Kaoru Tone - Academia.edu (original) (raw)

Professor Kaoru Tone is a Professor Emeritus at the National Graduate Institute for Policy Studies (GRIPS), Japan. He holds B.S. in Mathematics from the University of Tokyo and Ph.D. in Operations Research from the Keio University, Japan. He has served as professor at GRIPS, Saitama University and Keio University over 40 years. He was the President of the Operations Research Society of Japan, from 1996 to 1998. Professor Tone has achieved a high level of distinction both in Japan and internationally, and is known for being a world leading expert in Data Envelopment Analysis (DEA) and performance evaluation. His contribution to DEA has a variety of attainments. He authored a classical book “Data Envelopment Analysis: A Comprehensive Text with Models, Applications, References and DEA-Solver Software,” under the co-authorship with Professor Cooper (University of Texas) and Professor Seiford (University of Michigan), published by Springer. He also published many papers on DEA in prestigious international journals, such as European Journal of Operational Research, Omega, Journal of the Operational Research Society, Journal of Productivity Analysis, Socio-Economic Planning Sciences, Annals of Operations Research, and International Transactions of Operational Research. He opened a new avenue for performance evaluation, called Slacks-based Measure (SBM). This model is widely utilized over the world. Recently, European Journal of Operational Research announced that the SBM model by Tone is among the 20 most cited papers among 14,617 papers during 1977-2017 (40 year Anniversary). His recent innovations include Network SBM, Dynamic SBM, Dynamic DEA with Network Structure, Congestion, Returns to growth in DEA, Ownership-specified Network DEA, Non-convex Frontier DEA, Past-Present-Future Inter-temporal DEA and Resampling DEA. He had served as Editorial Board member of Omega, The Journal of Data Envelopment Analysis, Socio-Economic Planning Sciences, Journal of Optimization Theory and Applications, and Metamorphosis. Furthermore, Professor Tone’s research activity has made significant impact in the public sectors. For example, the National Land Agency Japan Committee has adopted his proposed consensus-marking methodology to solve the site selection for relocating Japanese government agencies out of Tokyo. The committee has reported his conclusion to the Prime Minster of Japan at the end of December 1999. More recently, he acted as a specialist in designing the decision methodology for a government project on the site selection for the Next Generation Supercomputing Centre in Japan (cost about US$1.3 billion). Professor Tone proposed the use of Analytic Hierarchy Process and Assurance Region DEA models to devise the conclusion. The selection committee reported his recommendation to the RIKEN (an Independent Administrative Institute funded by the Japanese Government). On March 29, 2007, RIKEN announced to the public “The Winner is Kobe.” The “Supercomputer–K” is now in operation and takes consecutive top rank in world ranking.

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Papers by Kaoru Tone

Measures of inefficiency in data envelopment analysis and stochastic frontier estimation

European Journal of Operational Research, May 1, 1997

ABSTRACT This paper discusses recent work in developing scalar measures of inefficiency which (a)... more ABSTRACT This paper discusses recent work in developing scalar measures of inefficiency which (a) comprehend all inefficiencies, including non-zero slacks, and (b) are readily interpretable and easily used in a wide variety of contexts. The opening section of the paper discusses some of the varied contexts in which uses of DEA are now being reported. This provides background for some of these measures. The closing section turns to simulation studies of DEA-regression combinations and possible inefficiency measures. Serious problems of bias in SF (Stochastic Frontier) regression approaches are identified. Extensions and modifications are suggested which can make a development of other inefficiency measures worthwhile for SF extensions to input-specific and multiple output evaluations.

Cost Elasticity: A Re-examination in DEA

When we estimate l11e relative distance between cities or the telative area. o( figures by the An... more When we estimate l11e relative distance between cities or the telative area. o( figures by the Analytic Hierarchy Process (AHP), it is often observed that a group decision usually outperforms an individual one. This paper addresses tliis phenomena and shows that the 'accuracy o( estimates is improved in approximate proportion to the square root of t.J1e number of individuals in the group.

Super-Efficiency Dea Models

John Wiley & Sons, Ltd eBooks, May 6, 2017

As a natural extension of Roos and Vial's "Long steps with logarithmic penalty barrier function i... more As a natural extension of Roos and Vial's "Long steps with logarithmic penalty barrier function in llnear programming" (1989) and Ye's "An O(n 3 L) potential reduction algorithm for linear programming" (1989), it will be shown that the classical logarithmic barrier function method can be adjusted so that it generates the optimal solution in O(/IlL) iterations, where n is the number of variables and L is the data length.

Site Selection for a Large Scale Integrated Circuits Factory

Springer eBooks, 1989

A Japanese manufacturer of electronic goods is planning to construct a new, state-of-the-art fact... more A Japanese manufacturer of electronic goods is planning to construct a new, state-of-the-art factory to manufacture large scale integrated circuits. A team of company managers must decide on the appropriate location for the factory taking many different criteria into account. This paper reports on the decision process that the project team employed to model the site selection problem.

Non-Radial Dea Models

John Wiley & Sons, Ltd eBooks, May 6, 2017

Appendix A: DEA-SOLVER-PRO

John Wiley & Sons, Ltd eBooks, May 6, 2017

1-C-3 Consistent Measurement Using Artificial Target DMU in Data Envelopment Analysis(DEA・AHP(1),Abstracts,The 2006 Spring National Conference of Operations Research Society of Japan)

日本オペレーションズ・リサーチ学会春季研究発表会アブストラクト集, Mar 14, 2006

Semi-infinite programs will be solved by bisections within the framework of LPs. No gradient info... more Semi-infinite programs will be solved by bisections within the framework of LPs. No gradient information is needed, contrary to the usual Newton-Raphson type methods for solving semi-infinite programs. The rate of convergence is linear. The method has a stable convergence feature derived from the bisection rule.

In this paper, we will discuss subjects related to virtual multipliers in the cone-rati'o model i... more In this paper, we will discuss subjects related to virtual multipliers in the cone-rati'o model in DEA. Usually, there exists ambiguity in the virtual multipliers in the polyhedral cone-ratio method when some exemplary efficient DMU s' multipliers are employed as the admissible directions of the cone. Firstly, we ,;,ill show a convex cell subdivision of the multiplier simplex. Then, three practical methods for resolving this ambiguity will be presented •with an example.

The slacks-based measure (SBM) of super-efficiency in data envelopment analysis (DEA) developed b... more The slacks-based measure (SBM) of super-efficiency in data envelopment analysis (DEA) developed by Tone [Tone, K., 2002. A slacks-based measure of super-efficiency in data envelopment analysis. European Journal of Operational Research 143, 32-41] is a non-radial super-efficiency model compared to the traditional radial super-efficiency DEA models. This note extends the SBM of super-efficiency to the additive (slacks-based) DEA model. Alternative slacks-based objective functions can be used. Unlike the traditional radial super-efficiency DEA, additive (slacks-based) super-efficiency models are always feasible.

ISAHP proceedings, Aug 1, 1996

This paper describes two technical subjects of the Analytic Hierarchy Process. The first one rela... more This paper describes two technical subjects of the Analytic Hierarchy Process. The first one relates with group decision making. When we estirnate the relative distance between cities or the relative area of figures by the AHP, it is often observed that a group decision usually outperforms an individual one. This note addresses this phenomena and shows that the accuracy of estimates is improved in approximate proportion to the square mot of the number of individuals in the group. The second one deals with the method for estiMating the relative weight of alternatives when some entries of the pairwise comparisons matrix areimissing, based on the geometric mean method.

Empirical Economics, Jan 7, 2017

This paper develops a dynamic-network DEA (data envelopment analysis) model where total output is... more This paper develops a dynamic-network DEA (data envelopment analysis) model where total output is jointly produced from two sectors: a human capital sector and a physical capital sector. Each prefecture produces a final output and an intermediate product which is used to augment future physical capital. The optimization method allows future production possibilities to be enhanced if some final output in the current period is foregone so that larger amounts of the intermediate product can be produced. The goal is to choose the amounts of final output and intermediate product so as to maximize the size of the production possibility set. The method also allows identification of whether output is constrained by a lack of physical capital, a lack of human capital or a lack of both types of capital. We apply our method to 47 Japanese B Hirofumi Fukuyama

A modified slacks-based measure of efficiency in data envelopment analysis

European Journal of Operational Research, Dec 1, 2020

Abstract The slacks-based measure (SBM) model can divide the set of observations into two mutuall... more Abstract The slacks-based measure (SBM) model can divide the set of observations into two mutually exclusive and collectively exhaustive sets: efficient and inefficient. However, it fails to provide more details about efficient DMUs, which reveals the lack of discrimination power in the SBM model. With the aim of addressing this issue, the super SBM (SupSBM) model has been suggested which can rank the SBM-efficient DMUs without providing any useful information about SBM-inefficient DMUs. As a result, in order to fully rank both efficient and inefficient DMUs, one needs to run both SBM and SupSBM models which leads to a significant increase in the number of required computations. This paper tackles this problem and modifies the SBM model which measures SBM-efficiency score for inefficient DMUs and SupSBM-efficiency score for strong efficient DMUs, simultaneously. Finally, a simulation study is presented to illustrate the superiority of our proposed model over the existing models with various problem sizes.

arXiv (Cornell University), Mar 31, 2015

In order to express a polyhedron as the (Minkowski) sum of a polytope and a polyhedral cone, Motz... more In order to express a polyhedron as the (Minkowski) sum of a polytope and a polyhedral cone, Motzkin (1936) made a transition from the polyhedron to a polyhedral cone. Based on his excellent idea, we represent a set by a characteristic cone. By using this representation, we then reach four main results: (i) expressing a closed convex set containing no line as the direct sum of the convex hull of its extreme points and conical hull of its extreme directions, (ii) establishing a convex programming (CP) based framework for determining a maximal element-an element with the maximum number of positive components-of a convex set, (iii) developing a linear programming problem for finding a relative interior point of a polyhedron, and (iv) proposing two procedures for the identification of a strictly complementary solution in linear programming.

Keio engineering reports, 1976

In this paper, we present a postoptimization analysis of convex quadratic programmings, that is, ... more In this paper, we present a postoptimization analysis of convex quadratic programmings, that is, (i) modification of coefficients or constants of the problem, (ii) addition of a constraint or a variable and (iii) parameterization of coefficients or constants. The analysis is done mainly by means of the principal pivoting method of DANTZIG and COTTLE. Notes Genre Departmental Bulletin Paper URL 0001 慶應義塾大学学術情報リポジトリ(KOARA)に掲載されているコンテンツの著作権は、それぞれの著作者、学会または出版社/発行者に帰属し、その権利は著作権法によって 保護されています。引用にあたっては、著作権法を遵守してご利用ください。 The copyrights of content available on the KeiO Associated Repository of Academic resources (KOARA) belong to the respective authors, academic societies, or publishers/issuers, and these rights are protected by the Japanese Copyright Act. When quoting the content, please follow the Japanese copyright act.

Corporate Failure Analysis Using SBM

John Wiley & Sons, Ltd eBooks, May 6, 2017

Site Selection for the Next-Generation Supercomputing Center of Japan

John Wiley & Sons, Ltd eBooks, May 6, 2017

Measures of inefficiency in data envelopment analysis and stochastic frontier estimation

European Journal of Operational Research, May 1, 1997

ABSTRACT This paper discusses recent work in developing scalar measures of inefficiency which (a)... more ABSTRACT This paper discusses recent work in developing scalar measures of inefficiency which (a) comprehend all inefficiencies, including non-zero slacks, and (b) are readily interpretable and easily used in a wide variety of contexts. The opening section of the paper discusses some of the varied contexts in which uses of DEA are now being reported. This provides background for some of these measures. The closing section turns to simulation studies of DEA-regression combinations and possible inefficiency measures. Serious problems of bias in SF (Stochastic Frontier) regression approaches are identified. Extensions and modifications are suggested which can make a development of other inefficiency measures worthwhile for SF extensions to input-specific and multiple output evaluations.

Cost Elasticity: A Re-examination in DEA

When we estimate l11e relative distance between cities or the telative area. o( figures by the An... more When we estimate l11e relative distance between cities or the telative area. o( figures by the Analytic Hierarchy Process (AHP), it is often observed that a group decision usually outperforms an individual one. This paper addresses tliis phenomena and shows that the 'accuracy o( estimates is improved in approximate proportion to the square root of t.J1e number of individuals in the group.

Super-Efficiency Dea Models

John Wiley & Sons, Ltd eBooks, May 6, 2017

As a natural extension of Roos and Vial's "Long steps with logarithmic penalty barrier function i... more As a natural extension of Roos and Vial's "Long steps with logarithmic penalty barrier function in llnear programming" (1989) and Ye's "An O(n 3 L) potential reduction algorithm for linear programming" (1989), it will be shown that the classical logarithmic barrier function method can be adjusted so that it generates the optimal solution in O(/IlL) iterations, where n is the number of variables and L is the data length.

Site Selection for a Large Scale Integrated Circuits Factory

Springer eBooks, 1989

A Japanese manufacturer of electronic goods is planning to construct a new, state-of-the-art fact... more A Japanese manufacturer of electronic goods is planning to construct a new, state-of-the-art factory to manufacture large scale integrated circuits. A team of company managers must decide on the appropriate location for the factory taking many different criteria into account. This paper reports on the decision process that the project team employed to model the site selection problem.

Non-Radial Dea Models

John Wiley & Sons, Ltd eBooks, May 6, 2017

Appendix A: DEA-SOLVER-PRO

John Wiley & Sons, Ltd eBooks, May 6, 2017

1-C-3 Consistent Measurement Using Artificial Target DMU in Data Envelopment Analysis(DEA・AHP(1),Abstracts,The 2006 Spring National Conference of Operations Research Society of Japan)

日本オペレーションズ・リサーチ学会春季研究発表会アブストラクト集, Mar 14, 2006

Semi-infinite programs will be solved by bisections within the framework of LPs. No gradient info... more Semi-infinite programs will be solved by bisections within the framework of LPs. No gradient information is needed, contrary to the usual Newton-Raphson type methods for solving semi-infinite programs. The rate of convergence is linear. The method has a stable convergence feature derived from the bisection rule.

In this paper, we will discuss subjects related to virtual multipliers in the cone-rati'o model i... more In this paper, we will discuss subjects related to virtual multipliers in the cone-rati'o model in DEA. Usually, there exists ambiguity in the virtual multipliers in the polyhedral cone-ratio method when some exemplary efficient DMU s' multipliers are employed as the admissible directions of the cone. Firstly, we ,;,ill show a convex cell subdivision of the multiplier simplex. Then, three practical methods for resolving this ambiguity will be presented •with an example.

The slacks-based measure (SBM) of super-efficiency in data envelopment analysis (DEA) developed b... more The slacks-based measure (SBM) of super-efficiency in data envelopment analysis (DEA) developed by Tone [Tone, K., 2002. A slacks-based measure of super-efficiency in data envelopment analysis. European Journal of Operational Research 143, 32-41] is a non-radial super-efficiency model compared to the traditional radial super-efficiency DEA models. This note extends the SBM of super-efficiency to the additive (slacks-based) DEA model. Alternative slacks-based objective functions can be used. Unlike the traditional radial super-efficiency DEA, additive (slacks-based) super-efficiency models are always feasible.

ISAHP proceedings, Aug 1, 1996

This paper describes two technical subjects of the Analytic Hierarchy Process. The first one rela... more This paper describes two technical subjects of the Analytic Hierarchy Process. The first one relates with group decision making. When we estirnate the relative distance between cities or the relative area of figures by the AHP, it is often observed that a group decision usually outperforms an individual one. This note addresses this phenomena and shows that the accuracy of estimates is improved in approximate proportion to the square mot of the number of individuals in the group. The second one deals with the method for estiMating the relative weight of alternatives when some entries of the pairwise comparisons matrix areimissing, based on the geometric mean method.

Empirical Economics, Jan 7, 2017

This paper develops a dynamic-network DEA (data envelopment analysis) model where total output is... more This paper develops a dynamic-network DEA (data envelopment analysis) model where total output is jointly produced from two sectors: a human capital sector and a physical capital sector. Each prefecture produces a final output and an intermediate product which is used to augment future physical capital. The optimization method allows future production possibilities to be enhanced if some final output in the current period is foregone so that larger amounts of the intermediate product can be produced. The goal is to choose the amounts of final output and intermediate product so as to maximize the size of the production possibility set. The method also allows identification of whether output is constrained by a lack of physical capital, a lack of human capital or a lack of both types of capital. We apply our method to 47 Japanese B Hirofumi Fukuyama

A modified slacks-based measure of efficiency in data envelopment analysis

European Journal of Operational Research, Dec 1, 2020

Abstract The slacks-based measure (SBM) model can divide the set of observations into two mutuall... more Abstract The slacks-based measure (SBM) model can divide the set of observations into two mutually exclusive and collectively exhaustive sets: efficient and inefficient. However, it fails to provide more details about efficient DMUs, which reveals the lack of discrimination power in the SBM model. With the aim of addressing this issue, the super SBM (SupSBM) model has been suggested which can rank the SBM-efficient DMUs without providing any useful information about SBM-inefficient DMUs. As a result, in order to fully rank both efficient and inefficient DMUs, one needs to run both SBM and SupSBM models which leads to a significant increase in the number of required computations. This paper tackles this problem and modifies the SBM model which measures SBM-efficiency score for inefficient DMUs and SupSBM-efficiency score for strong efficient DMUs, simultaneously. Finally, a simulation study is presented to illustrate the superiority of our proposed model over the existing models with various problem sizes.

arXiv (Cornell University), Mar 31, 2015

In order to express a polyhedron as the (Minkowski) sum of a polytope and a polyhedral cone, Motz... more In order to express a polyhedron as the (Minkowski) sum of a polytope and a polyhedral cone, Motzkin (1936) made a transition from the polyhedron to a polyhedral cone. Based on his excellent idea, we represent a set by a characteristic cone. By using this representation, we then reach four main results: (i) expressing a closed convex set containing no line as the direct sum of the convex hull of its extreme points and conical hull of its extreme directions, (ii) establishing a convex programming (CP) based framework for determining a maximal element-an element with the maximum number of positive components-of a convex set, (iii) developing a linear programming problem for finding a relative interior point of a polyhedron, and (iv) proposing two procedures for the identification of a strictly complementary solution in linear programming.

Keio engineering reports, 1976

In this paper, we present a postoptimization analysis of convex quadratic programmings, that is, ... more In this paper, we present a postoptimization analysis of convex quadratic programmings, that is, (i) modification of coefficients or constants of the problem, (ii) addition of a constraint or a variable and (iii) parameterization of coefficients or constants. The analysis is done mainly by means of the principal pivoting method of DANTZIG and COTTLE. Notes Genre Departmental Bulletin Paper URL 0001 慶應義塾大学学術情報リポジトリ(KOARA)に掲載されているコンテンツの著作権は、それぞれの著作者、学会または出版社/発行者に帰属し、その権利は著作権法によって 保護されています。引用にあたっては、著作権法を遵守してご利用ください。 The copyrights of content available on the KeiO Associated Repository of Academic resources (KOARA) belong to the respective authors, academic societies, or publishers/issuers, and these rights are protected by the Japanese Copyright Act. When quoting the content, please follow the Japanese copyright act.

Corporate Failure Analysis Using SBM

John Wiley & Sons, Ltd eBooks, May 6, 2017

Site Selection for the Next-Generation Supercomputing Center of Japan

John Wiley & Sons, Ltd eBooks, May 6, 2017