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On the uniqueness of solutions to linear programs

Author

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  • G Appa

    (London School of Economics)

Abstract

We provide a constructive method of checking whether a linear programming problem (LPP) has a unique feasible or a unique optimal solution. Our method requires the solution of only one extra LPP such that the original problem has alternative solutions if and only if the optimal value of the new LPP is positive. If the original solution is not unique, an alternative solution is displayed. Possible applications are discussed.

Suggested Citation

  • G Appa, 2002. "On the uniqueness of solutions to linear programs," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 53(10), pages 1127-1132, October.
    • Handle: RePEc:pal:jorsoc:v:53:y:2002:i:10:d:10.1057_palgrave.jors.2601320
    DOI: 10.1057/palgrave.jors.2601320
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    Citations

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    Cited by:

    1. Mangasarian, O.L. & Recht, Benjamin, 2011. "Probability of unique integer solution to a system of linear equations," European Journal of Operational Research, Elsevier, vol. 214(1), pages 27-30, October.
    2. Laurent, Monique & Vargas, Luis Felipe, 2022. "Finite convergence of sum-of-squares hierarchies for the stability number of a graph," Other publications TiSEM 3998b864-7504-4cf4-bc1d-f, Tilburg University, School of Economics and Management.
    3. Louis Abraham, 2023. "A Game of Competition for Risk," Papers 2305.18941, arXiv.org.
    4. Halidias Nikolaos, 2024. "A novel portfolio optimization method and its application to the hedging problem," Monte Carlo Methods and Applications, De Gruyter, vol. 30(3), pages 249-267.
    5. Onur Şeref & J. Paul Brooks & Bernice Huang & Stephen S. Fong, 2017. "Enumeration and Cartesian Product Decomposition of Alternate Optimal Fluxes in Cellular Metabolism," INFORMS Journal on Computing, INFORMS, vol. 29(2), pages 197-210, May.
    6. Louis Abraham, 2023. "A Game of Competition for Risk," Working Papers hal-04112160, HAL.
    7. D. T. K. Huyen & J.-C. Yao & N. D. Yen, 2024. "Characteristic sets and characteristic numbers of matrix two-person games," Journal of Global Optimization, Springer, vol. 90(1), pages 217-241, September.
    8. Amir Akbari & Paul I. Barton, 2018. "An Improved Multi-parametric Programming Algorithm for Flux Balance Analysis of Metabolic Networks," Journal of Optimization Theory and Applications, Springer, vol. 178(2), pages 502-537, August.
    9. Asimit, Alexandru V. & Bignozzi, Valeria & Cheung, Ka Chun & Hu, Junlei & Kim, Eun-Seok, 2017. "Robust and Pareto optimality of insurance contracts," European Journal of Operational Research, Elsevier, vol. 262(2), pages 720-732.
    10. Xiong, Beibei & Chen, Haoxun & An, Qingxian & Wu, Jie, 2019. "A multi-objective distance friction minimization model for performance assessment through data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 279(1), pages 132-142.
    11. Bruce Golden & Linus Schrage & Douglas Shier & Lida Anna Apergi, 2021. "The power of linear programming: some surprising and unexpected LPs," 4OR, Springer, vol. 19(1), pages 15-40, March.

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