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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., Shoja, N., & Sanei, M. (2004). An alternative approach for equitable allocation of shared costs by using DEA. Applied Mathematics and Computation, 153(1), 267–274.
Abstract: In many applications to which data envelopment analysis could be applied, there is often a fixed or common cost, which is imposed on all decision making units (DMUs), so that this cost can be assigned in an equitable way to the various DMUs. In a proposed approach by Cook and Kress [Eur. J. Oper. Res. 119 (1999) 652] of equitable allocation of shared costs between all DMUs, several problems should be solved, which gives rise to computational difficulties. In this paper, an approach is presented in which without solving linear programming problems only using simple formula, the equitable allocation is achieved.
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Jahanshahloo, G. R., Hosseinzadeh Lotfi, F., Shoja, N., & Tohidi, G. (2004). A method for finding efficient DMUs in DEA Using linear programming. Applied Mathematics and Computation, 159(1), 37–45.
Abstract: In this paper, by using 0-1 linear programming a method is proposed to find efficient decision making units (DMUs). In proposed method, we put aside the production possibility set principles of the data envelopment analysis (DEA) models and only consider the observations set. The presented method compares each DMU with observed DMUs and identifies the efficient DMUs. This method consists of a one-stage algorithm. In each iteration of this algorithm, by solving a 0-1 linear programming problem, at least one efficient DMU is identified.
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Jahanshahloo, G. R., Hosseinzadeh Lotfi, F., Shoja, N., Tohidi, G., & Razavyan, S. (2004). Input estimation and identification of extra inputs in inverse DEA models. Applied Mathematics and Computation, 156(2), 427–437.
Abstract: In this paper we show that the inverse data envelopment analysis (DEA) models can be used to estimate inputs for a decision making unit (DMU) when some or all outputs and efficiency level of this DMU are increased or preserved. An approach is also introduced to identify extra inputs (maximum reduction amounts in inputs) when the outputs are estimated using the proposed models by Yan et al. [European Journal of Operational Research 136 (2002) 19] and Jahanshahloo et al. [Applied Mathematics and Computation 19 (2003)]. Numeric results are presented for an example taken from the literature.
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Jahanshahloo, G. R., Hosseinzadeh Lotfi, F., Shoja, N., Tohidi, G., & Razavyan, S. (2004). Ranking using I1-norm in data envelopment analysis. Applied Mathematics and Computation, 153(1), 215–224.
Abstract: In this paper, we present a method for previous termrankingnext term extreme efficient decision making units in previous termdata envelopment analysisnext term models with constant and variable returns to scale. In this method, we exploit the leave-one-out idea and l1-previous termnorm.next term The proposed method in this paper is able to remove the existing difficulties in some methods.
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Jahanshahloo, G. R., Hosseinzadeh Lotfi, F., Shoja, N., Tohidi, G., & Razavyan, S. (2004). The outputs estimation of a DMU according to improvement of its efficiency. Applied Mathematics and Computation, 147(2), 409–413.
Abstract: This paper develops the presented method by Yan et al. [Eur. J. Operat. Res. 136 (2002) 19]. In this paper, by using inverse data envelopment analysis model, a method to estimate output levels of a decision making unit is presented when some or all of its input entities are increased and its current efficiency level is improved.
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Jahanshahloo, G. R., Sanei, M., Hosseinzadeh Lotfi, F., & Shoja, N. (2004). Using the gradient line for ranking DMUs in DEA. Applied Mathematics and Computation, 151(1), 209–219.
Abstract: In this paper a method, based on using gradient line, for ranking DMUs is proposed. The advantage of this method is its stability and robustness, where data have special structure. Some numerical examples are presented to show the results.
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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., 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., Shoja, N., Tohidi, G., & Razavyan, S. (2005). A one-model approach to classification and sensitivity analysis in DEA. Applied Mathematics and Computation, 169(2), 887–896.
Abstract: In this paper we use a simple but very important modification of proposed model by Cooper et al. [Journal of Productivity Analysis 15 (2001) 217-246] for classification and determining stability radius and variations ranges of efficient and inefficient decision making units (DMUs). In the suggested method, the number of problems which are solved, is less than of previous methods. We apply the presented approach for real world data set.
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