
Chen, L.  H., & Lu, H.  W. (2008). Responses and comments to ’A comment on ’An extended assignment problem considering multiple inputs and outputs”. Applied Mathematical Modelling, 32(11), 2463–2466.
Abstract: This note is to response the comments from Jahanshahloo and Afzalinejad for the problem of DEA model formulation in Chen and Lu’s paper [L.H. Chen, H.W. Lu, An extended assignment problem considering multiple inputs and outputs, Appl. Math. Model. 31 (2007) 22392248]. The models adopted in that paper are formulated as the outputoriented BCC models, but not inputoriented BCC models stated in Jahanshahloo and Afzalinejad’s comments. Actually, the applied models are adopted in the relevant literature. Four examples, including the example from Jahanshahloo and Afzalinejad, are provided for justifying the responses.



Chen, L.  H., & Lu, H.  W. (2007). An extended assignment problem considering multiple inputs and outputs. Applied Mathematical Modelling, 31(10), 2239–2248.
Abstract: The existing assignment problems for assigning n jobs to n individuals are limited to the considerations of cost or profit incurred by each possible assignment. However, in real applications, various inputs and outputs are usually concerned in an assignment problem, such as a general decisionmaking problem. This paper develops a procedure for resolving assignment problems with multiple incommensurate inputs and outputs for each possible assignment. The concept of the relative efficiency in using various resources, instead of cost or profit, is adopted for each possible assignment of the problem. Data envelopment analysis (DEA) is employed in this paper to measure the efficiency of one assignment relative to that of the others according to a set of decisionmaking units. A composite efficiency index, consisting of two kinds of relative efficiencies under different comparison bases, is defined to serve as the performance measurement of each possible assignment in the problem formulation. A mathematical programming model for the extended assignment problem is proposed, which is then expressed as a classical integer linear programming model to determine the assignments with the maximum efficiency. A numerical example is used to demonstrate the approach.



Emrouznejad, A., & Amin, G. R. (2009). DEA models for ratio data: Convexity consideration. Applied Mathematical Modelling, 33(1), 486–498.
Abstract: Data envelopment analysis (DEA) is defined based on observed units and by finding the distance of each unit to the border of estimated production possibility set (PPS). The convexity is one of the underlying assumptions of the PPS. This paper shows some difficulties of using standard DEA models in the presence of inputratios and/or outputratios. The paper defines a new convexity assumption when data includes a ratio variable. Then it proposes a series of modified DEA models which are capable to rectify this problem.



Farahani, R. Z., Seifi, M. S., & Asgari, N. (2010). Multiple criteria facility location problems: A survey. Applied Mathematical Modelling, 34(7), 1689–1709.
Abstract: This paper provides a review on recent efforts and development in multicriteria location problems in three categories including biobjective, multiobjective and multiattribute problems and their solution methods. Also, it provides an overview on various criteria used. While there are a few chapters or sections in different location books related to this topic, we have not seen any comprehensive review papers or book chapter that can cover it. We believe this paper can be used as a complementary and updated version.



Foroughi, A. A., & Jafari, Y. (2009). A modified method for constructing efficient solutions structure of MOLP. Applied Mathematical Modelling, 33(5), 2403–2410.
Abstract: This paper deals with a recently proposed algorithm for obtaining all weak efficient and efficient solutions in a multi objective linear programming (MOLP) problem. The algorithm is based on solving some weighted sum problems, and presents an easy and clear solution structure. We first present an example to show that the algorithm may fail when at least one of these weighted sum problems has not a finite optimal solution. Then, the algorithm is modified to overcome this problem. The modified algorithm determines whether an efficient solution exists for a given MOLP and generates the solution set correctly (if exists) without any change in the complexity.



Giokas, D. I., & Pentzaropoulos, G. C. (1995). Evaluating the relative operational efficiency of largescale computer networks: An approach via data envelopment analysis. Applied Mathematical Modelling, 19(6), 363–370.
Abstract: The objective of the present study was the development of a methodology to be used as an aid in decision making for the attainment of optimum operational efficiency in largescale computer communications networks. The above methodology is realized in two stages. In the first stage, a queueing model (M/M/1/K) of a typical network is developed, and analytical results for the main performance indicators are obtained. The results are used, in the second stage, as a starting point for the application of a data envelopment analysis (DEA) procedure to obtain characteristics of network operational efficiency. Emphasis is placed on suggestions for improving the efficiency level of (relatively) inefficient nodes; numerical examples are also provided to illustrate the applicability of various options. Finally, possible routes for achieving a higher level of overall network efficiency are discussed, within the context of a performance tuning procedure, which are aimed at reducing the effects of performance bottlenecks.



Gutiérrez, E., & Lozano, S. (2010). Data Envelopment Analysis of multiple response experiments. Applied Mathematical Modelling, 34(5), 1139–1148.
Abstract: Taguchi method is the usual strategy in robust design and involves conducting experiments using orthogonal arrays and estimating the combination of factor levels that optimizes a given performance measure, typically a signaltonoise ratio. The problem is more complex in the case of multiple responses since the combinations of factor levels that optimize the different responses usually differ. In this paper, an Artificial Neural Network, trained with the experiments results, is used to estimate the responses for all factor level combinations. After that, Data Envelopment Analysis (DEA) is used first to select the efficient (i.e. nondominated) factor level combinations and then for choosing among them the one which leads to a most robust quality loss penalization. Mean Square Deviations of the quality characteristics are used as DEA inputs. Among the advantages of the proposed approach over traditional Taguchi method are the nonparametric, nonlinear way of estimating quality loss measures for unobserved factor combinations and the nonparametric character of the performance evaluation of all the factor combinations. The proposed approach is applied to a number of case studies from the literature and compared with existing approaches.



Hatefi, S. M., & Jolai, F. (2010). A new model for classifying inputs and outputs and evaluating the performance of DMUs based on translog output distance function. Applied Mathematical Modelling, 34(6), 1439–1449.
Abstract: In conventional data envelopment analysis it is assumed that the input versus output status of each chosen performance measures is known. In some conditions finding a statue of some variables from the point view of input or output is very difficult; these variables treat as both an input and output and are called flexible measures. This paper proposes a new model based on translog output distance function for classifying inputs and outputs and evaluating the performance of decisionmaking units by considering flexible measures. Monte Carlo simulation is applied to evaluate the presented model comparing with that of the recent model found in the literature. The result shows that the measure efficiencies of our model are statistically closer to true efficiencies and have higher rank correlation with true efficiencies. Also results obtained from simulated data show that there are high correlation between our model and that of the recent model.



Jahanshahloo, G. R., & Afzalinejad, M. (2008). A comment on ’An extended assignment problem considering multiple inputs and outputs’. Applied Mathematical Modelling, 32(11), 2459–2462.
Abstract: This note shows that the data envelopment analysis (DEA) models formulated by Chen and Lu [L.H. Chen, H.W. Lu, An extended assignment problem considering multiple inputs and outputs, Appl. Math. Modell. 31 (2007) 2239–2248] are not correct. The enveloping form of the Chen and Lu formulation is studied and a simple example is presented to demonstrate the differences between the efficiency scores resulted of the Chen and Lu formulation, and the true ones.



Jahanshahloo, G. R., & Afzalinejad, M. (2006). A ranking method based on a fullinefficient frontier. Applied Mathematical Modelling, 30(3), 248–260.
Abstract: Since in evaluating by traditional data envelopment analysis (DEA) models many decision making units (DMUs) are classified as efficient, a large number of methods for fully ranking both efficient and inefficient DMUs have been proposed. In this paper a ranking method is suggested which basically differs from previous methods but its models are similar to traditional DEA models such as BCC, additive model, etc. In this ranking method, DMUs are compared against an fullinefficient frontier, which will be defined in this paper. Based on this point of view many models can be designed, and we mention a radial and a slacksbased one out of them. This method can be used to rank all DMUs to get analytic information about the system, and also to rank only efficient DMUs to discriminate between them.

