IDEA and AR-IDEA: Models for Dealing with Imprecise Data in DEA

An overall profit Malmquist productivity index with fuzzy and interval data

Park proposed a pair of mathematical data envelopment analysis (DEA) models to estimate the lower and upper bound of efficiency scores in the presence of imprecise data. This article illustrates that his approach suffers from some drawbacks: (i) it may convert weak ordinal data into an incorrect set of precise data; (ii) it utilizes various production frontiers to obtain an interval efficiency score for each decision making unit (DMU); (iii) in the absence of exact output data (pure ordinal output data), the approach leads to a meaningless model; (iv) the built model is infeasible with pure ordinal input data; (v) it may include free or unlimited production output which results in unreliable and suspicious results. Moreover, the utilized models by Park involve a positive lower bound (non-Archimedean epsilon) for the weights to deter them from being zero. However, the author ignored the requirement of determining a suitable value for the epsilon. This study constructs two new DEA models with a fixed and unified production frontier (the same constraint set) to compute the upper and lower bounds of efficiency. It is demonstrated that the suggested models can successfully capture the aforementioned shortcomings. Although these models are also epsilon-based, a new model is developed to obtain a suitable epsilon value for the proposed models. It is proved that the suggested approach effectively eliminates all the weaknesses. Additionally, a case study of Iranian Space Agency (ISA) industry is taken as an example to illustrate the superiority of the new approach over the previous ones.

The author of the article describes the theoretical assumptions of the DEA method used for measuring the productivity of airports described in the article ‘Research into the methods of analysing the productivity indicators of transport terminals’ (Jaržemskienė 2009). The essential insights presented in the above mentioned paper reveal that Data Envelopment Analysis (DEA) is a relatively new ‘data oriented’ approach to evaluating the performance of the so-called Decision Making Units (DMU) that convert multiple inputs into multiple outputs. The article focuses on the findings of the study carried out by the author in accordance with those assumptions. Research represents the Data Envelopment Analysis (DEA) method testing 15 selected airports situated in the Baltic Region, including Vilnius, Kaunas, Palanga, Riga, Tallinn, St. Petersburg, Helsinki, Turku, Stockholm, Malme, Copenhagen, Hamburg, Gdansk, Warsaw and Minsk. Airport productivity indicators are ranked considering importance and using the method of Delphi expert survey made of two rounds. The author presented the following indicators (expressed as ‘ratio’) as the major ones estimated by PAX/LAND, AIR/LAND, PAX/AIR, PAX/RW, PAX/RWA, GA and INTER experts. The succeeding indicators were introduced by PAX/TERMAREA, PAX/GATES, AIR/RW, AIR/RWA, AIR/TERMAREA, AIR/GATES, FR/LAND and FR/RW. 10 indicators were accepted as the most important and selected from the current set in the following sequence: AIR/LAND, AIR/RW, PAX/RW, PAX/LAND, AIR/RWA, PAX/AIR, PAX/RWA, AIR/TERMAREA, PAX/GATES and PAX/TERMAREA. AIR/LAND and AIR/RW were submitted as two main indicators. The acronyms are explained as follows: LAND – airport area, RWA – runway length, PAX – the number of passengers, AIR – the number of aircraft take-offs and landings, RW – the number of runways, GATES – the number of gates, FR – the amount of freight served, TERMAREA – the area of passenger terminal, GA – a general aviation market share of airport served aircraft by percentage, INTER – the percentage of international passengers considering all passengers served by airports. After two key productivity indicators were chosen conducting the expert survey, airport productivity was compared applying the DEA method.

Environmental sustainability is a growing trend in the retail industry as climate change issues are becoming more visible. Customers around the globe are also showing interest in brands that are adopting green practices along with the increasing attention of the government on regulations to manage the environmental impact of businesses. Focus of retailers on energy efficiency and the use of renewable energy can significantly contribute to the environmental impact management. On this premise this study proposes data envelopment analysis (DEA) based resource allocation model for effective deployment of centralised additional fixed investment among the retail stores with the target of reducing the use of non-renewable energy consumption and improving its energy sustainability index. Resource allocation DEA models (RADEA) discussed in the existing literature mostly assume precise data on input/output is available. In practice variability is observed over time in the input consumption as well as output production. To account for the imprecise nature of the real life data the proposed RADEA model is developed with respect to the interval data for effective distribution of centralised resources among decision making units (DMUs), simultaneously considering goals of environmental performance management and output target setting. To tradeoff the conflicting goals the proposed RADEA model is extended as a goal programming formulation. The application of the proposed model is demonstrated through a case study.

The article describes the Data Envelopment Analysis (DEA) method and the main features of its application. The main problems of heat and power systems are described, which are addressed by the DEA method of efficiency assessment presented in the article. The approbation of this method is presented at the objects of the centralized municipal heat supply system of the fuel and energy complex: boiler houses and heat and power plants. 9 objects were analyzed according to four input indicators: available heat capacity, installed heat capacity, heat consumption for own needs, fuel consumption. Also, the efficiency of the system was evaluated according to two output indicators: the release of thermal energy to the grid and the mass of the emission. As a result of the analysis and calculations made, it was revealed that 5 objects have the maximum possible efficiency indicator equal to 1, that is, they function as efficiently as possible. 4 objects of the centralized municipal heat supply system have an efficiency indicator less than 1. Accordingly, improvements are required for the operation of the above Decision-Making Units (DMU)s. These objects have deviations in terms of the inputs and outputs of the actual data and those obtained using the DEA method. Based on the calculations obtained for these 4 objects, the article provides recommendations for changing the quantitative values of their input and output indicators. For example, for object number 2, it is recommended to reduce the installed heat capacity in the grid by 72.57%, without changing the available heat capacity and fuel consumption. Reduce the heat consumption for your own needs by 69.383%. In addition, it is recommended to increase the supply of thermal energy to the grid by 6,034%, and reduce the mass of emission by 11.5%. Specific measures have also been developed to modernize the studied objects in order to achieve the recommended indicators of inputs and outputs. The research results presented in the article are of scientific and practical interest and can be used to improve the efficiency of heat and power systems facilities

Entrepreneurship orientation (EO) approach provides universities with a plan and roadmap for getting over rising uncertainty and complexity. Inspiring universities to embrace transformation and innovation, risk taking and proactive policy for planning and executing development strategies for success in the dynamic competitive environment arise from entrepreneurship orientation spirit. To reach this status, the key factors of success in entrepreneurship should be taken into consideration and assessed in universities. Structural and entrepreneurial policies as key non-financial factors are two concepts that have received considerable attention over the past years. Measuring efficiency of universities by the mentioned factors and using mathematical programming like Data Envelopment Analysis (DEA) method is the aim of this study. Hence, this paper applied DEA method for measuring efficiency of 16 faculties and institutes in Ferdowsi University of Mashhad (FUM) in Iran. Descriptive-survey methodology was used and data were collected through questionnaire survey. The faculties and institutes were ranked based on structural policies and EO through DEA. Finally, the DEA method recommended the development roadmaps template for the 11 faculties and institutes which were inefficient.

Data Envelopment Analysis (DEA) method is used to evaluate the efficiency of the bank branches. The present paper prioritized the indicators, using fuzzy questionnaires and by gathering the managers’ ideas, in order to obtain the most important evaluating indicators. After obtaining these indicators, Data Envelopment Analysis method was used to determine the performance bound interval, regarding the fact that the data are related to a certain period of time and their nature is imprecise and fuzzy. Then, Fuzzy Theory method and Fuzzy Data Envelopment Analysis method were employed to rank the branches, and finally the results were presented.

Globally, insurance and takaful companies play a crucial role in economic and financial development of a country. Malaysia’s insurance sector has undergone substantial changes compared to two decades ago. Due to intense competition observed in Malaysian insurance industry, efficiency measurement and a complete efficiency ranking of insurance companies are very important for the decision makers so that necessary changes and improvement can be made. Data Envelopment Analysis (DEA) is a non-parametric method that has been acknowledged as an effective method to measure the efficiency of homogeneous decision-making units (DMUs). The main advantage of DEA is its ability to handle multiple inputs and outputs. However, standard DEA has poor discrimination power since it generates too many efficient units especially when the number of DMUs under study is insufficient in comparison to number of inputs and outputs. It cannot discriminate efficient units and therefore unable to give a complete ranking of DMUs. This study aimed to overcome the ranking problem found in standard DEA by integrating DEA and Preference Ranking Organization Method for Enrichment Evaluations (PROMETHEE) II. The hybrid method was applied to evaluate the efficiency and ranking of 22 life insurance and takaful companies in Malaysia from the period of 2017 to 2018. Input variables used in this study comprised of fees and commission, and management expenses. Meanwhile, output variables were net premium and generated investment income. The proposed method involved two stages. In the first stage, DEA was applied to obtain the efficient scores for the DMUs. In the second stage, PROMETHEE II was implemented to rank the efficient units. This hybrid method has successfully obtained full ranking of all the insurance companies under study. The inefficient companies can learn strategies and practices from efficient companies to enhance their services. It is recommended for future research to integrate DEA with other Multi Criteria Decision Making (MCDM) methods such as TOPSIS and VIKOR to fully rank the DMUs.

Park (2010) [8] presented a method to obtain the upper bound on efficiency in imprecise data envelopment analysis (IDEA) in which the envelopment model with imprecise data had been used. In this paper, we consider the dual model, the multiplier model, which involves the non-Archimedean element $epsilon$. Then, we define a model to determine the upper bound of $epsilon$. An assurance interval for the non-Archimedean element $epsilon$ is obtained in IDEA which is important when solving the model directly.

The method of data envelopment analysis (DEA) is a nonparametric statistical method, which is widely used in energy efficiency analysis of complex industrial process. However, there are many factors for affecting the energy efficiency, so the input and output indexes of the DEA is too much to get the low resolution of analysis results. Therefore, this paper proposes an energy efficiency analysis method based on the DEA cross model (DEACM) integrating principal component analysis (PCA) (PCA-DEACM). After using the PCA to reduce the dimensions of input and output indexes, the DEACM is used to further improve the effective resolution of decision-making units (DMUs). And the analysis results are more objective and reasonable. Finally, the proposed PCA-DEACM method is applied in energy efficiency analysis of PTA plants. By comparing with the classical DEA method and the PCA-DEA method, the validity and applicability of the PCA-DEACM is verified, which provides accurate analysis results for optimizing the operation of PTA plants.

The traditional data envelopment analysis (DEA) model can evaluate the relative efficiencies of a set of decision making units (DMUs) with exact values of inputs and outputs, 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 ordinal data. In this study, a cross-efficiency method is introduced into the DEA model to calculate the interval of cross-efficiency values, based on which a new TOPSIS method is proposed to rank the DMUs. Two examples are presented to illustrate and validate the proposed method.

Determining the appropriate supplier is a crucial strategic consideration in supply chain management. Worst-practice frontier data envelopment analysis (WPF-DEA) model is one of the new models in data envelopment analysis (DEA). In this paper, the concept of imprecise data envelopment analysis (IDEA) approach and dual-role factor is used to develop WPF-DEA model. Then, the proposed model is applied for supplier selection problem. A numerical example demonstrates the application of the proposed model.

Waqf is a voluntary charity that cannot be disposed of and the ownership cannot be transferred once it is declared as waqf assets. Waqf institutions play an important role in helping the development of Muslims ummah through wealth distribution. State Islamic Religious Councils (SIRCs) in Malaysia are the sole trustee that manage and develop waqf assets. Based on selected input and output, the intermediary approach assumes that cash waqf received as output while total expenditure of SIRCs as input. Under this approach SIRCs act as intermediary between waqif (giver) and beneficiaries. Thus, this paper attempts to analyze the efficiency of waqf institutions in Malaysia by using Data Envelopment Analysis (DEA) method under output-orientation using Variable Return to Scale (VRS) assumptions. Four SIRCs were selected as decision making units (DMU) for the period of 2011 to 2015. The result indicates that changes in average technical efficiency for every year is contributed by both pure technical and scale. However, inefficiency of Malaysian waqf institutions is mostly contributed by pure technical efficiency aspects rather than scale. 2012 showed the highest average technical efficiency with 73.9% as most of the institutions operated in optimum level of input to produce output. Thus, the result suggests that both technical and scale efficiency should be improved to achieve the most efficient and productive level of performance in order to fulfill objectives of the institutions as an intermediary between waqif and beneficiaries.

Data envelopment analysis (DEA) is a method for measuring efficiency of peer decision-making units (DMUs). Conventional DEA evaluates the performance of each DMU using a set of most favourable weights. As a result, traditional DEA models can be considered methods for the analysis of the best relative efficiency or analysis of the optimistic efficiency. DEA efficient DMUs obtained from conventional DEA models create an efficient production frontier. Traditional DEA can be used to identify units with good performance in the most desirable scenarios. There is a similar approach that evaluates the performance indicators of each DMU using a set of most unfavourable weights. Accordingly, such models can be considered models for analysing the worst relative efficiency or pessimistic efficiency. This approach uses the inefficient production frontier for determining the worst relative efficiency that can be assigned to each DMU. DMUs lying on the inefficient production frontier are referred to as DEA inefficient while those neither on the efficient frontier nor on the inefficient frontier are declared DEA inefficient. It can be argued that both relative efficiencies should be considered simultaneously and any approach with only one of them would be biased. This paper proposed the integration of both efficiencies as an interval so that the overall performance score would belong to this interval. It was shown that efficiency interval provided more information than either of the two efficiencies, which was illustrated using two numerical examples.

This study aims to determine the level of efficiency of Zakat Management Organization period 2012-2014 using Data Envelopment Analysis (DEA) method with the production approach. Data Envelopment Analysis (DEA) is a non-parametric method used to measure the efficiency level of Decision Making Units (DMU). This method measures the ratio between output and input which are compared between the studied Zakat Management Organization. Output variables used are fund collected and channeled fund. While input variables used are personnel costs, socialization costs, and other operational costs. The results of this study show that the efficiency of Zakat Management Organization in the year 2013 is still better than in 2012 and 2014, both technically (93,50%), scale (73,28%), and overall (70,54%). Calculation of 7 Zakat Management Organization in 2013 with the assumption of Constant Return to Scale (CRS), shows only 3 Zakat Management Organization efficient, that is YBM BRI, BSM Ummat, and BAMUIS BNI. The main cause of inefficiency from the output oriented measures is channeled fund and fund collected, which is equal 49,23% and 48,13%. While the input oriented measures states that the source of inefficiency is the personnel costs (33,42%), the socialization costs (33,72%), and the cost of other operational (32,29%).