A Non-radial Approach for Setting Integer-valued Targets in Data Envelopment Analysis

Data Envelopment Analysis (DEA) has been widely studied in the literature since its inception with Charnes, Cooper and Rhodes work in 1978. The methodology behind the classical DEA method is to determine how much improvements in the outputs (inputs) dimensions is necessary in order to render them efficient. One of the underlying assumptions of this methodology is that the units consume and produce real valued data. This paper deals with the extension of this methodology for the case of integer-valued data. Based on an additive DEA model, a mixed integer linear programming model is proposed for setting integer-valued targets. An empirical example illustrates the approach.</p

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

Trade-offs analysis of sustainability dimensions using integer-valued data envelopment analysis

Conducting an in-depth exploration of trade-offs between sustainability aspects is a notable matter of taking decisions. Furthermore, there are many real world investigations that trade-offs and sustainability should be dealt with in the presence of desirable and undesirable materials while some of them accept integer amounts. Therefore, this study addresses trade-offs of sustainability dimensions when undesirable and integer-valued measures are presented. For this purpose, approaches based upon data envelopment analysis (DEA) are proposed. To explain, DEA models are introduced to calculate individual and group marginal rates of substitution and also directional marginal rates of substitution when integer and undesirable variables are observed. These procedures are applied to calculate trade-offs between different sustainability dimensions, including economic, environmental and social ones. The applications of ports and industrial parks are provided to clarify the approaches appeared in this study. The results derived from the proposed strategies show the usefulness and validity of them

Increasing Sustainability of Logistic Networks by Reducing Product Losses: A Network DEA Approach

This paper considers a multiproduct supply network, in which losses (e.g., spoilage of perishable products) can occur at either the nodes or the arcs. Using observed data, a Network Data Envelopment Analysis (NDEA) approach is proposed to assess the efficiency of the product flows in varying periods. Losses occur in each process as the observed output flows are lower than the observed input flows. The proposed NDEA model computes, within the NDEA technology, input and output targets for each process. The target operating points correspond to the minimum losses attainable using the best observed practice. The efficiency scores are computed comparing the observed losses with the minimum feasible losses. In addition to computing relative efficiency scores, an overall loss factor for each product and each node and link can be determined, both for the observed data and for the computed targets. A detailed illustration and an experimental design are used to study and validate the proposed approach. The results indicate that the proposed approach can identify and remove the inefficiencies in the observed data and that the potential spoilage reduction increases with the variability in the losses observed in the different periods.Ministerio de Ciencia DPI2017-85343-PFondo Europeo de Desarrollo Regional DPI2017-85343-

Interval and fuzzy optimization. Applications to data envelopment analysis

Enhancing concern in the efficiency assessment of a set of peer entities termed Decision Making Units (DMUs) in many fields from industry to healthcare has led to the development of efficiency assessment models and tools. Data Envelopment Analysis (DEA) is one of the most important methodologies to measure efficiency assessment through the comparison of a group of DMUs. It permits the use of multiple inputs/outputs without any functional form. It is vastly applied to production theory in Economics and benchmarking in Operations Research. In conventional DEA models, the observed inputs and outputs possess precise and realvalued data. However, in the real world, some problems consider imprecise and integer data. For example, the number of defect-free lamps, the fleet size, the number of hospital beds or the number of staff can be represented in some cases as imprecise and integer data. This thesis considers several novel approaches for measuring the efficiency assessment of DMUs where the inputs and outputs are interval and fuzzy data. First, an axiomatic derivation of the fuzzy production possibility set is presented and a fuzzy enhanced Russell graph measure is formulated using a fuzzy arithmetic approach. The proposed approach uses polygonal fuzzy sets and LU-fuzzy partial orders and provides crisp efficiency measures (and associated efficiency ranking) as well as fuzzy efficient targets. The second approach is a new integer interval DEA, with the extension of the corresponding arithmetic and LU-partial orders to integer intervals. Also, a new fuzzy integer DEA approach for efficiency assessment is presented. The proposed approach considers a hybrid scenario involving trapezoidal fuzzy integer numbers and trapezoidal fuzzy numbers. Fuzzy integer arithmetic and partial orders are introduced. Then, using appropriate axioms, a fuzzy integer DEA technology can be derived. Finally, an inverse DEA based on the non-radial slacks-based model in the presence of uncertainty, employing both integer and continuous interval data is presented

Ranking efficient DMUs using cooperative game theory

The problem of ranking Decision Making Units (DMUs) in Data Envelopment Analysis (DEA) has been widely studied in the literature. Some of the proposed approaches use cooperative game theory as a tool to perform the ranking. In this paper, we use the Shapley value of two different cooperative games in which the players are the efficient DMUs and the characteristic function represents the increase in the discriminant power of DEA contributed by each efficient DMU. The idea is that if the efficient DMUs are not included in the modified reference sample then the efficiency score of some inefficient DMUs would be higher. The characteristic function represents, therefore, the change in the efficiency scores of the inefficient DMUs that occurs when a given coalition of efficient units is dropped from the sample. Alternatively, the characteristic function of the cooperative game can be defined as the change in the efficiency scores of the inefficient DMUs that occurs when a given coalition of efficient DMUs are the only efficient DMUs that are included in the sample. Since the two cooperative games proposed are dual games, their corresponding Shapley value coincide and thus lead to the same ranking. The more an ef- ficient DMU impacts the shape of the efficient frontier, the higher the increase in the efficiency scores of the inefficient DMUs its removal brings about and, hence, the higher its contribution to the overall discriminant power of the method. The proposed approach is illustrated on a number of datasets from the literature and compared with existing methods