Updated on 2024/12/22

写真a

 
MOHRI, Hiroaki
 
Affiliation
Faculty of Commerce, School of Commerce
Job title
Professor
Degree
Master of Science ( Tokyo Institute of Technology )
Doctor of Engineering. ( Tokyo Institute of Technology )

Research Experience

  • 2023.04
    -
    Now

    Waseda University, Professor

  • 2001
    -
    2022

    Waseda University, Associate Professor

  • 2006.10
    -
    2007.09

    University of Bonn   Research Institute for Discrete Mathematics

  • 2005.10
    -
    2006.09

    University of Bonn   Research Institute for Discrete Mathematics   Visiting professor

  • 1999
    -
    2001

    Waseda University, Assistant Professor

Committee Memberships

  • 2000.03
    -
    2014.02

    The Operations Research Society of Japan,  IAOR Committee

  • 2012.01
    -
    2012.03

    Cabinet Office  Government of Japan, "Committee for improving Composite Index"

Professional Memberships

  • 2024.07
    -
    Now

    Mathematical Association of America

  • 2024.06
    -
    Now

    Game Theory Society

  • 2019
    -
    Now

    The Japanese Society for the Study of Circus

  • 　
    　
    　

    COMBINATORIAL MATHEMATICS SOCIETY OF AUSTRALASIA

  • 　
    　
    　

    Japan Society for Industrial and Applied Mathematics

  • 　
    　
    　

    Operations Research Society of Japan

  • 　
    　
    　

    Mathematical Optimazation Society

▼display all

Research Interests

  • Applied Stochastic Process

  • Optimization

  • Operations Research

 

Papers

  • Catastrophic Failure and Cumulative Damage Models Involving Two Types of Extended Exponential Distributions

    Hiroaki Mohri, Jun-ichi Takeshita

    International Journal of Reliability, Quality and Safety Engineering   29 ( 4 )  2022.08  [Refereed]

    Authorship：Lead author

    　View Summary

    This study supposes a single unit and investigates cumulative damage and catastrophic failure models for the unit, in situations where the interarrival times between the shocks, and the magnitudes of the shocks, involve two different stochastic processes. In order to consider two essentially different stochastic processes, integer gamma and Weibull distributions are treated as distributions with two parameters and extensions of exponential distributions. With respect to the cumulative damage models, under the assumption that the interarrival times between shocks follow exponential distributions, the case in which the magnitudes of the shocks follow integer gamma distributions is analyzed. With respect to the catastrophic failure models, the respective cases in which the interarrival times between shocks follow integer gamma and Weibull distributions are discussed. Finally, the study provides some characteristic values for reliability in such models.

    DOI

    Scopus

  • Graph reliability evaluation via random K-out-of-N systems

    Hiroaki Mohri, Jun-ichi Takeshita

    Communications in Statistics - Theory and Methods     1024 - 1034  2022.07  [Refereed]

    Authorship：Lead author

    　View Summary

    The present study was concerned with network failure problems for simple connected undirected graphs. A connected graph becomes unconnected through edge failure, under the assumptions that only edges can fail and each edge has an identical failure distribution. The main purpose of the present study was to show recurrent relations with respect to the number of edges in graph generation procedures. To this end, simple connected undirected graphs were correlated to random K-out-of-N systems, and key features of such systems were applied. In addition, some simple graph cases and examples were analyzed.

    DOI

    Scopus

  • Analysis of damage induced by two types of shocks

    Hiroaki Mohri, Jun-ichi Takeshita

    Proceedings - 24th ISSAT International Conference on Reliability and Quality in Design     147 - 150  2018.08  [Refereed]

    　View Summary

    In the literature of reliability theory, many studies have concentrated on single types of shock (e.g., aging). Previous studies have investigated the following cases. (1) When a shock of a given magnitude is applied to a unit, it immediately fails. (2) When the shocks are additive and the total shock magnitude is greater than K, a unit fails. (3) When the shocks are not additive, and the magnitude of a given shock is greater than K, the unit fails. In this paper, we suppose case (2). In addition, suppose two types of shocks are applied to a single unit (i.e., not a single shock type). Each type of shock occurs by a different stochastic process, and the respective magnitude of each type of shock shows a different probabilistic distribution. We perform damage analysis for a single unit when both types of event occur by general stochastic processes and both shock magnitudes follow general probabilistic distributions. Thus, we perform a detailed analysis while the events occur by Poisson processes and both shock magnitudes show different exponential distributions.

  • The Mechanism of Commitment Problems of Separatist Conflicts in Post-Cold War Era: -Analysis of Negotiations between Russia Federation and Separatist Regions by using 2 Level Game Theory-

    Kosuke TOGASHI, Hiroaki MOHRI

    Journal of the Faculty of Liberal Arts, Tokai University   48   75 - 105  2018.03  [Refereed]

  • A Water Line Network Failure Application of Network Design Problems

    Hiroaki Mohri, Jun'ichi Takeshita

    Journal of Mathematics and System Science   2015 ( 5 ) 493 - 500  2015.12  [Refereed]

    　View Summary

    This study investigated a water supply recovery problem involving municipal water service piping. The problem consisted

    in recovering full service after network failure, in order to rapidly satisfy all urgent citywide demands. The optimal recovery solution

    was achieved through the application of so-called network design problems (NDPs), which are a form of combinatorial optimization

    problem. However, a conventional NDP is not suitable for addressing urgent situations because (1) it does not utilize the non-failure

    arcs in the network, and (2) it is solely concerned with stable costs such as flow costs. Therefore, to adapt the technique to such

    urgent situations, the conventional NDP is here modified to deal with the specified water supply problem. In addition, a numerical

    illustration using the Sendai water network is presented.

  • A Network Failure Recovery Problem with Simple Structures

    Jun'ichi Takeshita, Hiroaki Mohri

    Theory and Application of Mathematical Decision Making under Uncertainty/RIMS Kokyuroku   1912   131 - 140  2014.08

  • Investigation of a Network Failure Problem with a Significant Path, from the Perspective of Crisis Management

    Junichi Takeshita, Hiroaki Mohri

    Journal of Mathematics and System Science   4 ( 7 ) 479 - 485  2014.07  [Refereed]

  • A cooperative game theoretical approach to risk analysis, using network structure

    Takeshita Jun-ichi, Mohri Hiroaki

    Journal of Risk Analysis and Crisis Response   4 ( 1 ) 43 - 48  2014  [Refereed]

  • A Combined Analysis of Game Theory and Stochastic Process for Financial Securities

    Hiroaki Mohri

    Applied Stochastic Models and Data Analysis (ASMDA) 2007 Proceedings (CD-ROM)   ( 1 )  2007.05  [Refereed]

  • A Stochastic and Optimization Analysis for a Network on Activation in Human Brain

    Jobu Watanabe, Hiroaki Mohri

    Applied Stochastic Models and Data Analysis (ASMDA) 2007 Proceedings(CD-ROM)   ( 1 )  2007.05  [Refereed]

  • 施設配置を考慮したネットワークデザイン問題に対するラグランジュ緩和法

    Ming Zhe Chen, Naoto Katayama, Hiroaki Mohri

    Journal of Japan Industrial Management Association   56 ( 5 ) 331 - 338  2005.12  [Refereed]

  • 確率過程ゲームの計算機ネットワークの制御への応用

    毛利裕昭

    Mathematical Theory of Applications of Uncertainty Sciences and Decision Making /Research Institute of Mathematical Sciences, Kyoto University, Kokyuroku   1457 ( 1457 ) 62 - 68  2005.11

    CiNii

  • Stochastic Game for Tree Queueing Networks

    Hiroaki MOHRI

    Kokyuroku/ Research Institute for Mathematical Sciences, Kyoto University   1461 ( 1461 ) 214 - 224  2005.07

  • A lagrange relaxation method for the network design problem considering facility location

    Ming Zhe Chen, Naoto Katayama, Hiroaki Mohri

    Journal of Japan Industrial Management Association   56 ( 5 ) 330 - 338  2005

    　View Summary

    The network design problem, which attempts to simultaneously take into account facility location and network topology, has a number of applications in transportation network design, distribution systems, telecommunication network planning, and other areas. In this paper, we investigate a new model that simultaneously optimizes facility locations for distribution centers and concentrators, network topology for line-haul trucks and fiber-optic communication lines, and routes of commodity flow for freight and communication data. Our model consists of uncapacitated facility location, uncapaci-tated arc design, general network design, an unlimited number of freight transshipment at facilities, and multi-commodity flow routing that has a large number of origin-destination pairs. It has been noted that this model is not suitable for solving problems that exist in the real world with current OR software on the market. We present a new formulation of this problem that minimizes the sum of flow costs, arc design costs, and facility location costs, and a new Lagrange relaxation problem with relaxed flow conservation constraints and some forcing constraints. We present an exact solution method for this Lagrange relaxation problem, and a subgradient method for Lagrange multipliers. In addition, we present an approximate solution method for obtaining good upper bound using solutions of a Lagrange relaxation problem, which is called Lagrange heuristics. Numerical examples up to 100 nodes are given to show the effectiveness of our formulation and solution methods for lower and upper bound.

  • Network Design Problem and its Graph Structure

    Hiroaki Mohri

    Decision Theory and Optimization Algorithms / Research Institute of Mathematical Sciences, Kyoto University, Kokyuroku   1409 ( 1409 ) 195 - 204  2005.01

  • Game Theoretical Approach for Resource Allocation of Logistics Systems

    Hiroaki Mohri, Takhiro Watanabe

    Communications of Operations Research of Japan/ The Operations Research Society of Japan   49 ( 11 ) 681 - 686  2004.11

  • Composite Mathematical Finance Model by Stochastic Process and Game Theory

    Hiroaki Mohri

    Mathematical Programming concerning Decision Makings and Uncertainties   1373 ( 1373 ) 213 - 221  2004.05

    CiNii

  • Network design problem for some graphs

    Hiroaki Mohri

    ICNAAM 2004: INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2004   Special Issue of ICNAAM   269 - 272  2004  [Refereed]  [International journal]

    　View Summary

    Network Design Problem is difficult to solve in terms of Computing Complexity Theory, it is an NP-hard Problem like the Traveling Salesman Problem, Facility Location Problem and so on. But we can solve it in polynomial time in special cases. In this paper, we discuss about such types of Network Design Problem, which are solved in polynomial time. We pay attention to underlying graph structures. (c) 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

  • Tractable Co-Operative Game and Intractable Co-Operative Game Arising from Combinatorial Optimization Problems

    Hiroaki Mohri

    Mathematical Economics/ Research Institute of Mathematical Sciences, Kyoto University, Kokyuroku   1337 ( 1337 ) 224 - 229  2003.09

  • The Operations Research Society of Japan, "Integrated Operation" Report

    Hiroaki Mohri

    The Operations Research Society of Japan   担当箇所:pp.112-116, pp.123-127   112, 123 - 116, 127  2003.06

  • On Solutions of a Type of Network Design Game

    Hiroaki Mohri

    The Proceedings of Second International Conference on Nonlinear Analysis and Convex Analysis (Yokohama Publishers)   International Conference on Nonlinear Analysis and Convex Analysis  2003.02  [Refereed]

    CiNii

  • Discrete Optimization and Co-operative Game(2)

    Hiroaki Mohri, Yoshio Okamoto

    Communications of Operations Research of Japan/ The Operations Research Society of Japan   2003 ( 2 ) 42 - 49  2003.02

  • Network Design Game concerning Stochastic Process

    Hiroaki Mohri

    Mathematics for decision-making under uncertainty / Research Institute for Mathematics Sciences, Kyoto University, Kokyuroku   1306 ( 1306 ) 57 - 62  2003.02

  • Discrete Optimization and Co-operative Game (1)

    Hiroaki Mohri

    Communications of Operations Research of Japan / The Operations Research Society of Japan   2003 ( 1 ) 36 - 41  2003.01

    CiNii

  • Network Design Problem with Facility Location

    Hiroaki Mohri

    Mathematics and Algorithms of Optimization /Research Institute for Mathematical Sciences, Kyoto University, Kokyuroku   1297 ( 1297 ) 89 - 95  2002.12

  • In Serialization for "Discrete Optimization and Its Applications

    Hiroaki Mohri

    Communications of Operations Research of Japan /The Operations Research Society of Japan   47 ( 11 ) 729 - 729  2002.11

    CiNii

  • Cost Allocation Arising from Hybrid Problem of Facility Location and Network Design

    Hiroaki Mohri

    International Congress of Mathematicians 2002, GTA Proceedings   International Congress of Mathematicians 2002 GTA Proceedings Volume,pp.579-583   579 - 583  2002.08  [Refereed]

  • 社会システムとしての超流通システム再考

    毛利裕昭

    情報処理学会   Vol.2001, No.118, 2001-EIP-14, pp.43-49  2001.11

  • OR事典2000(CD-ROM)

    Hiroaki Mohri

    The Operations Research Society of Japan    2000.05

  • The development of software components for solving the vehicle routing and facility location problems

    Masahiko Shimomura, Mikio Kubo, Hiroaki Mohri

    IEICE Transactions on Information and Systems   E83-D ( 3 ) 510 - 518  2000.03  [Refereed]

    　View Summary

    The vehicle routing and facility location Fields are well-developed areas in management science and operations research application. There is an increasing recognition that effective decision-making in these Fields requires the adoption of optimization software that can be embedded into a decision support system. In this paper, we describe the implementation details of our software components for solving the vehicle routing and facility location problems.

  • 数理的技法によるサプライチェーン設計・運用支援システムの構築

    下村雅彦, 久保幹雄, 毛利裕昭

    高度情報化支援ソフトウェア育成事業最終成果発表会論文集/情報処理振興事業協会   pp.37-44   37 - 44  1999.05  [Refereed]  [Domestic journal]

  • The Logic of Logistics

    Mikio Kubo, Masahiko Shimomura, Hiroaki Mohri

    Communications of Operations Research of Japan / The Operations Research Society of Japan   43 ( 11 ) 633  1998.11

  • 特殊なハードウェアを使用しない超流通システムの開発

    毛利裕昭, 新部裕

    創造的ソフトウェア育成事業及びエレクトロニック・コマース推進事業 最終成果発表会論文集 創造的ソフトウェア育成事業編/情報処理振興事業協会   pp.713-716   713 - 716  1998.05  [Refereed]

    CiNii

  • Cost allocation on vehicle routing problem

    Hiroaki Mohri, Takahiro Watanabe, Masao Mori, Mikio Kubo

    Journal of the Operations Research Society of Japan   40 ( 4 ) 463 - 465  1997.12  [Refereed]

    　View Summary

    Co-operative logistics is important to solve several logistics problems, such as a shortage of tracks and drivers, inefficient loading, NO_x Pollution and so on. While, current evolvement of computer networks makes it possible to provide various information for common use through networks. And further development of information infrastructure is under way. Under these circumstances, co-operative logistics is socially desired in order to solve logistics problems. However, cost allocation method for co-operative logistics has not been clearly stated so far, and that becomes obstacle for implementating co-operative logistics. This is the paper which gives a solution about how to allocate the transportation costs out of logistics costs. We do not adopt the traditional solutions of co-operative game theory (i.e. Shapley values, core, nucleus, etc.). Instead, we use the expantion solution of Fishburn and Pollark on the Traveling Sales-man Game. That is because the number of NP hard problems i.e. Vehicle Routing Problems for getting traditional solutions increases exponentially as the number of customers increases. Furthermore, this paper shows that participants of co-operative logistics should be able to choose their own costs allocaiton method based on their policies for rental costs and road costs, and also on allocation of saving costs by cooperation. We propose two axioms for cost allocation functions, and some saving functions as well. The furture themes of this problem are how to allocate logistics costs on various conditions (ex. time windows).

    DOI CiNii

    Scopus

    2
    Citation
    (Scopus)

  • A split delivery vehicle routing problem

    Hitoaki Mohri, Mikio Kubo, Yasutoshi Yajima, Masao Mori

    Journal of the Operations Research Society of Japan   39 ( 3 ) 372 - 387  1996.09  [Refereed]

    　View Summary

    We consider a standard vehicle routing problem, i.e. a routing problem where all nodes (customers) should be visited only once by only one vehicle and without exceeding a vehicle's capacity. The objective function minimizes total distance traveled. In this paper, we relax the first standard problem condition. We call this problem the Split Delivery Vehicle Routing Problem (SDVRP). The term "split delivery" means, as long as the total delivery equals the demand, the demand may be satisfied using more than one vehicle. Under the relaxed condition, we are able to reduce the number of vehicles and the total distribution cost (time). Hence, it will find practical application. SDVRP has been little researched. On a mathematical programming base, Suzuki et al. (1987) suggested an exact algorithm using a Branch and Bound Method for this problem. But it is only useful for a small number of nodes. On a local search base, Doror and Trudeau (1990) proposed heuristic algorithm. In this paper, we take another formulation. Solving this problem on mathematical programming base, we decompose it into two problems: First, a problem of which vehicle serves the node and to what extent each vehicle serves each node. Second, the problem of the route that each vehicle takes. This idea is based on Fisher and Jaikumar (1981) whose solutions is very good one for a standard vehicle routing problem. The second problem is the Traveling Salesman Problem. Therefore, the first problem is the essential one. We suggest that by method of Fisher (1985) we can generate a heuristic solution from the Lagrangean Solution for the first problem. From this we are able to solve a large size SDVRP.

    DOI CiNii

    Scopus

    9
    Citation
    (Scopus)

▼display all

Presentations

  • Multi-commodity Network Flow Problem with Arc failures

    Hiroaki MOHRI, Jun'ichi TAKESHITA

    The 3rd Stochastic Modeling Techniques and Data Analysis International Conference (SMTDA) 2014  (Lisbon) 

    Presentation date： 2014.06

  • Modified Network Design Problem for Special Graph Structures

    Hiroaki Mohri  [Invited]

    2nd International Conference of Applied Mathematics  (Plovdiv) 

    Presentation date： 2005.08

  • Lagrangian Approach for Hybrid Problem of Facility Location and Network Design

    Hiroaki Mohri, Naoto Katayama, Ming Zhe Chen

    18th International Symposium on Mathematical Programming  (Copenhagen)  Mathematical Programming Society

    Presentation date： 2003.08

  • Mathematical Problem on the crosspoint of Discrete Mathematics, Game Theory and Stochastic Process

    Hiroaki MOHRI  [Invited]

    Kansai Probabilistic Theory Seminar  (Kyoto)  Dept of Mathematics and Mathematical Sciences, Faculty of Science, Kyoto University

    Presentation date： 2002.12

  • Network Design Problem with Facility Locations

    Hiroaki Mohri

    The Japan Society for Industrial and Applied Mathematics 2002 Annual Meeting  (Yokohama)  The Japan Society for Industrial and Applied Mathematics

    Presentation date： 2002.09

  • Hybrid Problem of Facility Location and Network Design

    HIROAKI MOHRI

    Society for Industrial and Applied Mathematics, Discrete Mathematics, Geometry Session  (San Diego)  Society for Industrial and Applied Mathematics

    Presentation date： 2002.08

  • Cost Allocation Arising from Hybrid Problem of Facility Location and Network Design

    Hiroaki Mohri

    Games of Networks Session, International Congress of Mathematicians 2002, Satellite Conference in “Game Theory and Applications”  (Qingdao)  International Mathematical Union

    Presentation date： 2002.08

  • Network Design Problem with Facility Locations

    HIROAKI MOHRI

    RIMS Workshop, "Mathematics and Algorithms of Optimization"(Research Institute for Mathematical Sciences)2002/11  (Kyoto)  Research Institute for Mathematical Sciences

    Presentation date： 2002.07

  • Cost Allocation arising from Network Design Problem

    Hiroaki Mohri  [Invited]

    Discrete Mathematics in relation to Computer Science, The Tenth International Colloquium on Numerical Analysis and Computer Science and Applications  (Plovdiv) 

    Presentation date： 2001.08

  • On Solutions of a type of Network Design Game

    Hiroaki Mohri  [Invited]

    The 2nd International Conference on Nonlinear Analysis and Convex Analysis  (Hirosaki) 

    Presentation date： 2001.07

  • Graph Failure Distribution of Random K-out-of-N System

    Hiroaki Mohri, Jun-ichi Takeshita

    RIMS Workshop "New Developments on Mathematical Decision Making Under Uncertainty" 

    Presentation date： 2021.11

    Event date：
    2021.11
    　
    　

  • Graph Reliability by Random K-out-of N System

    Hiroaki MOHRI, Jun-ichi TAKESHITA

    The 2019 Fall National Conference of Operations Research Society of Japan(Operations Research Society of Japan), Sep 16, 2021, Operations Research Society of Japan 

    Presentation date： 2021.09

    Event date：
    2021.09
    　
    　

  • Renewal Failure Events and Cumulative Damage Processes by Two Types of Shocks

    Hiroaki MOHRI, Jun-ichi Takeshita

    The Reliability and Maintenance Engineering Summit 2021 (Virtual Meeting) 

    Presentation date： 2021.09

    Event date：
    2021.09
    　
    　

  • Network Failure Problem of Random K-out-of-N Systems

    Hiroaki MOHRI, Jun-ichi TAKESHITA

    The 19th Conference of the Applied Stochastic Models and Data Analysis International Society ASMDA2021 and DEMOGRAPHICS2021 WORKSHOP 

    Presentation date： 2021.06

    Event date：
    2021.06
    　
    　

  • What are young Ukrainian young people thinking now (focusing on cosmetics and Japanese language study) -Based on a survey by the top universities in Ukraine-

    Nanami Kobayshi, Miju Shirotori, Rei Kayama, Hiroaki Mohri

    The 42nd conference of Japanese Association for Ukrainian Studies  (Tokyo)  Japanese Association for Ukrainian Studies

    Presentation date： 2019.12

  • Separatist conflict Analysis by Coalition Coincidence Index Considering External pressure

    Hiroaki MOHRI (speaker, Kosuke TOGASHI

    The 2019 Fall National Conference of Operations Research Society of Japan(Operations Research Society of Japan)  (Higashi-Hiroshima)  Operations Research Society of Japan

    Presentation date： 2019.09

  • Erlang distribution damage analysis on failures immediately after shocks by two factors

    Hiroaki MOHRI, Jun'ichi TAKESHITA  [Invited]

    The 6th Asian Conference on Nonlinear Analysis and Optimization  (Okinawa) 

    Presentation date： 2018.11

  • Analysis for mechanism of commitment problems of separatist conflicts by 2 level game theory and coalition cooperation degree

    Kosuke Togashi, Hiroaki Mohri(Speaker  [Invited]

    The 6th Asian Conference on Nonlinear Analysis and Optimization  (Okinawa) 

    Presentation date： 2018.11

  • The Mechanism of Commitment Problems of Separatist Conflicts

    Kosuke TOGASHI, Hiroaki MOHRI  [Invited]

    International Political and Economic Workshop 2018 (Kobe University)  (Kobe)  International Political Economy Study Group of Kobe University

    Presentation date： 2018.09

  • Secession Negotiation Analysis by 2 Level Games and Coalition Coincidence Index

    Kosuke TOGASHI, Hiroaki MOHRI

    The 2018 Fall National Conference of Operations Research Society of Japan  (Nagoya)  Operations Research Society of Japan

    Presentation date： 2018.09

  • Damage Analysis for 2 faults factors by Erlang Distributions

    Hiroaki MOHRI, Jun'ichi Takeshita

    The 2018 Fall National Conference of Operations Research Society of Japan  (Nagoya)  Operations Research Society of Japan

    Presentation date： 2018.09

  • Analysis of Damage Induced by Two Types of Shocks

    Hiroaki MOHRI, Jun'ichi TAKESHITA

    24th International Society of Science and Applied Technologies on Reliability and Quality in Design  (Toronto)  International Society of Science and Applied Technologies

    Presentation date： 2018.08

  • Damage Analysis induced by 2 Stochastic Processes

    Hiroaki MOHRI, Jun'ichi TAKESHITA

    The 5th Stochastic Modeling Techniques and Data Analysis International Conference (SMTDA 2018)  (Chania) 

    Presentation date： 2018.06

  • The Mechanism of Commitment Problems of Separatist Conflicts in Post-Cold War Era: Analysis of Negotiations between Russia Federation and Separatist Regions by using 2 Level Game Theory

    Kosuke Togashi, Hiroaki Mohri

    (Tokyo)  The Operations Research Society of Japan

    Presentation date： 2017.12

  • Short-term Exchange Programs to the Former Soviet Union Counties and Statistical Surveys by Japanese Students

    HIROAKI MOHRI  [Invited]

    "EX ORIENT LUX" ( Japanese Study Conference) Russia-Armnia Univ 20th Anniversary Conference  (Yerevan)  Russia-Armenia University (Slavonic University)

    Presentation date： 2017.09

  • Simple Network Recovery Optimization Problem with Multiple Types of Failures

    HIROAKI MOHRI, JUN'ICHI TAKESHITA

    The 10th International Conference on Nonlinear Analysis and Convex Analysis  (CHITOSE)  International Conference on Nonlinear Analysis and Convex Analysis

    Presentation date： 2017.07

  • Optimal Arc Replacement Problem with internal and external factors.

    Hiroaki MOHRI, Jun'ichi TAKESHITA

    The International Meeting on Applied Mathematics in Errachidia 2016  (Errachidia) 

    Presentation date： 2016.05

  • Risk Analysis for Networks with Cooperative Games

    Hiroaki MOHRI, Jun'ichi TAKESHITA

    Society for Risk Analysis (SRA) 2013 Annual Meeting, Baltimore, USA, Dec. 9, 2013.  Society for Risk Analysis

    Presentation date： 2013.12

  • Network Failure Recovery Problem for Simple Networks

    Jun'ichi Takeshita, Hiroaki Mohri

    Research Research Institute for Mathematical Sciences, Kyoto University, Research Workshop  (Kyoto)  Research Research Institute for Mathematical Sciences, Kyoto Universit

    Presentation date： 2013.11

  • Optimization Problems for Network Failure Recovery

    HIROAKI MOHRI, JUN'ICHI TAKESHITA

    The Eighth International Conference on Nonlinear Analysis and Convex Analysis (NACA2013)  (Hirosaki) 

    Presentation date： 2013.08

  • On a short period exchange program to Caucasus and Central Asia

    Yuka Maruyama, Hiroaki MOHRI  [Invited]

    The 2nd Japanese language seminars in Caucasus  (Tbilisi) 

    Presentation date： 2012.11

  • A Stochastic Graph Generation Problem for some different cultural societies

    HIROAKI MOHRI

    2nd Stochastic Modeling Techniques and Data Analysis International Conference (SMTDA) 2012  (Chania, Crete) 

    Presentation date： 2012.06

  • The Network Design Problem with Stochastic Game

    HIROAKI MOHRI

    Stochastic Modeling Techniques and Data Analysis (SMTDA) 2010, Chania, Crete, Greece  (Chania, Crete) 

    Presentation date： 2010.06

  • A Decomposition graph method for fixed charge minimal network flow problems

    HIROAKI MOHRI

    International conference "Optimization and applications" (OPTIMA2009)  (Montenegro, Petrovac)  The Montenegrin Academy of Sciences and Arts University of Montenegro Dorodnicyn Computing Center Russian Academy of Sciences

    Presentation date： 2009.09

  • A Combined Analysis of Game Theory and Stochastic Process for Financial Securities

    Hiroaki Mohri

    Applied Stochastic Models and Data Analysis International Conference (ASMDA) 2007  (Chania) 

    Presentation date： 2007.05

  • A Stochastic and Optimization Analysis for a Network on Activation in Human Brain

    Jobu Watanabe, Hiroaki Mohri

    Applied Stochastic Models and Data Analysis (ASMDA) 2007  (Chania) 

    Presentation date： 2007.05

  • Hybrid Problem of Facility Location and Network Design for special graphs

    Hiroaki Mohri  [Invited]

    Conference on Routing and Location 2006-Satelite Conference of International Congress of Mathematicians 2006  (Puerto de la Cruz (Tenerife, Spain))  International Mathematical Union

    Presentation date： 2006.09

  • Hybrid Problem of Facility Location and Network Design for special graph

    Hiroaki Mohri

    International Congress of Mathematicians MADRID 2006  (Madrid)  International Mathematical Union

    Presentation date： 2006.08

  • Fixed Charge Network Flow Problem and its Ｃo-Oparative Game

    Hiroaki MOHRI

    Mathematical Analysis and Graph Theory(MAGT) 2006 -Satellite Conference of International Congress of Mathematicians 2006  (Belgrade)  International Mathematical Union

    Presentation date： 2006.08

  • A Polynomial Time Algorithm for Fixed Charge Network Design Problem on a series-parallel graph

    Hiroaki Mohri, Naoto Katayama, CHEN Mingzhe

    19th International Symposium on Mathematical Programming  (Rio de Janeiro)  Mathematical Programming Society

    Presentation date： 2006.07

  • Stochastic Game Application for Open Type Tree Queuing Network

    Hiroaki Mohri

    Research Research Institute for Mathematical Sciences, Kyoto University, Research Workshop, "Mathematics of Optimization: Methods and Practical Solutions"  (Kyoto)  Research Research Institute for Mathematical Sciences, Kyoto University

    Presentation date： 2005.07

  • Hybrid Problem of Facility Location and Network Design for Some Graph Structures

    Hiroaki Mohri

    The 2004 NZIMA Conference in Combinatorics and The 29th Australasian Conference in Combinatorial Mathematics and Combinatorial Computing (29th ACCMCC)  (Taupo)  Combinatorial Mathematics Society of Australasia

    Presentation date： 2004.12

  • Stochastic Game for Computer Network Control

    Hiroaki Mohri

    Research Institute for Mathematical Sciences, Kyoto University, Research Workshop, "Mathematical Theory and Applications of Uncertainty Sciences and Decision Making"  (Kyoto)  Research Institute for Mathematical Sciences, Kyoto University

    Presentation date： 2004.11

  • Network Design Problem for Some Graphs

    HIROAKI MOHRI

    International Conference of Numerical Analysis and Applied Mathematics  (Chalkida) 

    Presentation date： 2004.07

  • Network Design Problem and its graph structure

    Hiroaki Mohri

    Research Research Institute for Mathematical Sciences, Kyoto University, Research Workshop, "Decision Theory and Optimization Algorithms"  (Kyoto)  Research Research Institute for Mathematical Sciences, Kyoto University

    Presentation date： 2004.07

  • Lagrangian Approach for Hybrid Problem of Facility Location and Network Design

    Ming Zhe Chen, Naoto Katayama, Hiroaki Mohri

    Japan Industrial Management Association

    Presentation date： 2003.10

  • Solvability and Convexity on Some Co-Operative Game Solutions Arising From Combinatorial Optimization Problems

    Hiroaki Mohri  [Invited]

    The Third International Conference on Nonlinear Analysis and Convex Analysis  (Tokyo) 

    Presentation date： 2003.08

  • A Note for Convexity of Optimization Games

    Hiroaki Mohri

    Research Institute for Mathematical Sciences, Kyoto University, Research Workshop,"Captivation of Convexity : Fascination of Non-convexity"  (Kyoto)  Research Institute for Mathematical Sciences, Kyoto University

    Presentation date： 2003.07

  • A Note for Hybrid Problem for Network Design Problem and Facility Location Problem

    Hiroaki Mohri

    (Tokyo)  Masakazu Kojima Lab., Dept. of Mathematical and Computing Sciences, Tokyo Institute of Technology

    Presentation date： 2003.07

  • Tractable Co-Operative Game and Intractable Co-Operative Game Arising from Combinatorial Optimization Problems

    Hiroaki MOHRI

    Research Institute for Mathematical Sciences, Kyoto University, Research Workshop,"Mathematical Economics"  (Kyoto)  Institute for Mathematical Sciences, Kyoto University

    Presentation date： 2002.11

  • Network Design Game considering Stochastic Process

    Hiroaki Mohri

    RIMS Workshop, "Mathematics of Decision-making under uncertainty"  (Kyoto)  Research Institute for Mathematical Sciences

    Presentation date： 2002.11

  • What we have to consider for Superdistribution System to be a Social System

    Hiroaki Mohri

    Information Processing Society of Japan, Electronic Intellectual Property  (Tokyo)  Information Processing Society of Japan, Electronic Intellectual Property

    Presentation date： 2001.11

  • On Network Design Problem Considering Stochastic Factors and Cost Allocation

    Hiroaki Mohri

    Research Institute for Mathematical Sciences, Kyoto University, Research Workshop, "Decision-Making for Ambiguity and Uncertainty Situations,"  (Kyoto)  Research Institute for Mathematical Sciences, Kyoto University

    Presentation date： 2001.11

  • A Game-Theoretic Approach to Resource Allocation for logistics

    Hiroaki Mohri

    The Operations Research Society of Japan, Integrated Operation G3 Group  (Tokyo)  The Operations Research Society of Japan

    Presentation date： 2001.10

  • Cost Allocation Game arising from Combinatorial Optimization Problems

    Hiroaki Mohri

    Annual Meeting of 2001, The Japan Society for Industrial and Applied Mathematics  (Fukuoka)  The Japan Society for Industrial and Applied Mathematics

    Presentation date： 2001.10

  • On Economics for Communication and Broadcasting from the viewpoint of Information Engineering

    Hiroaki Mohri

    The Japan Society of Public Utility Economics 2001 Annual Meeting  The Japan Society of Public Utility Economics

    Presentation date： 2001.06

  • 2 Problems on Cost Allocation for Networks

    Hiroaki Mohri

    The Operations Research Society of Japan, Integrated Operation G3/SG3 Group  (Tokyo)  The Operations Research Society of Japan

    Presentation date： 2001.06

  • Resource Allocation Problems for logistics

    Hiroaki Mohri, Takahiro Watanabe, Shigeo Muto

    The Operations Research Society of Japan, 2001 Spring Meeting  (Okayama)  The Operations Research Society of Japan

    Presentation date： 2001.05

  • Cost allocation and its Application for Cooperative Distribution

    Hiroaki Mohri

    Tokyo Institute of Technology, VALDES Game Theory Seminar  (Tokyo)  Tokyo Institute of Technology, VALDES

    Presentation date： 2000.01

▼display all

Research Projects

  • 激化する紛争を制御するための国際関与の研究－和平仲介と紛争力学に関する理論と事例の融合－ 公益財団法人村田学術振興財団

    公益財団法人 村田学術振興財団  研究助成

    Project Year :

    2022.07
    -
    2023.06
     

    富樫耕介, 毛利裕昭, 五十嵐元道, 中村長史, 中束友幸, 佐藤圭史, 立花優, 松嵜英也, 齋藤竜太

  • An Interdisciplinary Study on the Effect of Non-Military Engagement in Preventing Escalation of Conflicts: A Bridge between Theoretical and Empirical Approaches through the Cases of Conflict in the Former Soviet Union

    Nomura Foundation  Research Grant

    Project Year :

    2020.04
    -
    2022.03
     

  • Interaticnal Joint Study 0n Digital Convergence of Telecommunicaticns and Broadcasting

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research

    Project Year :

    2001
    -
    2002
     

    NAKAMURA Kiyoshi, MITOMO Hitoshi, KANOU Sadahiko, AGATA Koichiro, MORI Hiroaki, TAKAHASHI Yoshitake

    　View Summary

    Due to digital innovation, telecommunications and broadcasting is converging, which makes the market boundaries blur. The convergence is progressing in the three layers : networks, platforms and content. When new markets based on digital convergence are rapidly creating and firms are taking such strategic behaviors as vertical and horizontal integration and grand alliances, what sorts of policies are needed to achieve allocative and productive efficiency, to promote technological progress, and to enhance equity? Recent developments in technology and recent evolvements in regulatory policy have made economic analysis central to the study of convergence policy issues. To deepen our understanding of theoretical developments and policy trend, the international study group vas organized in 1998. Since then we have been collaborate to apply economic analysis to convergence problems. The first part of our academic achievement was published as a book titled Convergence of Telecommunications and Broadcasting is Japan, UK and Germany, Curzon Press, UK. In the second period of our cooperative research works, we had a seminar on convergence policy, focusing the efficient spectrum allocation in January 2002 at Waseda University and Osaka University. We also had an international seminar at Warwick University, UK from November 2-4, 2003, in which three major topics were extensively discussed : spectrum allocation and within a few years

  • The Operations Research Society of Japan, 40th Anniversary Research Grant Project "Integrated Operation Resource Planning"

    The Operations Research Society of Japan  Research grant

    Project Year :

    2000
    -
    2002
     

Other

  • 旧共産圏から学ぶ⽂明の交差点における国際関係、物流、多⽂化社会の現状 プログラム （ハンガリー）

    2022.11
    　
    　

    　View Summary

    国際学生交流プログラム

  • 旧共産圏から学ぶ⽂明の交差点における国際関係、物流、多⽂化社会の現状 インターネットセミナー（ジョージア）

    2022.05
    -
    　

    　View Summary

    国際インターネットセミナーZOOM

  • 旧ソ連から学ぶ⽂明の交差点における国際関係、物流、多⽂化社会の現状 インターネットセミナー（ウクライナ）

    2021.08
    -
    　

    　View Summary

    国際インターネットセミナーZOOM

  • 旧ソ連から学ぶ⽂明の交差点における国際関係、物流、多⽂化社会の現状 プログラム（ジョージア）

    2019.10
    -
    　

    　View Summary

    国際学生交流プログラム

  • 旧ソ連から学ぶ⽂明の交差点における国際関係、物流、多⽂化社会の現状 インターネット（ジョージア）

    2019.06
    -
    　

  • 旧ソ連から学ぶ⽂明の交差点における国際関係、物流、多⽂化社会の現状 プログラム（ウクライナ、ベラルーシ）

    2018.10
    -
    　

    　View Summary

    国際学生交流プログラム

  • 旧ソ連から学ぶ⽂明の交差点における国際関係、物流、多⽂化社会の現状 プログラム（アルメニア）

    2017.10
    -
    　

  • 旧ソ連から学ぶ⽂明の交差点における国際関係、物流、多⽂化社会の現状 インターネットセミナー（ジョージア）

    2017.06
    -
    　

    　View Summary

    国際インターネットセミナーPolycom

  • 中央アジア・コーカサス 学生交流 プログラム （ジョージア）

    2016.10
    -
    　

    　View Summary

    国際学生交流プログラム

  • 中央アジア・コーカサス 学生交流 プログラム インターネットセミナー（ジョージア）

    2016.06
    -
    　

    　View Summary

    国際インターネットセミナーPolycom

  • 中央アジア・コーカサス 学生交流 プログラム （トルクメニスタン）

    2016.02
    -
    　

    　View Summary

    国際学生交流プログラム

  • 中央アジア・コーカサス 学生交流 プログラム （アゼルバイジャン）

    2015.10
    -
    　

    　View Summary

    国際学生交流プログラム

  • 中央アジア・コーカサス 学生交流 プログラム （グルジア）

    2015.02
    -
    　

    　View Summary

    学生国際交流プログラム

  • 中央アジア・コーカサス 学生交流 プログラム （タジキスタン）

    2014.10
    -
    　

    　View Summary

    国際学生交流プログラム

  • 中央アジア・コーカサス 学生交流 プログラム （アルメニア）

    2013.10
    -
    　

    　View Summary

    国際学生交流プログラム

  • 中央アジア・コーカサス 学生交流 プログラム （グルジア＆アゼルバイジャン）

    2012.10
    -
    2012.11

    　View Summary

    学生交流プログラム

  • 中央アジア・コーカサス 学生交流 プログラム インターネット（グルジア）

    2012.02
    -
    　

    　View Summary

    国際インターネットセミナーPolycom
    グルジアのトビリシ自由大学、トビリシ国立大学と実施

  • 中央アジア・コーカサス 学生交流 プログラム （グルジア）

    2011.10
    -
    　

    　View Summary

    学生交流プログラム

  • 中央アジア・コーカサス 学生交流 プログラム （カザフスタン）

    2010.10
    -
    2010.11

    　View Summary

    国際学生交流プログラム（早稲田大学国際部国際課の補助）
    交流大学；カザフ民族大学
    １）カザフスタン学生と日本学生によるラウンドテーブル・ディスカッション
    ２）両国の文化交流交換（カザフ料理教室、ロシア語による日本クイズなど）
    ３）モスク、正教会訪問（宗教の多様性）
    ４）バザール訪問（カザフの地元経済の考察）

▼display all

 

Syllabus

Teaching Experience

  • 数理計量分析研究IIB

    早稲田大学 商学学術院  

    2022.04
    -
    Now
     

  • 数理計量分析研究IIA

    早稲田大学 商学学術院  

    2022.04
    -
    Now
     

  • 数理計量分析研究IB

    早稲田大学 商学学術院  

    2022.04
    -
    Now
     

  • 数理計量分析研究IA

    早稲田大学 商学学術院  

    2022.04
    -
    Now
     

  • 経済統計II（内容は確率過程）

    早稲田大学 商学学術院  

    2022.04
    -
    2023.07
     

  • 経済統計I（内容は数理最適化）

    早稲田大学 商学学術院  

    2022.04
    -
    2023.07
     

  • 確率・統計基礎

    早稲田大学 理工学術院  

    2020.04
    -
    2023.07
     

  • 機械学習と数理

    早稲田大学 商学学術院  

    2022.04
    -
    2023.03
     

  • 数理統計学

    早稲田大学 商学学術院  

    2022
    -
    2023.03
     

  • 基礎統計学

    早稲田大学 商学学術院  

    2022
    -
    2023.03
     

  • 確率・統計と機械学習

    早稲田大学 理工学術院  

    2020.09
    -
    2022.03
     

▼display all

 

Sub-affiliation

  • Faculty of Science and Engineering   School of Creative Science and Engineering

Research Institute

  • 2019
    -
    　

    Research Institute of Business Administration   Concurrent Researcher

Internal Special Research Projects

  • 最適化協力ゲームの数学的構造および解の計算量に関する研究

    2004  

    　View Summary

    いままでの特定課題の研究成果を受けた形での研究である。研究題名に入っている「数学的構造」とは、大きく以下のように考えられる。まず、離散最適化問題を考える上でのグラフのトポロジカルな構造、そしてそれ以外のグラフの属性（距離、容量等）が第一にあげられる。そして、離散最適化問題を離散最適化関数と見なした時、良いとされる構造は、計算量の理論の視点から（強）多項式時間で解ける構造を持つこと、特に劣モジュラ性（さらに広くは離散凸性）の構造を持つことである。 こういった性質を調べることはゲーム理論の特性関数の構造を研究するに当たり、重要な役割を果たす。 今年度の成果としては、以前から研究しているネットワーク・デザイン問題および、ネットワーク・デザイン問題と施設配置問題を合成した問題について、グラフが森（木を含む）、直並列枝グラフについて研究を進め、多項式時間で解けるグラフ構造に関していくつかの定理を証明し、国際学会等で論文発表した。　また、ゲームの確率過程の要素についても研究し、それが情報ネットワークの制御や数理ファイナンスへの応用につながるということも示し、確率過程ゲームまで含めた幅の広い研究を進めている。　　さらに、こうした数学モデルが現実問題への広く応用されるための指針となる論文も発表した。

  • 組み合わせ最適化問題の値が提携値となる協力ゲームの研究

    2002  

    　View Summary

    昨年、一昨年の特定課題の研究成果を受けた形での研究である。まず、コンピュータネットワークへの応用を考え、コンピュータ（通信）ネットワーク設備がIT技術の発展によりコストが下がることにより、その設備施設の配置は、ネットワーク・デザインと同時考慮すべきという新しいモデルを提案し、その最適化モデルを口頭および、論文発表した。その上で、各提携に対してその最適化問題が提携値となる協力ゲームを考えその費用配分を考える協力ゲームについても口頭発表、論文発表を行なった。また、コンピュータネットワークにおいては、確率過程を考慮しなければならない場合が一般的である。こうした要素を考慮した研究発表を昨年度も行なっている。しかし、昨年度の研究方向で考えることは、数学的厳密性は保てるものの現実にコンピュータを実時間（利用者にとって不便を感じない時間）で計算することが大規模ネットワークに対しては不可能であるため、近似解法についての口頭発表、論文発表を行なった。　また、関数解析的な数学議論により「組み合わせ最適化問題の値が提携値となる協力ゲーム」の解を求める計算量に関する問題をグローバルな視点から見つめなおすことを考え、口頭および論文（近日中、公表）を行なった。　さらには、「組み合わせ最適化問題の値が提携値となる協力ゲームの研究」は研究者人口が少なく解説論文を書くことも研究者を裾野を広げる重要な作業と考え、解説論文２編を発表した。

  • ネットワーク構造（特に通信ネットワーク、ロジスティックスネットを中心に）をもつ組み合わせ最適化問題における費用配分解に関する研究

    2001  

    　View Summary

    2000年度の特定課題による成果を受けて2001年度には以下の研究成果が得られた。（１）現実の現象と数学モデルとの乖離に関する問題解決の可能性の模索　日本OR学会 2001年度春季研究発表会において、実務家から提起された上記問題についての整理を行いその成果を発表した。さらには、日本OR学会 統合オペレーション　2001/6G3/SG3　合同研究発表会において、この問題についての解決の可能性に関する方向性を提示した。（２）ネットワークデザイン問題に関する具体的な費用配分解とアルゴリズムの提示　ネットワークデザイン問題は、組み合わせ最適化問題の中でも通信ネットワーク、ロジスティックスネットワークだけでなく幅広い応用をもつ問題である。この問題は、ベーシックな条件のみでも計算量の理論の見地からは、NP-hardのクラスに属する問題である。The Second International Conference on Nonlinear Analysis and Convex Analysis 2001 においては、ベーシックな条件でのネットワークデザイン問題での費用配分解を提案し、その数学的特性をチェックした上で、計算量の問題を克服しうる費用配分解計算のアルゴリズムを示した。　さらに、The Tenth International Colloquium on Numerical Analysis and Computer Science with Applicationsにおいては、基本的ネットワークデザイン問題にさらに、施設配置問題（組み合わせ最適化問題で、計算量の理論からはこの問題もNP-hardのクラスに属する）の要素を加味した問題について数学的解の性質に関する考察を行い、発表を行った。　また、あいまいさと不確実性を含む状況の数理的意思決定　京大数理解析研究所研究集会　においては、通信ネットワークの処理時間を考慮し、確率過程を数学モデルに導入したネットワークデザイン問題の費用配分解に関する。具体的な解とその解を求めるアルゴリズムの提示を行った。（３）性質の良い組み合わせ最適化の構造をもつ費用配分ゲームに関する考察　上記に示した問題は、数学的性質が計算量の理論の見地をはじめとして良いとは言えないものである。したがって、チャレンジすることは非常に意味があると考える。しかし、その一方で、性質の良い組み合わせ最適化の構造をもつ費用配分ゲームの特性に関して、きちんと整理されているとは言いがたい現状がある。日本応用数理学会２００１年度年会　における発表においては、性質が良い問題に関する一考察を行った結果を発表した。●今年度得られた研究成果は、現実と数学モデルとの解決の方向性、ネットワークデザイン問題のいくつかのバリエーションに　ついて、具体的解と解を計算するに当たってのできる限り計算量の問題解決したアルゴリズムの提示、および、性質の良い問　題に関する、一つの見地からの整理である。今後の展開として、解の数学的性質を更に詳細にチェックすることとアルゴリズ　ムの一層の改良、性質の良い問題に関する様々な観点からの整理を行う余地が残されている。

  • 通信ネットワークにおける費用配分問題

    2000  

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    　（１）関連文献のサーベイ　本研究の基礎理論は、グラフ理論、組合せ最適化理論（数理計画法）、ゲーム理論と多岐にわたる。Web of Science等のデータベースでこれらの最新研究の動向を調査した。グラフ理論に関しては基本的な理論のみで十分と考えられた。また、組合せ最適化理論では、質の良い近似解を高速で求める多くの近似解法発表されおり、その一方で厳密解法は分枝カット法を援用したものが多く発表されている。最終目的が費用配分であることを考えると、計算量の問題を一旦考慮せずに、厳密解法の研究を中心にサーベイを行なった。そのことを踏まえて組合せ最適化問題を元問題とするゲーム理論に関するサーベイを行なった。注目すべきは、オランダのTijsのグループによる研究結果で組合せ最適化問題の性質を利用した結果を次々と発表している。　一方、応用面の視点からの研究をサーベイすると、通信ネットワークの数理モデルは、ロジスティクスの数理モデルとの共通する点が多く、考慮すべき問題点も共通する部分が多いことが判明した。この立場からも並行してしてサーベイを行なった。その成果は、早稲田商学第387号に掲載した論文で発表済みである。また、学会発表では日本ＯＲ学会の統合プロジェクトＧ３研究部会で2000年10月にすでに発表済である。（２）既存の通信ネットワークモデルに対する費用配分アルゴリズムの検討　既存の通信ネットワークに関する費用配分アルゴリズムは、それほど多く発表されておらず。ネットワークの規模が小さければGranotらによる研究が初期研究としては、有効であると考えられるが、実用面を考えると久保らのJORSJにおける論文が唯一と言えよう。久保らが元にしている組合せ最適化問題のモデルを数理計画ソフトで解かせてみても十分といえる。しかし、久保論文で提案されている費用配分は、コアの概念を元にした近似的解による費用配分である。そこで、筆者は厳密な意味で費用配分解を考え直すこと、さらには、伝統的なゲーム理論の解によらない、解の公理系を考案している段階である。（３）新しい通信ネットワークモデルの検討　元通信事業者の勤務であった学会の同僚から通信ネットワークの数学的表現自体についてインタビューし、（２）で検討されていたような抽象度の高いモデルで何が、現実の問題解決に不足しているかを検討した。抽象化モデルに何が不足しているかは判明したが、現状の数学的定式化に不足しているものを現段階で考慮すれば、理論的に取り扱いのできないモデルであるだけでなく、近似的な解法さえも考えるのが困難なモデルとなることが判明した。●今年度得られた研究成果は、アカデミック･レベル抽象数学モデルのサーベイ。現実面からの要請のヒアリングを行ない、抽象数学モデルへの検討事項を明確にしたこと。そして、費用配分解の計算量を減らすことを目的にした公理系の再検討までである。