Andrey Lychev - Academia.edu (original) (raw)

Papers by Andrey Lychev

Journal of Global Optimization, Jul 25, 2019

In data envelopment analysis, methods for constructing sections of the frontier have been recentl... more In data envelopment analysis, methods for constructing sections of the frontier have been recently proposed to visualize the production possibility set. The aim of this paper is to develop, prove and test the methods for the visualization of production possibility sets using parallel computations. In this paper, a general scheme of the algorithms for constructing sections (visualization) of production possibility set is proposed. In fact, the algorithm breaks the original large-scale problems into parallel threads, working independently, then the piecewise solution is combined into a global solution. An algorithm for constructing a generalized production function is described in detail.

Doklady Mathematics, Sep 1, 2017

An approach based on optimization methods is developed for visualizing multidimensional frontiers... more An approach based on optimization methods is developed for visualizing multidimensional frontiers in nonconvex FDH models. This approach has earlier been used for frontier visualization in DEA models. Such an approach facilitates the computation of various scale characteristics in FDH models.

In this paper we consider the application of proposed analytics software for performance analysis... more In this paper we consider the application of proposed analytics software for performance analysis and visualization of complex financial systems. We give theoretical background of underlying mathematical method and present its application in information and communication technologies. Two nonparametric approaches data envelopment analysis (DEA) and free disposal hull (FDH) are used in this paper to develop a software system for convex and nonconvex frontier visualization and performance analysis of financial systems. Our theoretical results are validated by computational experiments on the data taken from financial accounts of Russian banks. Potential applications of proposed approach in situation room for decision support and strateuic nerformance manaaement are considered.

Annals of Operations Research, Apr 26, 2015

Inevitable simplifications of models of real world activities lead to some inadequacies. In the D... more Inevitable simplifications of models of real world activities lead to some inadequacies. In the DEA literature several methods were proposed to overcome such difficulties. Some authors proposed to use specific production units in the primal space of inputs and outputs as a starting point in order to improve the frontier of the DEA models. In our previous papers, we introduced the notion of terminal units. It was proved that only terminal units form necessary and sufficient set of units for improving the frontier. In this paper, the relationship between all sets of units proposed for improving the frontier is established. Our theoretical results are confirmed by extensive and instructive graphical examples and also verified by computational experiments using real-life data sets.

Doklady Mathematics, Nov 1, 2017

Free Disposal Hull (FDH) model was proposed in the end of 20-th century for performance measureme... more Free Disposal Hull (FDH) model was proposed in the end of 20-th century for performance measurement and management of complex units. Production possibility set of FDH model is a nonconvex set. For this reason, nonlinear integer programming methods and enumeration methods have been used for computations of various characteristics of units' performance. However, as Cesaroni, Kerstens and Van de Woestyne noted, there are no methods in the world scientific literature for frontier visualization in nonconvex FDH models. In this paper, an approach is proposed for frontier visualization with the use of methods of purposeful enumeration. Computational experiments, conducted with the use of real-life data sets, confirm reliability and effectiveness of proposed algorithms.

Computational Mathematics and Mathematical Physics, Mar 1, 2019

The free disposal hull (FDH) model of production technology assumes free disposability of all inp... more The free disposal hull (FDH) model of production technology assumes free disposability of all inputs and outputs, but does not make any convexity assumptions. In this paper, we develop an algorithm for the reconstruction of the frontier of the FDH technology that corresponds to its sections by different two-dimensional planes. From a practical perspective, the suggested algorithm is useful for the visualization and exploration of the efficient frontier of the FDH technology. Furthermore, based on the suggested algorithm, we develop a new procedure for the evaluation of returns to scale in the FDH technology. Compared to the existing methods, our approach does not require assessing the efficiency of productive units in the reference technologies, which is known to be a computationally intensive task. Our theoretical results are confirmed by computational experiments in applications with real-life data sets from different industries.

Data envelopment analysis journal, 2021

It is well known that many inefficient units are projected onto the weakly efficient parts of the... more It is well known that many inefficient units are projected onto the weakly efficient parts of the frontier under computing efficiency scores. However, according to the data envelopment analysis approach, the efficiency score of inefficient units has to be measured relative to efficient ones. In our previous papers, we introduced the notion of terminal units and proposed to use them for improving the frontier. In this paper, we describe two possible scenarios and discuss some aspects of algorithm implementation. Our theoretical results are verified by computational experiments using real-life data sets and confirmed by graphical examples.

Doklady Mathematics, Feb 1, 2012

Ima Journal of Management Mathematics, Mar 23, 2011

... As a result, significant distortion of the performance assessment of units takes place. Our t... more ... As a result, significant distortion of the performance assessment of units takes place. Our theo-retical results are validated by computational experiments on the data taken from financial accounts of Russian banks. ... (2) n ∑ j=1 yij λj − s+i = yio, i = 1,...,r, n ∑ ...

Doklady Mathematics, Feb 1, 2012

There are some specific features of the non-radial data envelopment analysis (DEA) models which c... more There are some specific features of the non-radial data envelopment analysis (DEA) models which cause some problems for the returns to scale measurement. In the scientific literature on DEA, some methods were suggested to deal with the returns to scale measurement in the non-radial DEA models. These methods are based on using Strong Complementary Slackness Conditions from optimization theory. However, our investigation and computational experiments show that such methods increase computational complexity significantly and may generate as optimal, solutions contradicting optimization theory. In this paper, we propose and substantiate a direct method for the returns to scale measurement in the nonradial DEA models. Our computational experiments documented that the proposed method works reliably and efficiently on the real-life data sets.

Nucleation and Atmospheric Aerosols, 2023

Advances in logistics, operations, and management science book series, Jun 24, 2015

In this chapter, an approach for evaluation of agreements on transnational projects during the ne... more In this chapter, an approach for evaluation of agreements on transnational projects during the negotiation process is proposed. One can show that the negotiation process can be represented as the behavior of decision-making units (countries) in the multidimensional space of economic indicators using Data Envelopment Analysis (DEA) models. In this case, the goals, which can be achieved by units as a result of accomplishment of a joint project, can be determined as points in the multidimensional space. Optimal directions toward these goals and cones of possible directions can be found with the help of Analytic Hierarchy Process (AHP). The efficiency measures for countries are calculated as ratios of the values of potential functions at the initial (intermediate) and final points. The increments of efficiencies measures are considered as arguments in the negotiation process. The approach is illustrated by the real-life data set taken from open international sources.

DEStech Transactions on Computer Science and Engineering, Feb 6, 2019

A lot of scientific literature in the world is devoted to the returns-to-scale (RTS) evaluation o... more A lot of scientific literature in the world is devoted to the returns-to-scale (RTS) evaluation of production units. Kerstens and Vanden Eeckaut were the first who considered the notion and evaluation of RTS for nonconvex Free Disposal Hull (FDH) models. Their methods are based on the comparison of the radial efficiency scores of a production unit in the FDH model and the corresponding non-increasing and non-decreasing RTS reference models. At the same time Cesaroni, Kerstens and Van de Woestyne noted the absence of papers in the world literature devoted to methods of frontier visualization in nonconvex models. In this paper, we developed methods for visualization of production function of nonconvex models and of the corresponding non-increasing and non-decreasing models. Our approach of frontier visualization can be used for decision making based on nonconvex models, it allows us to evaluate RTS for FDH models. Our results are confirmed by computational experiments in applications with real-life data sets.

Doklady Mathematics, Jun 1, 2009

The paper shows that many simple rating functions constructed on the basis of the ratio analysis ... more The paper shows that many simple rating functions constructed on the basis of the ratio analysis distort significantly the evaluation of the production units behavior. Opposite to the ratio analysis, the DEA approach investigate production units behaviour in the multidimentional space of indicators. In this paper, we compare the ration analysis and the DEA approach using properties of the mappings of the multidimentional sets, we also show that it is purposeful to construct rating functions on the basis of efficiency scores computed in DEA models.

Journal of Productivity Analysis, Dec 3, 2013

Applications of the DEA models show that inadequate results may arise in some cases, two of these... more Applications of the DEA models show that inadequate results may arise in some cases, two of these inadequacies being: a) too many efficient units may appear in some DEA models; b) a DEA model may show an inefficient unit from the point of view of experts as an efficient one. The purpose of this paper is to identify units that may unduly become efficient. The concept of a terminal unit is introduced for such units. A method for improving the adequacy of DEA models based on terminal units is suggested, and an example shown based on a real-life data set for Russian banks.

Journal of the Operational Research Society, Nov 1, 2009

Inadequate results may arise in some instances of DEA model applications. For example, a data env... more Inadequate results may arise in some instances of DEA model applications. For example, a data envelopment analysis (DEA) model may show 'a notoriously inefficient unit' as an efficient one. In addition, too many efficient units may appear in some DEA models. An elegant and subtle approach was proposed to deal with these problems, which is based on incorporating domination cones in DEA models. Yu, Wei and Brockett suggested the generalized DEA (GDEA) model that unifies and extends most of the well-known DEA models based on using domination cones. In this paper, we propose a model that is more general than the GDEA model, on the one hand, as it covers situations that the GDEA model cannot describe. On the other hand, our model enables one to construct step-by-step any model from the family of the GDEA models by incorporating artificial units and rays in the space of inputs and outputs in the Banker, Charnes, Cooper (BCC) model, which makes the process of model construction visible and more understandable. Moreover, we show that any GDEA model can be approximated by some BCC model.

Mathematics, Oct 2, 2022

This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY

Journal of Global Optimization, Jul 25, 2019

In data envelopment analysis, methods for constructing sections of the frontier have been recentl... more In data envelopment analysis, methods for constructing sections of the frontier have been recently proposed to visualize the production possibility set. The aim of this paper is to develop, prove and test the methods for the visualization of production possibility sets using parallel computations. In this paper, a general scheme of the algorithms for constructing sections (visualization) of production possibility set is proposed. In fact, the algorithm breaks the original large-scale problems into parallel threads, working independently, then the piecewise solution is combined into a global solution. An algorithm for constructing a generalized production function is described in detail.

Doklady Mathematics, Sep 1, 2017

An approach based on optimization methods is developed for visualizing multidimensional frontiers... more An approach based on optimization methods is developed for visualizing multidimensional frontiers in nonconvex FDH models. This approach has earlier been used for frontier visualization in DEA models. Such an approach facilitates the computation of various scale characteristics in FDH models.

In this paper we consider the application of proposed analytics software for performance analysis... more In this paper we consider the application of proposed analytics software for performance analysis and visualization of complex financial systems. We give theoretical background of underlying mathematical method and present its application in information and communication technologies. Two nonparametric approaches data envelopment analysis (DEA) and free disposal hull (FDH) are used in this paper to develop a software system for convex and nonconvex frontier visualization and performance analysis of financial systems. Our theoretical results are validated by computational experiments on the data taken from financial accounts of Russian banks. Potential applications of proposed approach in situation room for decision support and strateuic nerformance manaaement are considered.

Annals of Operations Research, Apr 26, 2015

Inevitable simplifications of models of real world activities lead to some inadequacies. In the D... more Inevitable simplifications of models of real world activities lead to some inadequacies. In the DEA literature several methods were proposed to overcome such difficulties. Some authors proposed to use specific production units in the primal space of inputs and outputs as a starting point in order to improve the frontier of the DEA models. In our previous papers, we introduced the notion of terminal units. It was proved that only terminal units form necessary and sufficient set of units for improving the frontier. In this paper, the relationship between all sets of units proposed for improving the frontier is established. Our theoretical results are confirmed by extensive and instructive graphical examples and also verified by computational experiments using real-life data sets.

Doklady Mathematics, Nov 1, 2017

Free Disposal Hull (FDH) model was proposed in the end of 20-th century for performance measureme... more Free Disposal Hull (FDH) model was proposed in the end of 20-th century for performance measurement and management of complex units. Production possibility set of FDH model is a nonconvex set. For this reason, nonlinear integer programming methods and enumeration methods have been used for computations of various characteristics of units' performance. However, as Cesaroni, Kerstens and Van de Woestyne noted, there are no methods in the world scientific literature for frontier visualization in nonconvex FDH models. In this paper, an approach is proposed for frontier visualization with the use of methods of purposeful enumeration. Computational experiments, conducted with the use of real-life data sets, confirm reliability and effectiveness of proposed algorithms.

Computational Mathematics and Mathematical Physics, Mar 1, 2019

The free disposal hull (FDH) model of production technology assumes free disposability of all inp... more The free disposal hull (FDH) model of production technology assumes free disposability of all inputs and outputs, but does not make any convexity assumptions. In this paper, we develop an algorithm for the reconstruction of the frontier of the FDH technology that corresponds to its sections by different two-dimensional planes. From a practical perspective, the suggested algorithm is useful for the visualization and exploration of the efficient frontier of the FDH technology. Furthermore, based on the suggested algorithm, we develop a new procedure for the evaluation of returns to scale in the FDH technology. Compared to the existing methods, our approach does not require assessing the efficiency of productive units in the reference technologies, which is known to be a computationally intensive task. Our theoretical results are confirmed by computational experiments in applications with real-life data sets from different industries.

Data envelopment analysis journal, 2021

It is well known that many inefficient units are projected onto the weakly efficient parts of the... more It is well known that many inefficient units are projected onto the weakly efficient parts of the frontier under computing efficiency scores. However, according to the data envelopment analysis approach, the efficiency score of inefficient units has to be measured relative to efficient ones. In our previous papers, we introduced the notion of terminal units and proposed to use them for improving the frontier. In this paper, we describe two possible scenarios and discuss some aspects of algorithm implementation. Our theoretical results are verified by computational experiments using real-life data sets and confirmed by graphical examples.

Doklady Mathematics, Feb 1, 2012

Ima Journal of Management Mathematics, Mar 23, 2011

... As a result, significant distortion of the performance assessment of units takes place. Our t... more ... As a result, significant distortion of the performance assessment of units takes place. Our theo-retical results are validated by computational experiments on the data taken from financial accounts of Russian banks. ... (2) n ∑ j=1 yij λj − s+i = yio, i = 1,...,r, n ∑ ...

Doklady Mathematics, Feb 1, 2012

There are some specific features of the non-radial data envelopment analysis (DEA) models which c... more There are some specific features of the non-radial data envelopment analysis (DEA) models which cause some problems for the returns to scale measurement. In the scientific literature on DEA, some methods were suggested to deal with the returns to scale measurement in the non-radial DEA models. These methods are based on using Strong Complementary Slackness Conditions from optimization theory. However, our investigation and computational experiments show that such methods increase computational complexity significantly and may generate as optimal, solutions contradicting optimization theory. In this paper, we propose and substantiate a direct method for the returns to scale measurement in the nonradial DEA models. Our computational experiments documented that the proposed method works reliably and efficiently on the real-life data sets.

Nucleation and Atmospheric Aerosols, 2023

Advances in logistics, operations, and management science book series, Jun 24, 2015

In this chapter, an approach for evaluation of agreements on transnational projects during the ne... more In this chapter, an approach for evaluation of agreements on transnational projects during the negotiation process is proposed. One can show that the negotiation process can be represented as the behavior of decision-making units (countries) in the multidimensional space of economic indicators using Data Envelopment Analysis (DEA) models. In this case, the goals, which can be achieved by units as a result of accomplishment of a joint project, can be determined as points in the multidimensional space. Optimal directions toward these goals and cones of possible directions can be found with the help of Analytic Hierarchy Process (AHP). The efficiency measures for countries are calculated as ratios of the values of potential functions at the initial (intermediate) and final points. The increments of efficiencies measures are considered as arguments in the negotiation process. The approach is illustrated by the real-life data set taken from open international sources.

DEStech Transactions on Computer Science and Engineering, Feb 6, 2019

A lot of scientific literature in the world is devoted to the returns-to-scale (RTS) evaluation o... more A lot of scientific literature in the world is devoted to the returns-to-scale (RTS) evaluation of production units. Kerstens and Vanden Eeckaut were the first who considered the notion and evaluation of RTS for nonconvex Free Disposal Hull (FDH) models. Their methods are based on the comparison of the radial efficiency scores of a production unit in the FDH model and the corresponding non-increasing and non-decreasing RTS reference models. At the same time Cesaroni, Kerstens and Van de Woestyne noted the absence of papers in the world literature devoted to methods of frontier visualization in nonconvex models. In this paper, we developed methods for visualization of production function of nonconvex models and of the corresponding non-increasing and non-decreasing models. Our approach of frontier visualization can be used for decision making based on nonconvex models, it allows us to evaluate RTS for FDH models. Our results are confirmed by computational experiments in applications with real-life data sets.

Doklady Mathematics, Jun 1, 2009

The paper shows that many simple rating functions constructed on the basis of the ratio analysis ... more The paper shows that many simple rating functions constructed on the basis of the ratio analysis distort significantly the evaluation of the production units behavior. Opposite to the ratio analysis, the DEA approach investigate production units behaviour in the multidimentional space of indicators. In this paper, we compare the ration analysis and the DEA approach using properties of the mappings of the multidimentional sets, we also show that it is purposeful to construct rating functions on the basis of efficiency scores computed in DEA models.

Journal of Productivity Analysis, Dec 3, 2013

Applications of the DEA models show that inadequate results may arise in some cases, two of these... more Applications of the DEA models show that inadequate results may arise in some cases, two of these inadequacies being: a) too many efficient units may appear in some DEA models; b) a DEA model may show an inefficient unit from the point of view of experts as an efficient one. The purpose of this paper is to identify units that may unduly become efficient. The concept of a terminal unit is introduced for such units. A method for improving the adequacy of DEA models based on terminal units is suggested, and an example shown based on a real-life data set for Russian banks.

Journal of the Operational Research Society, Nov 1, 2009

Inadequate results may arise in some instances of DEA model applications. For example, a data env... more Inadequate results may arise in some instances of DEA model applications. For example, a data envelopment analysis (DEA) model may show 'a notoriously inefficient unit' as an efficient one. In addition, too many efficient units may appear in some DEA models. An elegant and subtle approach was proposed to deal with these problems, which is based on incorporating domination cones in DEA models. Yu, Wei and Brockett suggested the generalized DEA (GDEA) model that unifies and extends most of the well-known DEA models based on using domination cones. In this paper, we propose a model that is more general than the GDEA model, on the one hand, as it covers situations that the GDEA model cannot describe. On the other hand, our model enables one to construct step-by-step any model from the family of the GDEA models by incorporating artificial units and rays in the space of inputs and outputs in the Banker, Charnes, Cooper (BCC) model, which makes the process of model construction visible and more understandable. Moreover, we show that any GDEA model can be approximated by some BCC model.

Mathematics, Oct 2, 2022

This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY