Multiobjective target setting in data envelopment analysis using AHP (original) (raw)
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Using interactive multiobjective methods to solve DEA problems with value judgements
Computers & Operations Research, 2009
Data envelopment analysis (DEA) is a performance measurement tool that was initially developed without consideration of the decision maker (DM)'s preference structures. Ever since, there has been a wide literature incorporating DEA with value judgements such as the goal and target setting models. However, most of these models require prior judgements on target or weight setting. This paper will establish an equivalence model between DEA and multiple objective linear programming (MOLP) and show how a DEA problem can be solved interactively without any prior judgements by transforming it into an MOLP formulation. Various interactive multiobjective models would be used to solve DEA problems with the aid of PROMOIN, an interactive multiobjective programming software tool. The DM can then search along the efficient frontier to locate the most preferred solution where resource allocation and target levels based on the DM's value judgements can be set. An application on the efficiency analysis of retail banks in the UK is examined. Comparisons of the results among the interactive MOLP methods are investigated and recommendations on which method may best fit the data set and the DM's preferences will be made.
Multi-Criteria Optimization Techniques In DEA: Methods And Its Applications
International Journal of Scientific & Technology Research, 2020
This research article explores on multi-objective optimization methods namely multi-objective model optimization, global criterion method, bounded objective function method, lexicon-graphic method etc. The multiplier problem proposed by Charnes, Cooper and Rhodes (CCR) problem has been discussed in this paper. Own efficiency and cross efficiency of DMU‘s are defined here. Aggressive formulation of cross efficiency and benevolent formulation of cross efficiency have been proposed in this article. Besides MCDEA and MOLP problems are presented. The global efficiency approach of a multi objective model and the concept of super efficiency which works as a tool to develop the discriminating power of DEA in the presence of efficiency DMU‘s are depicted here.
A New Decision Model Based on the Common Set of Weights DEA and Liner Goal Programming
Data envelopment analysis (DEA) has a wide application in measuring the relative efficiency of identical units with the same inputs and outputs. There are weaknesses in the classical models. One of the weaknesses is poor judgment and ranking among efficient decision making units, and another weakness is that the number of decision making units must greater than a certain limit. This model will not be valid when decision making units are relatively low. Also the most important weakness of classical model is changing weight of inputs and outputs that it makes the efficiency of decision units measured with different weight. Researchers believed that calculation with different weights for the same indexes in the set of homogeneous decision units is not logical. The important problem is how all decision units with a weight measured and simultaneously their efficiency is optimized. So, in this paper a model presented that all decision units measured with a weight and simultaneously efficiency of decision making units is optimized. [Hossein Safari, Abdol Hossein Jafarzadeh, Mohsen Moradi-Moghadam, Meysam Molavi. A New Decision Model Based on the Common Set of Weights DEA and Liner Goal Programming. Rep Opinion 2013;5(5):54-61]. (ISSN: 1553-9873). http://www.sciencepub.net/report. 8
2017
Selection problems which contain many criteria are important and complex problems that involve different approaches have been proposed to fulfill this job. The Analytic Hierarchy Process (AHP) can be very useful in obtaining a likely result which can consider the decision maker's subjective ideas. On the other hand, the Data Envelopment Analysis (DEA) has been a popular method for measuring the relative efficiency of decision making units (DMUs) and ranking them objectively in quantitative data. In this paper, a three-step procedure based on both DEA and AHP was formulated and applied to a case study. The procedure maintained the philosophy inherent in DEA by allowing each DMU to generate its own vector of weights. These vectors of weights were used to construct a group of pairwise comparison matrices which were perfectly consistent. Then, we utilized group AHP method to produce the best common weights compatible with the DMUs judgments. Using the proposed approach can give prec...
An interactive MOLP method for solving output-oriented DEA problems with undesirable factors
Journal of Industrial and Management Optimization, 2015
Data Envelopment Analysis (DEA) and Multiple Objective Linear Programming (MOLP) are widely used for performance assessment in organizations. Although DEA and MOLP are similar in structure, DEA is used to assess and analyze past performance and MOLP is used to predict future performance. Several equivalence models between output-oriented DEA models and MOLP models have been proposed in the literature. However these models are not applicable to performance evaluation problems with undesirable outputs. We propose an interactive method for solving output-oriented DEA models with undesirable outputs. We show that the output-oriented BCC model of Seiford and Zhu [47] can be equivalently stated as the maximization of the minimum of several objectives over the production possibility set, which in turn is a scalarization of a multi-objective linear program. We then employ the well-known Zionts-Wallenius procedure to solve the multi-objective optimization problem. We present an example to demonstrate the applicability of the proposed method and exhibit the efficacy of the procedures and algorithms.
A characteristic of data envelopment analysis (DEA) is to allow individual decision making units (DMUs) to select the most advantageous weights in calculating their efficiency scores. This flexibility, on the other hand, deters the comparison among DMUs on a common base. For dealing with this difficulty and assessing all the DMUs on the same scale, this paper proposes using a multiple objective linear programming (MOLP) approach for generating a common set of weights in the DEA framework.
A GOAL PROGRAMMING APPROACH TO SOLVE THE MULTIPLE CRITERIA DEA MODEL
2017
The lack of discrimination power and the inappropriate multipliers schemes remain major issues in data envelopment analysis (DEA). To overcome these problems, the multiple criteria DEA (MCDEA) model was introduced in the late 1990s, drawing from a multiple objective perspective. However, because the objectives of the MCDEA model are generally conflicting, an optimal solution satisfying all objectives simultaneously often does not exist. Within this context, goal programming (GP) approaches were proposed to solve the MCDEA model. This paper focuses specifically on the GP formulation, known as GPDEA. However, recently, the GPDEA models were found to be invalid, and no alternative formulation, under a GP framework, was proposed. Therefore, the aim here is to develop a formulation for adequately solving the MCDEA model using weighted GP. In order to do so, we point out inconsistencies in the existing GPDEA models, and we present the WGP-MCDEA model.
A Comparative Study of Ahp and Dea
Advances in DEA Theory and Applications, 2017
Both Analytic Hierarchy Process (AMP) and Data Envelopment Analysis (DEA). aim at making decisions under multiple criteria environments. AHP uses pairwise comparisons and eigenvector weightings, whereas DEA does linear fractional programmings. In this paper, we will point out some structural similarities among them, by comparing the benefit/cost analysis by AHP and DEA. Also, we will discuss on the fixed vs. variable weights In multiple criteria decision making.
can perform a benchmarking process to improve their performance. However, several practical problems need to be addressed in benchmark target selection. One issue discussed in this research is that it might not be feasible for an inefficient DMU to achieve its target's efficiency in a single step, especially when the DMU is far from the benchmark target DMU. To resolve this problem, various methods of stepwise benchmarking have been proposed. Most of these methods, however, only consider the efficiency score in selecting benchmark targets and ignore various practical aspects that should be considered. In this paper, we propose a new method of stepwise benchmarking based on three criteria: preference, direction and similarity. The first criterion, preference, is used for selecting an ultimate benchmark target; the second criterion, direction is used in selecting intermediate benchmark targets which are located more closely to the improving path; and the third criterion, similarity is used for determining intermediate benchmark targets which are similar to the DMU under evaluation. Considering these three criteria, we develop a method of constructing a more practical and feasible sequence of benchmark targets.
Multiple Objective Approach as an Alternative to Radial Projection in DEA
Journal of Productivity Analysis, 2003
Radial projection is a standard technique applied in data envelopment analysis (DEA) to calculate efficiency scores for input and/or output variables. In this paper, we have studied the appropriateness of radial projection for target setting. We have created a situation where the decision making units (DMUs) are free to choose their own target values on the efficient frontier and then compared the results to those of radial projection. In practice, target values are primarily used for future goal attainment; hence, not only preferences but also, and on the whole, change in time frame, affect the choice of target values. Based on that, we conducted an empirical experiment with an aim to study how the DMUs choose their most preferred target values on the efficient frontier. The subjects, who all were students of the Helsinki School of Economics, were given the freedom to explore their personalized efficient frontiers by using a multiple objective linear programming (MOLP) approach. To study various and relevant scenarios, the personalized efficient frontiers for all students were constructed in such a way that the current position of each student in relation to the frontier made him/her inefficient, efficient, or super-efficient. The results show that the use of radial projection for target setting is too restrictive.