The Criss-Cross Method for Solving Linear Programming Problems

Stanley Zionts
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Stanley Zionts: State University of New York at Buffalo

Management Science, 1969, vol. 15, issue 7, 426-445

Abstract: This paper describes the Criss-Cross Method of solving linear programming problems. The method, a primal-dual scheme, normally begins with a problem solution that is neither primal nor dual feasible, and generates an optimal feasible solution in a finite number of iterations. Convergence of the method is proved and flow charts of the method are presented. The method has been programmed in FORTRAN and has been run on a number of computers including the IBM 1620, the IBM 7044, the CDC G-20, and the CDC 6400. A number of problems have been solved using the Criss-Cross method, and some comparisons between the Criss-Cross method and the Simplex method have been made. The results, though scanty, are favorable for the Criss-Cross method. A means of using the product form of the inverse with the Criss-Cross method is also discussed.

Date: 1969
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