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A simplified algebraic method for system of linear inequalities with LP applications

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  • Arsham, Hossein
  • Adlakha, Veena
  • Lev, Benjamin

Abstract

In this pedagogical note we present an improved method to solve and analyze linear programming (LP) problems. The method depends on solving a system of equations and is free of any slack, surplus or artificial variables. The proposed method eliminates the need to manipulate linear inequalities to introduce additional variables and works only within the original decision variables space. We present applications of the method to handle linear optimization with varying objective function. The proposed method is easy to implement and enhances understanding of the simplex method and LP solvers transparent. We believe it is a useful alternative approach to present LP in the class room during the first few hours of introducing the subject.

Suggested Citation

  • Arsham, Hossein & Adlakha, Veena & Lev, Benjamin, 2009. "A simplified algebraic method for system of linear inequalities with LP applications," Omega, Elsevier, vol. 37(4), pages 876-882, August.
    • Handle: RePEc:eee:jomega:v:37:y:2009:i:4:p:876-882
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    References listed on IDEAS

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    1. Wang, Guoqing & Cheng, T.C. Edwin, 2007. "Customer order scheduling to minimize total weighted completion time," Omega, Elsevier, vol. 35(5), pages 623-626, October.
    2. Kuo, Ching-Chung & Nicholls, Gillian M., 2007. "A mathematical modeling approach to improving locomotive utilization at a freight railroad," Omega, Elsevier, vol. 35(5), pages 472-485, October.
    3. Shanmugam, Ramalingam & Johnson, Charles, 2007. "At a crossroad of data envelopment and principal component analyses," Omega, Elsevier, vol. 35(4), pages 351-364, August.
    4. Adlakha, Veena & Kowalski, Krzysztof & Vemuganti, R.R. & Lev, Benjamin, 2007. "More-for-less algorithm for fixed-charge transportation problems," Omega, Elsevier, vol. 35(1), pages 116-127, February.
    5. Sonia & Puri, M.C., 2008. "Two-stage time minimizing assignment problem," Omega, Elsevier, vol. 36(5), pages 730-740, October.
    6. Demirtas, Ezgi Aktar & Üstün, Özden, 2008. "An integrated multiobjective decision making process for supplier selection and order allocation," Omega, Elsevier, vol. 36(1), pages 76-90, February.
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    Cited by:

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    2. Holsapple, Clyde W. & Lee-Post, Anita, 2010. "Behavior-based analysis of knowledge dissemination channels in operations management," Omega, Elsevier, vol. 38(3-4), pages 167-178, June.
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    4. Liu, Yanwu & Tu, Yan & Zhang, Zhongzhen, 2021. "The row pivoting method for linear programming," Omega, Elsevier, vol. 100(C).
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    6. Li, Deng-Feng, 2011. "Linear programming approach to solve interval-valued matrix games," Omega, Elsevier, vol. 39(6), pages 655-666, December.

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