of undesirable outputs with specific risk (α), a new stochastic model called Expected Ranking Criterion is proposed. Based on this, the stochastic cross-efficiency evaluation is presented for robust ranking and discrimination of DMUs. Given the non-uniqueness of resulting optimal solutions, a model is introduced for ranking by which stochastic cross-efficiency is performed using aggressive approach. The proposed model provides ranking of all DMUs whereas current stochastic DEA models in literature fail in this regard. Finally, the proposed models are implemented for 32 thermal power plants with stochastic inputs and undesirable outputs. The results show the applicability of proposed models.

A Unified Mathematical Model for Stochastic Data Envelopment Analysis

Efficiency measurement is one aspect of organizational performance that managers are usually interested in determining. Data envelopment analysis (DEA) is a powerful quantitative tool that provides a means to obtain useful information about the efficiency and performance of organizations and all sorts of functionally similar, relatively autonomous operating units. DEA models are either with a constant rate of return (CRS) or variable return to scale (VRS). Furthermore, the models could be input-oriented or output-oriented. In many real-life applications, observations are usually random in nature; as a result, DEA efficiency measurement may be sensitive to such variations. The purpose of this study was to develop a unified stochastic DEA model that handles different natures of variables independently (random and deterministic) and can be adapted to model both input/output-oriented problems, whether it is CRS or VRS. The chance-constrained approach was adopted to handle the stochastic variables that exist in the model. The developed model is implemented through an illustrative example.

Measuring the efficiency of two-stage network processes: A satisficing DEA approach

Regular network data envelopment analysis (DEA) models deal with evaluating the performance of a set of decision-making units with a two-stage construction in the context of a deterministic data set. In the real world, however, observations may display a stochastic behavior. To the best of our knowledge, despite the existing research done with different data types, studies on two-stage processes with stochastic data are still very limited. This article proposes a two-stage network DEA model with stochastic data. The stochastic two-stage network DEA model is formulated based on the satisficing DEA models of chance-constrained programming and the leader–follower concepts. According to the probability distribution properties and under the assumption of the single random factor of the data, the probabilistic form of the model is transformed into its equivalent deterministic linear programming model. In addition, the relationship between the two stages as the leader and the follower, respectively, at different confidence levels and under different aspiration levels, is discussed. The proposed model is applied to a real case concerning 16 commercial banks in China in order to confirm the applicability of the proposed approach.

Multi-Attribute Decision Making Based on Stochastic DEA Cross-Efficiency with Ordinal Variable and Its Application to Evaluation of Banks’ Sustainable Development

Multi-attribute decision making (MADM) is a cognitive process for evaluating data with different attributes in order to select the optimal alternative from a finite number of alternatives. In the real world, a lot of MADM problems involve some random and ordinal variables. Therefore, in this paper, a MADM method based on stochastic data envelopment analysis (DEA) cross-efficiency with ordinal variable is proposed. First, we develop a stochastic DEA model with ordinal variable, which can derive self-efficiency and the optimal weight of each attribute for all decision making units (DMUs). To further improve its discrimination power, cross-efficiency as a significant extension is proposed, which utilizes peer DMUs’ optimal weight to evaluate the relative efficiency of each alternative. Then, based on self-efficiency and cross-efficiency of all DMUs, we construct corresponding fuzzy preference relations (FPRs) and consistent fuzzy preference relations (FPRs). In addition, we obtain the priority weight vector of all DMUs by utilizing the row wise summation technique according to the consistent FPRs. Finally, we provide a numerical example for evaluating operation performance of sustainable development of 15 listed banks in China, which illustrates the feasibility and applicability of the proposed MADM method based on stochastic DEA cross-efficiency with ordinal variable.

A Novel Stochastic Two-Stage DEA Model for Evaluating Industrial Production and Waste Gas Treatment Systems

In recent decades, the high-speed development in China has caused serious air pollution in China. The present paper proposes a stochastic data envelopment analysis (DEA) model based on a general two-stage structure with comprehensively considering the randomness in both desirable and undesirable outputs to calculate the environmental efficiency of the industry system. The new proposed model is more applicable to practical system, and is applied to evaluate the performance of production and waste gas treatment in the industrial sector for China’s regions along the “One Belt and One Road” in 2015. The results show that about half of the regions along “One Belt and One Road” in China are inefficient, where the performance on waste gas treatment is significantly worse than that of industrial production. Further, the managers should take different strategies for efficiency improvement in different areas because of the obvious differences in efficiency scores, in which the regions in the southeast area should pay more attention to improving waste gas treatment efficiency while that in the northwest area need to focus on industrial production efficiency.

Stochastic p-robust DEA efficiency scores approach to banking sector

PurposeThe purpose of this paper is to present a stochastic p-robust data envelopment analysis (DEA) model for decision-making units (DMUs) efficiency estimation under uncertainty. The main contribution of this paper consists of the development of a more robust system for the estimation of efficiency in situations of inputs uncertainty. The proposed model is used for the efficiency measurement of a commercial Iranian bank.Design/methodology/approachThis paper has been arranged to launch along the following steps: the classical Charnes, Cooper, and Rhodes (CCR) DEA model was briefly reviewed. After that, the p-robust DEA model is introduced and then calculated the priority weights of each scenario for CCR DEA output oriented method. To compute the priority weights of criteria in discrete scenarios, the analytical hierarchy analysis process (AHP) is used. To tackle the uncertainty of experts’ opinion, a synthetic technique is applied based on both robust and stochastic optimizations. In the sequel, stochastic p-robust models are proposed for the estimation of efficiency, with particular attention being paid to DEA models.FindingsThe proposed method provides a more encompassing measure of efficiency in the presence of synthetic uncertainty approach. According to the results, the expected score, relative regret score and stochastic P-robust score for DMUs are obtained. The applicability of the extended model is illustrated in the context of the analysis of an Iranian commercial bank performance. Also, it is shown that the stochastic p-robust DEA model is a proper generalization of traditional DEA and gained a desired robustness level. In fact, the maximum possible efficiency score of a DMU with overall permissible uncertainties is obtained, and the minimal amount of uncertainty level under the stochastic p-robustness measure that is required to achieve this efficiency score. Finally, by an example, it is shown that the objective values of the input and output models are not inverse of each other as in classical DEA models.Originality/valueThis research showed that the enormous decrease in maximum possible regret makes only a small addition in the expected efficiency. In other words, improvements in regret can somewhat affect the expected efficiency. The superior issue this kind of modeling is to permit a harmful effect to the objective to better hedge against the uncertain cases that are commonly ignored.

Two-stage DEA for Bank Efficiency Evaluation Considering Shared Input and Unexpected Output Factors

With the increasingly fierce market competition, only by relying on high-quality products and high customer satisfaction can enterprises survive in the fierce competition. Among many evaluation methods, Data Envelopment Analysis (DEA), as a non-parametric statistical method to effectively deal with multi-input and multi-output problems, has received more and more attention in evaluating the relative efficiency of decision-making units. In the process of bank efficiency evaluation based on DEA method, there will be a situation that banks have both dual role factors and unexpected output factors. The Two-stage DEA model provides an effective analysis method to solve the problem of bank efficiency evaluation of complex organizational structure. In order to evaluate the efficiency of unexpected output with uncertain information, a stochastic DEA model of unexpected output is established.

Fuzzy stochastic Data Envelopment Analysis with application to NATO enlargement problem

Data Envelopment Analysis (DEA) is a widely used technique for measuring the relative efficiencies of Decision Making Units (DMUs) with multiple deterministic inputs and multiple outputs. However, in real-world problems, the observed values of the input and output data are often vague or random. Indeed, Decision Makers (DMs) may encounter a hybrid uncertain environment where fuzziness and randomness coexist in a problem. Hence, we formulate a new DEA model to deal with fuzzy stochastic DEA models. The contributions of the present study are fivefold: (1) We formulate a deterministic linear model according to the probability–possibility approach for solving input-oriented fuzzy stochastic DEA model, (2) In contrast to the existing approach, which is infeasible for some threshold values; the proposed approach is feasible for all threshold values, (3) We apply the cross-efficiency technique to increase the discrimination power of the proposed fuzzy stochastic DEA model and to rank the efficient DMUs, (4) We solve two numerical examples to illustrate the proposed approach and to describe the effects of threshold values on the efficiency results, and (5) We present a pilot study for the NATO enlargement problem to demonstrate the applicability of the proposed model.

Haze Influencing Factors: A Data Envelopment Analysis Approach.

This paper investigates the meteorological factors and human activities that influence PM2.5 pollution by employing the data envelopment analysis (DEA) approach to a chance constrained stochastic optimization problem. This approach has the two advantages of admitting random input and output, and allowing the evaluation unit to exceed the front edge under the given probability constraint. Furthermore, by utilizing the meteorological observation data incorporated with the economic and social data for Jiangsu Province, the chance constrained stochastic DEA model was solved to explore the relationship between the meteorological elements and human activities and PM2.5 pollution. The results are summarized by the following: (1) Among all five primary indexes, social progress, energy use and transportation are the most significant for PM2.5 pollution. (2) Among our selected 14 secondary indexes, coal consumption, population density and civil car ownership account for a major portion of PM2.5 pollution. (3) Human activities are the main factor producing PM2.5 pollution. While some meteorological elements generate PM2.5 pollution, some act as influencing factors on the migration of PM2.5 pollution. These findings can provide a reference for the government to formulate appropriate policies to reduce PM2.5 emissions and for the communities to develop effective strategies to eliminate PM2.5 pollution.