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The Criss-Cross Method for Solving Linear Programming Problems

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  • Stanley Zionts

    (State University of New York at Buffalo)

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.

Suggested Citation

  • Stanley Zionts, 1969. "The Criss-Cross Method for Solving Linear Programming Problems," Management Science, INFORMS, vol. 15(7), pages 426-445, March.
    • Handle: RePEc:inm:ormnsc:v:15:y:1969:i:7:p:426-445
    DOI: 10.1287/mnsc.15.7.426
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    Cited by:

    1. Ma, Yanqin & Zhang, Lili & Pan, Pingqi, 2015. "Criss-cross algorithm based on the most-obtuse-angle rule and deficient basis," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 439-449.
    2. Konstantinos Paparrizos & Nikolaos Samaras & Angelo Sifaleras, 2015. "Exterior point simplex-type algorithms for linear and network optimization problems," Annals of Operations Research, Springer, vol. 229(1), pages 607-633, June.
    3. Adrienn Csizmadia & Zsolt Csizmadia & Tibor Illés, 2018. "Finiteness of the quadratic primal simplex method when s-monotone index selection rules are applied," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 26(3), pages 535-550, September.
    4. van Dam, Wim & Telgen, Jan, 1978. "Some Computational Experiments With A Primal-Dual Surrogate Simplex Algorithm," Econometric Institute Archives 272174, Erasmus University Rotterdam.
    5. Csizmadia, Zsolt & Illés, Tibor & Nagy, Adrienn, 2012. "The s-monotone index selection rules for pivot algorithms of linear programming," European Journal of Operational Research, Elsevier, vol. 221(3), pages 491-500.
    6. Santos-Palomo, Angel, 2004. "The sagitta method for solving linear programs," European Journal of Operational Research, Elsevier, vol. 157(3), pages 527-539, September.
    7. Zhang, Shuzhong, 1999. "New variants of finite criss-cross pivot algorithms for linear programming," European Journal of Operational Research, Elsevier, vol. 116(3), pages 607-614, August.
    8. Zhang, S., 1997. "New variants of finite criss-cross pivot algorithms for linear programming," Econometric Institute Research Papers EI 9707-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.

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