A Decomposition Method for Interval Linear Programming
An interval linear program is <disp-formula><tex-math><![CDATA[\begin{eqnarray*} (IP){:}\quad \mbox{maximize} && c^tx, \mbox{subject} && b^- \leqq Ax \leqq b^+ \end{eqnarray*}]]></tex-math></disp-formula> where the matrix A, vectors b<sup>-</sup>, b<sup>+</sup>, and c are given. If A has full row rank, the optimal solutions of (IP) can be written explicitly (A. Ben-Israel and A. Charnes: "An explicit solution of a special class of linear programming problems," Operations Research 16 (1968), 1166-1175). This result is used in conjunction with the Danteig-Wolfe decomposition principle to develop a finite iterative technique for solving the general (IP). Since any bounded linear program may be cast in form (IP) the technique may also be considered as an alternative method for linear programming.
Year of publication: |
1970
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Authors: | Ben-Israel, Adi ; Robers, Philip D. |
Published in: |
Management Science. - Institute for Operations Research and the Management Sciences - INFORMS, ISSN 0025-1909. - Vol. 16.1970, 5, p. 374-387
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Publisher: |
Institute for Operations Research and the Management Sciences - INFORMS |
Saved in:
Online Resource
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