A Decomposition Method for Interval Linear Programming

An interval linear program is

where the matrix A, vectors b⁻, b⁺, 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 Research16 (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.