Interval Data Envelopment Analysis Model Research Articles

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Introduction: One of the principal requirements for sustainable agriculture is efficient energy use. Energy use in agriculture has been increasing in response to the growing global population, limited arable land and desire for higher living standards. It should be noted that agriculture contributes significantly to atmospheric GHG emissions, with 10-12% of the net global CO2 (carbon dioxide) emissions. The scientific community believes global warming will pose one of the major environmental challenges in the future, with the bulk of GHG originating from fossil fuel consumption. Kiwifruit is an economically important fruit crop in northern Iran, because the northern region of Iran is a suitable, natural habitat for kiwifruit cultivation. The high kiwifruit production in Iran has reached a point that Iran is now well-known on global markets and in recent years this fruit has contributed a large share to agricultural exports. More recently, Mazandaran horticulturists have been encouraged to produce more kiwifruit. Increased production leads to greater energy consumption by Iranian kiwifruit orchards due to the added application of inputs, such as fertilizers and fuel. Besides, where there is no clear energy consumption pattern in agricultural production, especially fruit orchards, a lot of energy dissipates in the fruit production cycle. Therefore, it seems necessary to provide a model for the energy consumption of kiwifruit orchards in Mazandaran Province to prevent excessive energy utilization. Energy analysis is one of the methods has been used to evaluate the status of agricultural production. In this regard, many researchers have used Data Envelopment Analysis (DEA) for optimization the energy consumption in agricultural productions. DEA is recognized as a methodology widely used to evaluate the relative efficiency of a set of decision-making units (DMUs) involved in a production process. Although DEA is a powerful tool to measure efficiency but the uncertainty in the applied data in this model is inevitable and there is need to use different models that be able to control this uncertainty. Materials and Methods: In this study, in order to determine the efficiency of kiwifruit orchards in Mazandaran province and in terms of uncertainty of input data, the Robust Data Envelopment Analysis model (RDEA) and Fuzzy Interval Data Envelopment Analysis model (FIDEA) were used. The method incorporates the degree of conservatism in the maximum probability bound for constraint violation. The required data were collected by distributing and completing a questionnaire and face-to-face interview using random sampling method in 1397-98. Results and Discussion: The results showed that the average technical efficiency of all kiwi fields in RDEA model at three levels of probability include: 10, 50 and 100% is equal to 0.93, 0.96 and 0.98%, respectively. The results of FIDEA model showed that if the level of parameter α (optimal use of production factors) increases, the average efficiency of kiwi fields will increase. The highest energy savings are related to chemical pesticides and the lowest amount of savings is related to the chemical fertilizers and electricity inputs, respectively. So, holding the training courses on the correct and optimal use of production inputs from an economic and managerial point of view and improving the level of knowledge of farmers and factors involved in kiwi production in Mazandaran province can improve the efficiency and save energy consumptions. Conclusion: Evaluating the performance of many activities by a traditional DEA approach requires precise input and output data. However, input and output data in real-world problems are often imprecise or vague. To deal with imprecise data, this study uses RDEA and FIDEA approaches as a way to quantify vague data in DEA models. It is shown that the approaches can be a useful tool in DEA models without introducing additional complexity into the problem. A case study of kiwifruit orchard units is presented to illustrate the reliability and flexibility of the models. As a result, efficiency decreases as the constraint violation probability increased. Additionally, the RDEA approach provides both a deterministic guarantee about the efficiency level of the model, as well as a probabilistic guarantee that is valid for all symmetric distributions.

A methodology for supplier selection under the curse of dimensionality problem based on fuzzy quality function deployment and interval data envelopment analysis.

Supplier selection is an important decision-making problem, which involves many quantitative and qualitative factors incorporating vagueness and imprecision. This study proposes a novel fuzzy multi-criteria decision-making framework for supplier selection, which integrates quality function deployment (QFD) and interval data envelopment analysis (DEA). The proposed methodology allows for considering the relationships among the product features and supplier evaluation criteria (SEs) and the impacts of inner dependence among SEs by constructing a house of quality (HOQ). Considering that the number of supplier evaluation indicators is greater than the number of suppliers in some cases, the curse of dimensionality problem usually exists. To solve this problem, we combine the HOQ, interval DEA models, and forward-stepwise selection approach to screen supplier evaluation indicators and select the best supplier(s). Through the two-stage supplier selection method, we can achieve the double screening of indicators and determine the final supplier(s). Finally, the application of the proposed framework is demonstrated through a numerical example and a sensitivity analysis is also carried out to verify the stability of the proposed methodology. This study focuses on supplier selection based on the combination of fuzzy QFD and interval DEA, and also provide a new two-phase methodology for DEA indicator screening.

The Interval Efficiency Evaluation Model Based on Incentive Compatibility

Data envelopment analysis (DEA) is a method of measuring the efficiency of peer decision-making units (DMUs). Conventional DEA evaluates the performance of each DMU only from the optimistic point of view. In this paper, the efficiency of a DMU is measured by using an interval efficiency evaluation model based on incentive compatibility, which considers both the optimistic and pessimistic attitude of the DMU during the evaluation process. The efficiency of a DMU, which is computed by combining the two attitudes, can be expressed by interval and provide a more reasonable assessment of the DMU. The lower bound of the interval efficiency are computed by measuring the worst relative efficiency of the ADMU, which is between the results of bounded DEA models from the optimistic or pessimistic points of view. Two numerical examples were examined using the proposed interval DEA model to show its potential application and validity.

A new reliable performance evaluation model: IFB-IER–DEA

Data envelopment analysis (DEA) is a well-known performance evaluation model for measuring the relative efficiency of multiple homogeneous decision making units (DMUs). Input/output of the DMUs can be uncertain especially when they are obtained from subjective human judgments. In this paper, Evidential Reasoning approach with interval assessment score and linguistic interval fuzzy belief degree (IFB-IER approach) is proposed to deal with the uncertainties. This approach does not restrict experts to give a precise point and provides more reliable and realistic performance evaluation. Eventually, the IFB-IER data are converted to standard interval data. Then, the efficiency of the DMUs is calculated using interval DEA model and Anderson Peterson model is applied to rank them. Finally, a numerical example is given to illustrate the validity and applicability of the proposed model.

Measurement of returns-to-scale using interval data envelopment analysis models

Abstract The economic concept of Returns-to-Scale (RTS) has been intensively studied in the context of Data Envelopment Analysis (DEA). The conventional DEA models that are used for RTS classification require well-defined and accurate data whereas in reality observations gathered from production systems may be characterised by intervals. For instance, the heat losses of the Combined production of Heat and Power (CHP) systems may be within a certain range, hinging on a wide variety of factors such as external temperature and real-time energy demand. Enriching the current literature independently tackling the two problems; interval data and RTS estimation; we develop an overarching evaluation process for estimating RTS of Decision Making Units (DMUs) in Imprecise DEA (IDEA) where the input and output data lie within bounded intervals. In the presence of interval data, we introduce six types of RTS involving increasing, decreasing, constant, non-increasing, non-decreasing and variable RTS. The situation for non-increasing (non-decreasing) RTS is then divided into two partitions; constant or decreasing (constant or increasing) RTS using sensitivity analysis. Additionally, the situation for variable RTS is split into three partitions consisting of constant, decreasing and increasing RTS using sensitivity analysis. Besides, we present the stability region of an observation while preserving its current RTS classification using the optimal values of a set of proposed DEA-based models. The applicability and efficacy of the developed approach is finally studied through two numerical examples and a case study.

Dual-role factors for imprecise data envelopment analysis

Efficiency analyses are crucial to managerial competency for evaluating the degree to which resources are consumed in the production process of gaining desired services or products. Among the vast available literature on performance analysis, Data Envelopment Analysis (DEA) has become a popular and practical approach for assessing the relative efficiency of Decision-Making Units (DMUs) which employ multiple inputs to produce multiple outputs. However, in addition to inputs and outputs, some situations might include certain factors to simultaneously play the role of both inputs and outputs. Contrary to conventional DEA models which account for precise values for inputs, outputs and dual-role factors, we develop a methodology for quantitatively handling imprecision and uncertainty where a degree of imprecision is not trivial to be ignored in efficiency analysis. In this regard, we first construct a pair of interval DEA models based on the pessimistic and optimistic standpoints to measure the interval efficiencies where some or all observed inputs, outputs and dual-role factors are assumed to be characterized by interval measures. The optimal multipliers associated with the dual-role factors are then used to determine whether a factor is designated as an output, an input, or is in equilibrium even though the status of the dual-role factors may not be unique based upon the pessimistic and optimistic standpoints. To deal with the problem, we present a new model which integrates both pessimistic and optimistic models. The integrated model enables us to identify a unique status of each imprecise dual-role factor as well as to develop a structure for calculating an optimal reallocation model of each dual-role factor among the DMUs. As another method to investigate the role for dual-role factors, we introduce a fuzzy decision-making model which evaluates all DMUs simultaneously. We finally present an application to a data set of 20 banks to showcase the applicability and efficacy of the proposed procedures and algorithm.

Improved interval DEA models with common weight

The traditional data envelopment analysis (DEA) model can evaluate the relative efficiencies of a set of decision making units (DMUs) with exact values. But it cannot handle imprecise data. Imprecise data, for example, can be expressed in the form of the interval data or mixtures of interval data and exact data. In order to solve this problem, this study proposes three new interval DEA models from different points of view. Two examples are presented to illustrate and validate these models.

Consistent and robust ranking in imprecise data envelopment analysis under perturbations of random subsets of data

Data envelopment analysis (DEA) is a non-parametric method for measuring the relative efficiency of a set of decision making units using multiple precise inputs to produce multiple precise outputs. Several extensions to DEA have been made for the case of imprecise data, as well as to improve the robustness of the assessment for these cases. Prevailing robust DEA (RDEA) models are based on mirrored interval DEA models, including two distinct production possibility sets (PPS). However, this approach renders the distance measures incommensurate and violates the standard assumptions for the interpretation of distance measures as efficiency scores. We propose a modified RDEA (MRDEA) model with a unified PPS to overcome the present problem in RDEA. Based on a flexible formulation for the number of variables perturbed, MRDEA calculates the empirical distribution for the interval efficiency for the case of a random number of variables affected. The MRDEA approach also decreases the computational complexity of the RDEA model, as well as significantly increases the discriminatory power of the model without additional information requirements. The properties of the method are demonstrated for four different numerical instances.

A note on data envelopment analysis with missing values: an interval DEA approach

Smirlis et al. (Appl Math Comput 177(1):1–10, 2006) have proposed a pair of interval data envelopment analysis (DEA) models for computation of the efficiency of decision-making units (DMUs) in the presence of missing data. In this paper, we show that the interval DEA models presented by Smirlis et al. have some drawbacks due to the use of variable production frontier for computation of the efficiency intervals of DMUs. To overcome these drawbacks, this paper presents new interval DEA models based on interval arithmetic. It is shown that the proposed interval DEA models do not need extra variable changes and use a fixed, unified production frontier for computation of the efficiency intervals of the DMUs with interval input and output data. A numerical example is presented to illustrate the potential applications of the new interval DEA models and their effectiveness for measuring the interval efficiencies of the DMUs.

A Two Level DEA in Project Based Organizations

This paper presents a systematic approach for evaluating the performance of a project based organization. We applied a two level fuzzy Data Envelopment Analysis (DEA) technique in project based organizations. In order to determine the required inputs and outputs, important indicators have selected using both expert judgments and statistical analysis. Then the two-level DEA model is successfully adapted. In this model by considering the outputs through a hierarchical process, a large number of sub indicators have provided and then rolled up to the higher level. Since the exact amount cannot be attributed to the indicators and they includes interval of values during the project life cycle, the interval DEA model will be discussed as a model help to determine the most preferred solution. At the end, some of the projects have been successfully evaluated throughout the approach proposed in this paper.

Improved data envelopment analysis models for evaluating interval efficiencies of decision-making units

In a recent article, Wang et al. [Wang, N. S., Yi, R. H., & Wang, W. (2008). Evaluating the performances of decision-making units based on interval efficiencies. Journal of Computational and Applied Mathematics, 216, 328–343] proposed a pair of interval data envelopment analysis (DEA) models for measuring the overall performances of decision-making units (DMUs) with crisp data. In this paper, we demonstrate that interval DEA models face problems in determining the efficiency interval for each DMU when there are zero values for every input. To remedy this drawback, we propose a pair of improved interval DEA models which make it possible to perform a DEA analysis using the concepts of the best and the worst relative efficiencies. Two numerical examples will be examined using the improved interval DEA models. One of the examples is a real-world application about 42 educational departments in one of the branches of the Islamic Azad University in Iran that shows the advantages and applicability of the improved approach in real-life situations.

Measurement of the worst practice of decision-making units in the presence of non-discretionary factors and imprecise data

The objective of the present paper is to propose a novel pair of data envelopment analysis (DEA) models for measurement of relative efficiencies of decision-making units (DMUs) in the presence of non-discretionary factors and imprecise data. Compared to traditional DEA, the proposed interval DEA approach measures the efficiency of each DMU relative to the inefficiency frontier, also called the input frontier, and is called the worst relative efficiency or pessimistic efficiency. On the other hand, in traditional DEA, the efficiency of each DMU is measured relative to the efficiency frontier and is called the best relative efficiency or optimistic efficiency. The pair of proposed interval DEA models takes into account the crisp, ordinal, and interval data, as well as non-discretionary factors, simultaneously for measurement of relative efficiencies of DMUs. Two numeric examples will be provided to illustrate the applicability of the interval DEA models.

A new approach for selecting slightly non‐homogeneous vendors

PurposeThe purpose of this paper is to propose a straightforward model for selecting slightly non‐homogeneous vendors.Design/methodology/approachIn this paper the use of the interval data envelopment analysis (DEA) is suggested. The bounds of intervals are constant and can be obtained by various estimation techniques. The interval DEA model provides for the decision making units (DMUs) with missing values a lower and an upper bound of their efficiency score corresponding to their most favorable and unfavorable option.FindingsEmploying the proposed method for selecting slightly non‐homogeneous vendors largely reduced practical difficulties for vendor selection. This method does not exclude any vendor from the selection problem. For all the vendors it provides bounds of the efficiency scores depended on the particular data values that the vendors with missing data assign within the intervals so to maximize their efficiency score.Practical implicationsThe proposed model considers a slightly non‐homogeneous situation for vendor selection. The proposed approach is driven by multiple criteria. The joint consideration of multiple criteria in a slightly non‐homogeneous environment helps managers select vendors using a comprehensive approach that goes beyond just purchase costs.Originality/valueThis paper is believed to be the first to discuss the problem of slightly non‐homogeneous vendor selection with respect to interval mathematics.

Interval efficiency assessment using data envelopment analysis

This paper studies how to conduct efficiency assessment using data envelopment analysis (DEA) in interval and/or fuzzy input–output environments. A new pair of interval DEA models is constructed on the basis of interval arithmetic, which differs from the existing DEA models handling interval data in that the former is a linear CCR model without the need of extra variable alternations and uses a fixed and unified production frontier (i.e. the same constraint set) to measure the efficiencies of decision-making units (DMUs) with interval input and output data, while the latter is usually a nonlinear optimization problem with the need of extra variable alternations or scale transformations and utilizes variable production frontiers (i.e. different constraint sets) to measure interval efficiencies. Ordinal preference information and fuzzy data are converted into interval data through the estimation of permissible intervals and α - level sets, respectively, and are incorporated into the interval DEA models. The proposed interval DEA models are developed for measuring the lower and upper bounds of the best relative efficiency of each DMU with interval input and output data, which are different from the interval formed by the worst and the best relative efficiencies of each DMU. A minimax regret-based approach (MRA) is introduced to compare and rank the efficiency intervals of DMUs. Two numerical examples are provided to show the applications of the proposed interval DEA models and the preference ranking approach.