Complete Ranking Of Decision-making Units Research Articles

DEA cross-efficiency models with prospect theory and distance entropy: An empirical study on high-tech industries

Cross-efficiency evaluation with the data envelopment analysis (DEA) model is an effective way to assess performance and provide a complete ranking of decision-making units. However, it is generally assumed that decision makers are perfectly rational in the cross-efficiency model, which fails to consider the subjective preferences of decision-makers. Moreover, the arithmetic average method is usually adopted to aggregate efficiency scores in traditional cross-efficiency methods, which underestimates the importance of self-evaluation. To address these issues, we extend cross-efficiency with the DEA model by incorporating prospect theory and the distance entropy function. First, we calculate the prospect values of decision-making units to describe the non-rational subjective preferences under the risk of decision-makers. Second, based on prospect cross-efficiency, a new distance entropy function is developed to aggregate the ultimate prospect cross-efficiency values. More specifically, some traditional cross-efficiency evaluation models can be considered special cases of prospect cross-efficiency models with appropriate adjustments to the parameters. Finally, an empirical example is used to evaluate the prospect cross-efficiency results with the high-tech industries of 29 provinces in China to illustrate the applicability and effectiveness of the proposed model in ranking observations.

Fuzzy efficiency evaluation in relational network data envelopment analysis: application in gas refineries

In contrast to classical data envelopment analysis (DEA), network DEA has attention to the internal structure of a production system and reveals the relationship between the efficiency of system and efficiencies of the processes. However, the flexibility of weights and the need for crisp input and output data in the evaluation process are two major shortcomings of classical network DEA models. This paper presents a common weights approach for a relational network DEA model in a fuzzy environment to measure the efficiencies of the system and the component processes. The proposed approach first finds upper bounds on input and output weights for a given cut level and then it determines a common set of weights (CSW) for all decision-making units (DMUs). Hence, the fuzzy efficiencies of all processes and systems for all DMUs are obtained based on the resulting CSW. The developed fuzzy relational network DEA and the proposed common weights approach are illustrated with a numerical example. The obtained results confirm that the fuzzy data affects over the efficiency scores and complete ranking of DMUs. The applicability of the proposed network model is illustrated by performance evaluation of gas refineries in Iran.

Methodological Approach for Providing a Suitable Model for Financial Ranking of Educational Hospitals by using of Cross-Performance Procedures (Case Work, Hospitals of Ahvaz Jundishapur University of Medical Sciences)

Background: Hospitals are multi-specialist social security organizations that account for a significant portion of the health system’s budget. Given the economic conditions and the importance of hospitals in the field of social health, it seems important and necessary to pay attention to financial performance and compare them with each other. Objectives: The purpose of this study was to provide a model for evaluating the performance and financial ranking of Ahvaz Jundishapur University of Medical Sciences’ Hospitals during 2018. Methods: This cross-sectional study was conducted at Ahvaz hospitals. Twenty-two hospitals were chosen according to random stratified sampling. First, the financial performance indicators of hospital performance evaluations are identified using the previous study method. Then, the financial performance evaluation indicators of hospitals are finalized by interviews with managers and experts of Ahvaz Medical Sciences’ Hospitals. To rank the hospitals, a cross-performance approach was used. Cross-performance is an acceptable approach in data envelopment analysis that provides a complete ranking of decision-making units (DMUs). In addition, a new secondary goal is presented in cross-performance. In this paper, an algorithm based on cross-performance is presented, and we will provide a model for ranking hospitals. Data were entered and analyzed using Statistical Package for Social Sciences (SPSS) and t-student and ANOVA tests. Results: The results show that although the traditional data envelopment analysis model is not able to rank uniquely from hospitals, the introduced pattern offers a unique ranking of hospitals. According to the results of this study, Imam Khomeini Hospital of Ramhormoz has the first rank, and Baqaei Hospital has the rank (22nd) in this ranking. Conclusions: The findings of this study represent the Hospital of financial position at the other hospitals and can be used in the hospital with good rankings in the service level of self-awareness as a template.

A new method for complete ranking of DMUs

So far numerous models have been proposed for ranking the efficient decision-making units (DMUs) in data envelopment analysis (DEA). But, the most shortcoming of these models is their two-stage orientation. That is, firstly we have to find efficient DMUs and then rank them. Another flaw of some of these models, like AP-model (A procedure for ranking efficient units in data envelopment analysis, Management Science, 39 (10) (1993) 1261–1264), is existence of a non-Archimedean number in their objective function. Besides, when there is more than one weak efficient unit (or non-extreme efficient unit) these models could not rank DMUs. In this paper, we employ hyperplanes of the production possibility set (PPS) and propose a new method for complete ranking of DMUs in DEA. The proposed approach is a one stage method which ranks all DMUs (efficient and inefficient). In addition to ranking, the proposed method determines the type of efficiency for each DMU, simultaneously. Numerical examples are given to show applicability of the proposed method.

A new ranking method based on cross-efficiency in data envelopment analysis

Data envelopment analysis (DEA) models compute efficiency score for decision making units (DMUs) and discriminate between efficient and inefficient DMUs. Therefore, they rank DMUs except when multiple DMUs have an efficiency score of 1. This paper proposes a new method for complete ranking of DMUs that is based on cross-efficiency evaluation method. One of the drawbacks of the cross-efficiency evaluation method is the existence of multiple cross-efficiency scores due to the presence of alternative optimal solutions of the dual multiplier model. Hence choosing weights between alternative optimal solutions as part of a procedure for ranking DMUs is problematic. Liang et al. (2008) introduced alternative secondary goals in cross-efficiency evaluation. However, this paper finds that their approach is problematic in some situations. As a result, this paper seeks to introduce a new secondary objective function in cross-efficiency evaluation for removing their difficulties. Numerical demonstration reveals the validity of the proposed method by using a real data set of a case study which consists of 20 Iranian bank branches. Key words: Data envelopment analysis (DEA), ranking, cross-efficiency.

A complete ranking of DMUs using restrictions in DEA models

Data Envelopment Analyses (DEA) is a linear programming based method which evaluates relative efficiency of Decision Making Units (DMUs). It can include multiple outputs and inputs without a priori weights and without requiring explicit specification of functional forms between inputs and outputs. It computes a scalar measure of efficiency and determines efficient levels of inputs and outputs for each DMU under evaluation which has a range of zero to “1”; hence, it has the ability to rank DMUs, unless when some DMUs are the same in efficiency score, such as efficient DMUs or inefficient DMUs with the same efficiency score. In many cases, it is necessary to give a full ranking of the DMUs. Hence this paper introduces a new method for complete ranking of decision making units, which it does not need any changes in the models. Also, for presentation of the ability of this method, it is employed to rank the bank branch of a commercial bank branches in an empirical example.