Defuzzification of groups of fuzzy numbers using data envelopment analysis

Defuzzification is a critical process in the implementation of fuzzy systems that converts fuzzy numbers to crisp representations. Few researchers have focused on cases where the crisp outputs must satisfy a set of relationships dictated in the original crisp data. This phenomenon indicates that these crisp outputs are mathematically dependent on one another. Furthermore, these fuzzy numbers may exist as a group of fuzzy numbers. Therefore, the primary aim of this thesis is to develop a method to defuzzify groups of fuzzy numbers based on Charnes, Cooper, and Rhodes (CCR)-Data Envelopment Analysis (DEA) model by modifying the Center of Gravity (COG) method as the objective function. The constraints represent the relationships and some additional restrictions on the allowable crisp outputs with their dependency property. This leads to the creation of crisp values with preserved relationships and/or properties as in the original crisp data. Comparing with Linear Programming (LP) based model, the proposed CCR-DEA model is more efficient, and also able to defuzzify non-linear fuzzy numbers with accurate solutions. Moreover, the crisp outputs obtained by the proposed method are the nearest points to the fuzzy numbers in case of crisp independent outputs, and best nearest points to the fuzzy numbers in case of dependent crisp outputs. As a conclusion, the proposed CCR-DEA defuzzification method can create either dependent crisp outputs with preserved relationship or independent crisp outputs without any relationship. Besides, the proposed method is a general method to defuzzify groups or individuals fuzzy numbers under the assumption of convexity with linear and non-linear membership functions or relationships

An Integrated Approach of Discrete Event Simulation and a Non-Radial Super Efficiency Data Envelopment Analysis for Performance Evaluation of an Emergency Department

An emergency department (ED) has been considered as one of the most congested department in a hospital. The congestion is typically contributed by long waiting time to get medical service, primarily caused by insufficient resource allocation or improper resource configurations. However, how various resource allocation configurations affect ED performance and how their efficiency can correctly be evaluated, using an integrated approach is rarely discussed. This paper thus integrates discrete event simulation (DES) and data envelopment analysis (DEA) to measure ED performance and evaluate the efficiency of potential resource allocation configurations for future performance improvement. For this, a DES model for an ED is first designed and developed. Its performance improvement is then tested using 35 potential resource allocation configurations, and their impacts on the performance are measured. To evaluate their efficiency and identify the optimal configuration, a mixed integer super efficiency of slacks-based measure data envelopment analysis (SE-SBM-DEA) approach dealing with undesirable outputs is proposed. The model utilizes resource allocation as inputs and simulation performance measures as outputs. All inputs were considered as integer, while the outputs were classified into desirable and undesirable in mixed integer-valued data. The desirable real outputs are the utilization of receptionists, nurses and doctors. The undesirable real outputs are the average of patient cycle time and time spent in queues, while the undesirable integer output is average number of patients in queues. The desirable integer output is average number of patients received treatment. The results obtained from the DEA approach show that 21 efficient resource configurations have the capability to increase their inputs, undesirable outputs and/or decrease desirable outputs simultaneously without affecting their efficiency status. The integrated approach helps decision makers manage their healthcare facilities by identifying the sources of inefficiency and (the maximum levels of inputs-undesirable outputs and minimum levels of desirable outputs) to improve and (retain) efficienc

Additive super-efficiency in integer-valued data envelopment analysis

Conventional data envelopment analysis (DEA) methods assume that input and output variables are continuous. However, in many real managerial cases, some inputs and/or outputs can only take integer values. Simply rounding the performance targets to the nearest integers can lead to misleading solutions and efficiency evaluation. Addressing this kind of integer-valued data, the current paper proposes models that deal directly with slacks to calculate efficiency and super-efficiency scores when integer values are present. Compared with standard radial models, additive (super-efficiency) models demonstrate higher discrimination power among decision making units, especially for integer-valued data. We use an empirical application in early-stage ventures to illustrate our approach

Advancing efficiency analysis using data envelopment analysis: the case of German health care and higher education sectors

The main goal of this dissertation is to investigate the advancement of efficiency analysis through DEA. This is practically followed by the case of German health care and higher education organizations. Towards achieving the goal, this dissertation is driven by the following research questions: 1.How the quality of the different DEA models can be evaluated? 2.How can hospitals’ efficiency be reliably measured in light of the pitfalls of DEA applications? 3.In measuring teaching hospital efficiency, what should be considered? 4.At the crossroads of internationalization, how can we analyze university efficiency? Both the higher education and the health care industries are characterized by similar missions, organizational structures, and resource requirements. There has been increasing pressure on universities and health care delivery systems around the world to improve their performance during the past decade. That is, to bring costs under control while ensuring high-quality services and better public accessibility. Achieving superior performance in higher education and health care is a challenging and intractable issue. Although many statistical methods have been used, DEA is increasingly used by researchers to find best practices and evaluate inefficiencies in productivity. By comparing DMU behavior to actual behavior, DEA produces best practices frontier rather than central tendencies, that is, the best attainable results in practice. The dissertation primarily focuses on the advancement of DEA models primarily for use in hospitals and universities. In Section 1 of this dissertation, the significance of hospital and university efficiency measurement, as well as the fundamentals of DEA models, are thoroughly described. The main research questions that drive this dissertation are then outlined after a brief review of the considerations that must be taken into account when employing DEA. Section 2 consists of a summary of the four contributions. Each contribution is presented in its entirety in the appendices. According to these contributions, Section 3 answers and critically discusses the research questions posed. Using the Translog production function, a sophisticated data generation process is developed in the first contribution based on a Monte Carlo simulation. Thus, we can generate a wide range of diverse scenarios that behave under VRS. Using the artificially generated DMUs, different DEA models are used to calculate the DEA efficiency scores. The quality of efficiency estimates derived from DEA models is measured based on five performance indicators, which are then aggregated into two benchmark-value and benchmark-rank indicators. Several hypothesis tests are also conducted to analyze the distributions of the efficiency scores of each scenario. In this way, it is possible to make a general statement regarding the parameters that negatively or positively affect the quality of DEA estimations. In comparison with the most commonly used BCC model, AR and SBM DEA models perform much better under VRS. All DEA applications will be affected by this finding. In fact, the relevance of these results for university and health care DEA applications is evident in the answers to research questions 2 and 4, where the importance of using sophisticated models is stressed. To be able to handle violations of the assumptions in DEA, we need some complementary approaches when units operate in different environments. By combining complementary modeling techniques, Contribution 2 aims to develop and evaluate a framework for analyzing hospital performance. Machin learning techniques are developed to perform cluster analysis, heterogeneity, and best practice analyses. A large dataset consisting of more than 1,100 hospitals in Germany illustrates the applicability of the integrated framework. In addition to predicting the best performance, the framework can be used to determine whether differences in relative efficiency scores are due to heterogeneity in inputs and outputs. In this contribution, an approach to enhancing the reliability of DEA performance analyses of hospital markets is presented as part of the answer to research question 2. In real-world situations, integer-valued amounts and flexible measures pose two principal challenges. The traditional DEA models do not address either challenge. Contribution 3 proposes an extended SBM DEA model that accommodates such data irregularities and complexity. Further, an alternative DEA model is presented that calculates efficiency by directly addressing slacks. The proposed models are further applied to 28 universities hospitals in Germany. The majority of inefficiencies can be attributed to “third-party funding income” received by university hospitals from research-granting agencies. In light of the fact that most research-granting organizations prefer to support university hospitals with the greatest impact, it seems reasonable to conclude that targeting research missions may enhance the efficiency of German university hospitals. This finding contributes to answering research question 3. University missions are heavily influenced by internationalization, but the efficacy of this strategy and its relationship to overall university efficiency are largely unknown. Contribution 4 fills this gap by implementing a three-stage mathematical method to explore university internationalization and university business models. The approach is based on SBM DEA methods and regression/correlation analyses and is designed to determine the relative internationalization and relative efficiency of German universities and analyze the influence of environmental factors on them. The key question 4 posed can now be answered. It has been found that German universities are relatively efficient at both levels of analysis, but there is no direct correlation between them. In addition, the results show that certain locational factors do not significantly affect the university’s efficiency. For policymakers, it is important to point out that efficiency modeling methodology is highly contested and in its infancy. DEA efficiency results are affected by many technical judgments for which there is little guidance on best practices. In many cases, these judgments have more to do with political than technical aspects (such as output choices). This suggests a need for a discussion between analysts and policymakers. In a nutshell, there is no doubt that DEA models can contribute to any health care or university mission. Despite the limitations we have discussed previously to ensure that they are used appropriately, these methods still offer powerful insights into organizational performance. Even though these techniques are widely popular, they are seldom used in real clinical (rather than academic) settings. The only purpose of analytical tools such as DEA is to inform rather than determine regulatory judgments. They, therefore, have to be an essential part of any competent regulator’s analytical arsenal

Estimating efficiency and productivity growth of the Grain Silos and Flour Mills Organisation in Saudi Arabia

The Grain Silos and Flour Mills Organisation (GSFMO) is the responsible authority monopolising the Kingdom's milling industry. However, the organisation has recently been facing financial problems. The aim of this study is to estimate the technical, cost and allocative efficiency (TE, CE and AE) of the flour mills of the GSFMO (1988-2011), using Data Envelopment Analysis (DEA) and Stochastic Frontier Analysis (SFA) approaches. In addition, it seeks to explain variation in efficiency levels between the mills and conduct further analysis through the second stage regression to estimate the effect of managerial variables. Productivity growth over time was also estimated in this study using DEA (2008-2011) and SFA (1988-2011) approaches. Both primary data and secondary data (1988-2011) to cover the nine milling branches were utilised. Using DEA under constant return to scale (CRS), average TE ranged from 91.72% in Khamis branch to 97.63% in Almadinah. Average TE under input-orientated variable return to scale (VRS) was lower than TE estimated under output-orientated VRS. The older branches had the lowest TE compared to newer branches. Under VRS, TE was greater than TE for the same branches under CRS. TE results using SFA were quite analogous to the results using DEA. Regarding productivity growth, using DEA for the 2008-2011 data, no consistent patterns were found across the GSFMO branches in the mean total factor productivity growth (TFPG), technical change (TC), and efficiency change (EC). When using SFA to estimate productivity growth over the period 1988 to 2011, there was a decrease in productivity growth for most branches. With regards to the results of the second stage regression, branch managers’ age, local temperature and 'bad' infrastructure have a significant negative relationship with TE, while manager's experience did not seem to have any significant relationship with TE. However, new and mix machine conditions and number of mills in each branch have a significant positive relationship with TE. In terms of CE and AE using the DEA approach, the results show that major losses incurred by the organisation were partly due to the significant decrease in CE and AE and that there is a significant scope to reduce inputs costs in the production process

Estimating efficiency and productivity growth of the Grain Silos and Flour Mills Organisation in Saudi Arabia

The Grain Silos and Flour Mills Organisation (GSFMO) is the responsible authority monopolising the Kingdom's milling industry. However, the organisation has recently been facing financial problems. The aim of this study is to estimate the technical, cost and allocative efficiency (TE, CE and AE) of the flour mills of the GSFMO (1988-2011), using Data Envelopment Analysis (DEA) and Stochastic Frontier Analysis (SFA) approaches. In addition, it seeks to explain variation in efficiency levels between the mills and conduct further analysis through the second stage regression to estimate the effect of managerial variables. Productivity growth over time was also estimated in this study using DEA (2008-2011) and SFA (1988-2011) approaches. Both primary data and secondary data (1988-2011) to cover the nine milling branches were utilised. Using DEA under constant return to scale (CRS), average TE ranged from 91.72% in Khamis branch to 97.63% in Almadinah. Average TE under input-orientated variable return to scale (VRS) was lower than TE estimated under output-orientated VRS. The older branches had the lowest TE compared to newer branches. Under VRS, TE was greater than TE for the same branches under CRS. TE results using SFA were quite analogous to the results using DEA. Regarding productivity growth, using DEA for the 2008-2011 data, no consistent patterns were found across the GSFMO branches in the mean total factor productivity growth (TFPG), technical change (TC), and efficiency change (EC). When using SFA to estimate productivity growth over the period 1988 to 2011, there was a decrease in productivity growth for most branches. With regards to the results of the second stage regression, branch managers’ age, local temperature and 'bad' infrastructure have a significant negative relationship with TE, while manager's experience did not seem to have any significant relationship with TE. However, new and mix machine conditions and number of mills in each branch have a significant positive relationship with TE. In terms of CE and AE using the DEA approach, the results show that major losses incurred by the organisation were partly due to the significant decrease in CE and AE and that there is a significant scope to reduce inputs costs in the production process