Note--A Note on the Criss-Cross Algorithm

Lt. Commander W. S. Shields
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Lt. Commander W. S. Shields: Canadian Forces Staff School, Toronto, Ontario

Management Science, 1976, vol. 23, issue 1, 103-103

Abstract: The "Criss-cross" linear programming method formulated by Zionts (Zionts, Sanley. 1969. The criss-cross method for solving linear programming problems. Management Sci. 15 (7, March) 426-445.), although remarkably efficient for small problems (Zionts [Zionts, Sanley. 1972. Some empirical tests of the criss-cross method. Management Sci. 19 (4, December) 406-410.]), often requires an excessive number of iterations for problems of size 40 \times 40 or larger. Garfinkel and Yu (Garfinkel, Robert S., P. L. Yu. 1974. The composite simplex algorithm. Paper MA10.4. Joint National ORSA/TIMS Meeting, Boston, 22 April.) reported 3 such problems for which it terminated short of solution after 1000 pivots. Fortunately, the algorithm can be salvaged. All that is needed is a minor pivot rule change.

Date: 1976
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