Insitutional Repository at the National Graduate Institute for Policy Studies
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AHP事例集
Get PDF[目次]I. まえがきII. 事例（a）街路樹の選定（b）面接試験におけるAHPの適用について（c）株式投資分析 : 危険回避者と危険愛好者の選択（d）新アメリカ大統領の選択（e）21世紀の日本の首都像（f）関西新空港の候補地の選定III. あとがき[著者] 刀根 薫 / ［分析］（a）転馬 潤, 山下 慶一郎 （b）塚田 貴司, 藤崎 行男 （c）坂本 浩, 吉井 邦恒 （d）大山 敏彦, 中高 克郎 （e）串岡 勝明, 成澤 明史 （f）岩崎 敏和, 山根 健 / ［編集］尾仲 秀敏, 藤崎 行男departmental bulletin pape
線形計画法と Karmarkar 特許
Get PDFWe will briefly describe the three Karmarkar patents on linear programming: Karmarkar, Vanderbei and Bayer et al's. Also, algorithmic aspects of the patents will be shown. Recent trends in the intellectual property rights will be reported along with the pros and cons to the issues.departmental bulletin pape
An O(√nL) Iteration Large-Step Logarithmic Barrier Function Algorithm for Linear Programming
Get PDFAs a natural extension of Roos and Vial's "Long steps with logarithmic penalty barrier function in llnear programming" (1989) and Ye's "An O(n³L) 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(√nL) iterations, where n is the number of variables and L is the data length.departmental bulletin pape
A Computational Method for Solving DEA Problems with Infinitely Many DMUs
Get PDFSemi-infinite programs as related to DEA with infinitely many DMUs 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 convergency feature derived from the bisection rule.Reprinted from Research Report CCS 561, Center for Cybernetic Studies, The University of Texas, at Austin.departmental bulletin pape
A Comparative Study on AHP and DEA
Get PDFBoth Analytic Hierarchy Process (AHP) and Data Envelopment Analysis (DEA) aim at making decisions under multiple criteria environments. AHP uses pairwise comparisons and eigenvector weightings, whereas DEA does linear fractional programmings. In this paper, we will point out some structural similarities among them, by comparing the benefit/cost analysis by AHP and DEA. Also, we will discuss on the fixed vs. variable weights in multiple criteria decision making.departmental bulletin pape
An Implementation of a Revised Karmarkar's Method
Get PDFWe will show a variant of the Karmarkar's algorithm for LPs with sparse matrices. We deal with the standard form LP. Starting from an initial interior point, one interation of our method consists of choice of a basis, factorization of the basis, optimality test, reduced gradient, conjugate gradient method and determination of the next point of iterate. A combination of the reduced gradient and the conjugate gradient method is used for generating the steepest descent direction of the transformed objective function. Bases which are maintained and updated throughout the iterations are effectively utilized. As a basis, we choose the linearly independent columns of the coefficient matrix corresponding to the decreasing order of the variables. The basis is then factorized in the LU-form which is used in the computations throughout the iteration. Preliminary numerical experiments will be reported. Emphasis is laid on the implementational issues of the sparse basis.departmental bulletin pape
A Bisection Method for Solving Semi-Infinite Programs
Get PDFSemi-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.departmental bulletin pape
