Hosseinzadeh Lotfi, F., Jahanshahloo, G. R., & Esmaeili, M. (2007). Sensitivity analysis of efficient units in the presence of non-discretionary inputs. Applied Mathematics and Computation, 190(2), 1185–1197.
Abstract: Discretionary models of data envelopment analysis (DEA) assume that all inputs and outputs can be varied at the discretion of management or other users. In any realistic situation, however, there may exist ’exogenously fixed’ or non-discretionary factors that are beyond the control of a DMU’s management, which also need to be considered. This paper discusses and reviews the use of super-efficiency approach in data envelopment analysis (DEA) sensitivity analyses when some inputs are exogenously fixed. Super-efficiency data envelopment analysis (DEA) model is obtained when a decision making unit (DMU) under evaluation is excluded from the reference set. In this paper by means of modified Banker and Morey’s (BM hereafter) model [R.D. Banker, R. Morey, Efficiency analysis for exogenously fixed inputs and outputs, Operations Research 34 (1986) 513-521], in which the test DMU is excluded from the reference set, we are able to determine what perturbations of discretionary data can be tolerated before frontier DMUs become nonfrontier.
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Hosseinzadeh Lotfi, F., Jahanshahloo, G. R., & Esmaeili, M. (2007). An alternative approach in the estimation of returns to scale under weight restrictions. Applied Mathematics and Computation, 189(1), 719–724.
Abstract: This paper discusses the issue of returns to scale (RTS) under weight restrictions in data envelopment analysis (DEA). We first review Tone’s method [K. Tone, On returns to scale under weight restrictions in data envelopment analysis, Journal of Productivity Analysis 16 (2001) 31-47] for estimating returns to scale under weight restrictions. Then a new approach is introduced for this task, based upon the sum of the optimal lambda values in the weighted CCR model. The equivalence of this method and Tone?s method is proved. We then apply the method to a real world data set.
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Jahanshahloo, G. R., Hosseinzadeh Lotfi, F., & Moradi, M. (2005). A DEA approach for fair allocation of common revenue. Applied Mathematics and Computation, 160(3), 719–724.
Abstract: An issue of considerable importance, how to allocate a common revenue in an equitable manner across a set of competing entities. This paper introduces a new approach to obtaining allocation common revenue on all decision making units (DMUs) in such a way that the relative efficiency is not changed. In this method for determining allocation common revenue dose not need to solving any linear programming. A numerical example is provided to illustrate the results of the analysis.
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Jahanshahloo, G. R., Hosseinzadeh Lotfi, F., & Moradi, M. (2004). Sensitivity and stability analysis in DEA with interval data. Applied Mathematics and Computation, 156(2), 463–477.
Abstract: In this paper, we find radius of stability for all decision making units, with interval data. In this approach, organization classification remains unchanged under perturbations of the interval data. Some numerical examples for illustration are given.
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Jahanshahloo, G. R., Hosseinzadeh Lotfi, F., Rezai Balf, F., & Zhiani Rezai, H. (2008). Using Monte Carlo method for ranking interval data. Applied Mathematics and Computation, 201(1-2), 613–620.
Abstract: Some methods have been presented for ranking efficient decision making units (DMUs) in data envelopment analysis (DEA). This paper addresses the ranking of interval data by using Monte Carlo method. This method is based on a paper [G.R. Jahanshahloo, F. Hosseinzadeh Lotfi, H. Zhiani Rezai, F. Rezai Balf, Using Monte Carlo method for ranking efficient DMUs, Applied Mathematics and Computation 162 (2005) 371-–379]. The worthwhile this method is its ability in ranking of extreme and non-extreme efficient DMUs.
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Jahanshahloo, G. R., Hosseinzadeh Lotfi, F., Rezai Balf, F., & Zhiani Rezai, H. (2007). Discriminant analysis of interval data using Monte Carlo method in assessment of overlap. Applied Mathematics and Computation, 191(2), 521–532.
Abstract: In this paper we show that the method of discriminant analysis (DA), on interval data by data envelopment analysis (DEA). DEA-discriminant analysis (DEA-DA) is designed to identify the existence or non-existence of an overlap between two groups, by separating hyperplane. In addition it predicts a new observation to the group which it belongs to. Data envelopment analysis technique which is developed based on the mathematical programming, evaluates the relative efficiency of a set of homogeneous decision making units. However, there are similarities between DEA and DA. DA is a method for separating two sets with previous knowledge meanwhile DEA is a technique for separating two sets efficient and inefficient without previous knowledge. Also goal programming method can be used for both of these methods.
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Jahanshahloo, G. R., Hosseinzadeh Lotfi, F., Rezai, H. Z., & Balf, F. R. (2007). Finding strong defining hyperplanes of Production Possibility Set. European Journal of Operational Research, 177(1), 42–54.
Abstract: Production Possibility Set (PPS) is defined as the set of all inputs and outputs of a system in which inputs can produce outputs. Data Envelopment Analysis models implicitly use PPS to evaluate relative efficiency of Decision Making Units (DMUs). Although DEA models can determine the efficiency of a DMU, they cannot present efficient frontiers of PPS. In this paper, we propose a method for finding all Strong Defining Hyperplanes of PPS (SDHP). They are equations that form efficient surfaces. These equations are useful in Sensitivity and Stability Analysis, the status of Returns to Scale of a DMU, incorporating performance information into the efficient frontier analysis and so on.
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Jahanshahloo, G. R., Hosseinzadeh Lotfi, F., Rezai, H. Z., & Balf, F. R. (2005). Using Monte Carlo method for ranking efficient DMUs. Applied Mathematics and Computation, 162(1), 371–379.
Abstract: For ranking efficient DMUs some methods have been developed. These methods are not able to rank non-extreme efficient DMUs. In this paper, using Monte Carlo method, a method has been developed which is able to rank all (extreme and non-extreme) efficient DMUs.
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Jahanshahloo, G. R., Hosseinzadeh Lotfi, F., Rostamy Malkhalifeh, M., & Ahadzadeh Namin, M. (2009). A generalized model for data envelopment analysis with interval data. Applied Mathematical Modelling, 33(7), 3237–3244.
Abstract: Data envelopment analysis (DEA) is a method to estimate the relative efficiency of decision-making units (DMUs) performing similar tasks in a production system that consumes multiple inputs to produce multiple outputs. So far, a number of DEA models with interval data have been developed. The CCR model with interval data, the BCC model with interval data and the FDH model with interval data are well known as basic DEA models with interval data. In this study, we suggest a model with interval data called interval generalized DEA (IGDEA) model, which can treat the stated basic DEA models with interval data in a unified way. In addition, by establishing the theoretical properties of the relationships among the IGDEA model and those DEA models with interval data, we prove that the IGDEA model makes it possible to calculate the efficiency of DMUs incorporating various preference structures of decision makers.
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Jahanshahloo, G. R., Hosseinzadeh Lotfi, F., Shahverdi, R., Adabitabar, M., Rostamy-Malkhalifeh, M., & Sohraiee, S. (2009). Ranking DMUs by I1-norm with fuzzy data in DEA. Chaos, Solitons & Fractals, 39(5), 2294–2302.
Abstract: The relative efficiency of a DMU is the result of comparing the inputs and outputs of the DMU and those of other DMUs in the PPS (production possibility set). If the inputs and outputs are fuzzy, the DMUs cannot be easily evaluated and ranked using the obtained efficiency scores. In this paper, presenting a new idea for ranking of DMUs with fuzzy data. And finally, we introduce a numerical example.
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