The Cross-Section Method

An Algorithm for Linear Programming

by Janet Stone

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An algorithm that solves the linear-programming problem. This algorithm combines the usual phase one (obtaining feasibility) and phase two (obtaining optimality) of the simplex or dual methods into a single phase. The algorithm begins with either a single activity (column) or a constraint (equation) and proceeds to add either activities or constraints one at a time, solving the subproblems that arise for their optimal solutions. The final solution is attained after adding the last activity or constraint. The algorithm promises to be an efficient one and has several advantages arising from the information supplied about subproblems.

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