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Papers by Akram Dehnokhalaji

European Journal of Operational Research

Journal of New Researches in Mathemetics, Jan 27, 2019

The full ranking or complete ranking of decision making units is one of the main ‎issues in data ... more The full ranking or complete ranking of decision making units is one of the main ‎issues in data envelopment analysis. A full ranking is a ranking that considers all ‎efficient and inefficient units simultaneously and finds a ranking for them. Almost all ‎of the developed ranking methods consider only the efficient units. On the other hand, ‎ranking inefficient units by traditional data envelope analysis models are also ‎inaccurate due to ignoring the role of slacks. In the present paper two novel methodologies are proposed in order to fully ranking of decision making units. In the presented ‎approach, all of the decision making units participate in a competition in a way that all ‎are projected onto the efficient frontier considering common weights. Then, according ‎to the profit that each unit attains to reach this standard level, a rank order of all ‎decision making units are obtained.In the first method , the satisfaction of units is measured in the competition and the satisfact...

Computers & Industrial Engineering, 2019

In this paper, we propose two new centralized resource allocation methods extending Lozano and Vi... more In this paper, we propose two new centralized resource allocation methods extending Lozano and Villa's method (2004) to more general cases. The main assumption in this study is that all Decision Making Units (DMUs) are operating under the supervision of a central DMU in order to introduce the input and output targets for all units in the next production period. This paper considers two planning ideas. The first one is maximizing outputs produced with future planned resources and removing all input inefficiencies as much as possible while making all units strongly efficient. The second one is optimizing total revenue and cost functions to reach the best performance of the system. All units are assumed to be able to adjust their input consumptions and output productions in the current Production Possibility Set (PPS). Finally, we show that the two proposed methods provide the same results when input and output prices are replaced with their corresponding shadow prices. The proposed methods are illustrated with two empirical data sets.

European Journal of Operational Research, 2017

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service... more This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Highlights  A lexicographic approach radially projects units onto the efficient frontier.  Components of the radial projection vector are dropped step by step.  The target on the efficient frontier is found in the spirit of radial projection.  The (in)efficiency score is individual for all controllable variables.  A numerical illustration and an empirical example demonstrate the approach.

Foundations of Computing and Decision Sciences, 2021

In this paper, we consider the problem of allocating resources among Decision Making Units (DMUs)... more In this paper, we consider the problem of allocating resources among Decision Making Units (DMUs). Regarding the concept of overall (cost) efficiency, we consider three different scenarios and formulate three Resource Allocation (RA) models correspondingly. In the first scenario, we assume that overall efficiency of each unit remains unchanged. The second scenario is related to the case where none of overall efficiency scores is deteriorated. We improve the overall efficiencies by a pre-determined percentage in the last scenario. We formulate Linear Programming problems to allocate resources in all scenarios. All three scenarios are illustrated through numerical and empirical examples.

European Journal of Operational Research, 2018

Journal of the Operational Research Society, 2018

Abstract The conventional DEA models assume that all variables are measured on a ratio scale. How... more Abstract The conventional DEA models assume that all variables are measured on a ratio scale. However, in many applications, we have to deal with interval scale data. In Dehnokhalaji, A., Korhonen, P. J., Köksalan, M., Nasrabadi, N., & Wallenius, J. (2010). Efficiency analysis to incorporate interval scale data. European Journal of Operational Research 207(2), 1116–1121, we proposed a model for efficiency analysis to incorporate interval scale data in addition to ratio scale data. Our proposed model provides efficiency scores for each unit, but does not suggest target unit(s) for inefficient ones directly. In this paper, we investigate the concept of benchmarking in Dehnokhalaji et al.?s (2010) model. We propose an algorithm which results in a path of targets for each inefficient unit. All units on this path are better than the unit under evaluation in terms of efficiency scores defined for interval scale data. The intermediate targets belong to sequential layers obtained from a layering algorithm and the final unit on the path is an efficient unit.

Journal of the Operational Research Society, 2019

The goal in efficiency analysis is not only to evaluate a Decision Making Unit (DMU) performance,... more The goal in efficiency analysis is not only to evaluate a Decision Making Unit (DMU) performance, but also to find an efficient target which provides information on inputs reduction and outputs increment values that are necessary to remove inefficiencies for each inefficient DMU. In Data Envelopment Analysis (DEA) the target unit is located on the efficient frontier and possibly far from the unit under assessment. Therefore, in practice performance improvement seems to be disappointing or even impossible to achieve in only one step for some inefficient DMUs. In this regard, finding intermediate targets is of great importance in benchmarking literature. In this paper we find a sequence of targets instead of a single target for each inefficient unit. In our method, the intermediate target at each step has three properties:(I) the intermediate targets and the unit under evaluation are all similar in size; (II) efficiency scores are ascending through the sequence of targets; (III) the target unit at each step is close to the special part of the efficient frontier as much as possible. These properties lead to finding a target that is more achievable in real applications.

OR Spectrum, 2017

One of the major research streams in data envelopment analysis (DEA) is ranking decision-making u... more One of the major research streams in data envelopment analysis (DEA) is ranking decision-making units (DMUs). Utilizing a multicriteria decision-making technique, we develop a novel approach to fully rank all units. Motivated by the convex cone-based total order for multiple criteria alternatives proposed by Dehnokhalaji et al. (Nav Res Logist 61(2):155–163, 2014), we consider DMUs in DEA as multiple criteria alternatives and obtain their total ordering. Initially, some pairwise preference information is provided by the decision maker for units and the concepts of convex cones and polyhedral sets are defined in a DEA framework, correspondingly. We apply a modification of Dehnokhalaji et al. method to extract additional preference information for each pair of units and consequently obtain a full ranking (strict total ordering) of DMUs. The benefit of our approach to their method is that we apply non-radial models to overcome the instability drawback of radial models and their infeasibility occurring in DEA applications. The proposed approach is implemented for two numerical examples, and the accuracy of it is investigated through a computational test.

Naval Research Logistics (NRL), 2014

The problem of finding a strict total order for a finite set of multiple criteria alternatives is... more The problem of finding a strict total order for a finite set of multiple criteria alternatives is considered. Our research extends previous work by us, which considered finding a partial order for a finite set of alternatives. We merge the preference information extracted from the preference cones and corresponding polyhedral sets, with the information derived from pairwise comparisons of two alternatives, yielding a preference matrix. This preference matrix is used as input to an integer programming model to obtain a strict total order that provides a transitive ranking for the set of alternatives.

Decision Support Systems, 2011

In this paper, we consider the problem of finding a preference-based strict partial order for a f... more In this paper, we consider the problem of finding a preference-based strict partial order for a finite set of multiple criteria alternatives. We develop an approach based on information provided by the decision maker in the form of pairwise comparisons. We assume that the decision maker's value function is not explicitly known, but it has a quasi-concave form. Based on

Annals of Operations Research, 2011

In this paper the problem of allocating resources among Decision Making Units is considered. This... more In this paper the problem of allocating resources among Decision Making Units is considered. This study covers the case in which several homogeneous units are operating under the supervision of a central unit. The resource allocation is carried out by the DM (central unit) in such a way that the overall performance of the system is improved. Performance is defined by means of a convex combination of the ratio of the efficiencies before and after the resource allocation. It is assumed that each unit is allowed to modify its resources within the current production possibility set. A novel model is proposed which aims at achieving the best performance of the system. The method is capable of dealing with some additional constraints, imposed by the DM. The model is illustrated by a simple numerical example and a real application.

European Journal of Operational Research, 2010

European Journal of Operational Research

Expert Systems with Applications

Transportation Research Part D: Transport and Environment

Annals of Operations Research

International Journal of Operational Research

Numerical Algebra, Control & Optimization

European Journal of Operational Research

Journal of New Researches in Mathemetics, Jan 27, 2019

The full ranking or complete ranking of decision making units is one of the main ‎issues in data ... more The full ranking or complete ranking of decision making units is one of the main ‎issues in data envelopment analysis. A full ranking is a ranking that considers all ‎efficient and inefficient units simultaneously and finds a ranking for them. Almost all ‎of the developed ranking methods consider only the efficient units. On the other hand, ‎ranking inefficient units by traditional data envelope analysis models are also ‎inaccurate due to ignoring the role of slacks. In the present paper two novel methodologies are proposed in order to fully ranking of decision making units. In the presented ‎approach, all of the decision making units participate in a competition in a way that all ‎are projected onto the efficient frontier considering common weights. Then, according ‎to the profit that each unit attains to reach this standard level, a rank order of all ‎decision making units are obtained.In the first method , the satisfaction of units is measured in the competition and the satisfact...

Computers & Industrial Engineering, 2019

In this paper, we propose two new centralized resource allocation methods extending Lozano and Vi... more In this paper, we propose two new centralized resource allocation methods extending Lozano and Villa's method (2004) to more general cases. The main assumption in this study is that all Decision Making Units (DMUs) are operating under the supervision of a central DMU in order to introduce the input and output targets for all units in the next production period. This paper considers two planning ideas. The first one is maximizing outputs produced with future planned resources and removing all input inefficiencies as much as possible while making all units strongly efficient. The second one is optimizing total revenue and cost functions to reach the best performance of the system. All units are assumed to be able to adjust their input consumptions and output productions in the current Production Possibility Set (PPS). Finally, we show that the two proposed methods provide the same results when input and output prices are replaced with their corresponding shadow prices. The proposed methods are illustrated with two empirical data sets.

European Journal of Operational Research, 2017

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service... more This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Highlights  A lexicographic approach radially projects units onto the efficient frontier.  Components of the radial projection vector are dropped step by step.  The target on the efficient frontier is found in the spirit of radial projection.  The (in)efficiency score is individual for all controllable variables.  A numerical illustration and an empirical example demonstrate the approach.

Foundations of Computing and Decision Sciences, 2021

In this paper, we consider the problem of allocating resources among Decision Making Units (DMUs)... more In this paper, we consider the problem of allocating resources among Decision Making Units (DMUs). Regarding the concept of overall (cost) efficiency, we consider three different scenarios and formulate three Resource Allocation (RA) models correspondingly. In the first scenario, we assume that overall efficiency of each unit remains unchanged. The second scenario is related to the case where none of overall efficiency scores is deteriorated. We improve the overall efficiencies by a pre-determined percentage in the last scenario. We formulate Linear Programming problems to allocate resources in all scenarios. All three scenarios are illustrated through numerical and empirical examples.

European Journal of Operational Research, 2018

Journal of the Operational Research Society, 2018

Abstract The conventional DEA models assume that all variables are measured on a ratio scale. How... more Abstract The conventional DEA models assume that all variables are measured on a ratio scale. However, in many applications, we have to deal with interval scale data. In Dehnokhalaji, A., Korhonen, P. J., Köksalan, M., Nasrabadi, N., & Wallenius, J. (2010). Efficiency analysis to incorporate interval scale data. European Journal of Operational Research 207(2), 1116–1121, we proposed a model for efficiency analysis to incorporate interval scale data in addition to ratio scale data. Our proposed model provides efficiency scores for each unit, but does not suggest target unit(s) for inefficient ones directly. In this paper, we investigate the concept of benchmarking in Dehnokhalaji et al.?s (2010) model. We propose an algorithm which results in a path of targets for each inefficient unit. All units on this path are better than the unit under evaluation in terms of efficiency scores defined for interval scale data. The intermediate targets belong to sequential layers obtained from a layering algorithm and the final unit on the path is an efficient unit.

Journal of the Operational Research Society, 2019

The goal in efficiency analysis is not only to evaluate a Decision Making Unit (DMU) performance,... more The goal in efficiency analysis is not only to evaluate a Decision Making Unit (DMU) performance, but also to find an efficient target which provides information on inputs reduction and outputs increment values that are necessary to remove inefficiencies for each inefficient DMU. In Data Envelopment Analysis (DEA) the target unit is located on the efficient frontier and possibly far from the unit under assessment. Therefore, in practice performance improvement seems to be disappointing or even impossible to achieve in only one step for some inefficient DMUs. In this regard, finding intermediate targets is of great importance in benchmarking literature. In this paper we find a sequence of targets instead of a single target for each inefficient unit. In our method, the intermediate target at each step has three properties:(I) the intermediate targets and the unit under evaluation are all similar in size; (II) efficiency scores are ascending through the sequence of targets; (III) the target unit at each step is close to the special part of the efficient frontier as much as possible. These properties lead to finding a target that is more achievable in real applications.

OR Spectrum, 2017

One of the major research streams in data envelopment analysis (DEA) is ranking decision-making u... more One of the major research streams in data envelopment analysis (DEA) is ranking decision-making units (DMUs). Utilizing a multicriteria decision-making technique, we develop a novel approach to fully rank all units. Motivated by the convex cone-based total order for multiple criteria alternatives proposed by Dehnokhalaji et al. (Nav Res Logist 61(2):155–163, 2014), we consider DMUs in DEA as multiple criteria alternatives and obtain their total ordering. Initially, some pairwise preference information is provided by the decision maker for units and the concepts of convex cones and polyhedral sets are defined in a DEA framework, correspondingly. We apply a modification of Dehnokhalaji et al. method to extract additional preference information for each pair of units and consequently obtain a full ranking (strict total ordering) of DMUs. The benefit of our approach to their method is that we apply non-radial models to overcome the instability drawback of radial models and their infeasibility occurring in DEA applications. The proposed approach is implemented for two numerical examples, and the accuracy of it is investigated through a computational test.

Naval Research Logistics (NRL), 2014

The problem of finding a strict total order for a finite set of multiple criteria alternatives is... more The problem of finding a strict total order for a finite set of multiple criteria alternatives is considered. Our research extends previous work by us, which considered finding a partial order for a finite set of alternatives. We merge the preference information extracted from the preference cones and corresponding polyhedral sets, with the information derived from pairwise comparisons of two alternatives, yielding a preference matrix. This preference matrix is used as input to an integer programming model to obtain a strict total order that provides a transitive ranking for the set of alternatives.

Decision Support Systems, 2011

In this paper, we consider the problem of finding a preference-based strict partial order for a f... more In this paper, we consider the problem of finding a preference-based strict partial order for a finite set of multiple criteria alternatives. We develop an approach based on information provided by the decision maker in the form of pairwise comparisons. We assume that the decision maker's value function is not explicitly known, but it has a quasi-concave form. Based on

Annals of Operations Research, 2011

In this paper the problem of allocating resources among Decision Making Units is considered. This... more In this paper the problem of allocating resources among Decision Making Units is considered. This study covers the case in which several homogeneous units are operating under the supervision of a central unit. The resource allocation is carried out by the DM (central unit) in such a way that the overall performance of the system is improved. Performance is defined by means of a convex combination of the ratio of the efficiencies before and after the resource allocation. It is assumed that each unit is allowed to modify its resources within the current production possibility set. A novel model is proposed which aims at achieving the best performance of the system. The method is capable of dealing with some additional constraints, imposed by the DM. The model is illustrated by a simple numerical example and a real application.

European Journal of Operational Research, 2010

European Journal of Operational Research

Expert Systems with Applications

Transportation Research Part D: Transport and Environment

Annals of Operations Research

International Journal of Operational Research

Numerical Algebra, Control & Optimization