Solid transportation problem : A Lagrange’s interpolation polynomial strategy for handling improbability and multi-objective decision-making
*Vishwas Deep JoshiCorresponding authorvdjoshi.or@gmail.comDepartment of MathematicsFaculty of ScienceJECRC UniversityJaipur, Rajasthan, 303905, India0000-0001-8134-0282View full profile → , Medha Sharmamedhasharma1997@gmail.comDepartment of MathematicsFaculty of ScienceJECRC UniversityJaipur, Rajasthan, 303905, India0009-0004-9503-6686View full profile → , Huda Alsaudhalsand@ksu.edu.saDepartment of MathematicsCollege of SciencesKing Saud UniversityRiyadh, P. O. Box 22452, 11495, Saudi Arabia0000-0003-1659-4598View full profile → , Shrddhassaharan85@gmail.comDepartment of Computer Science and EngineeringJECRC UniversityJaipur, Rajasthan, 303905, India0009-0009-7135-4707View full profile → , Sapna Tyagityagisapna1990@gmail.comDepartment of MathematicsSchool of ScienceJECRC UniversityJaipur, Rajasthan, 303905, India0009-0003-0420-4254View full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Apr 2025
- Published Online:
- 26 Mar 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIOS-2161
- Pages:
- 1539–1555
Abstract
Keywords
Subject Classifications
References
[1] S. M. Sinha, Mathematical Programming: Theory and Methods, Amsterdam: Elsevier (2005).
[2] F. L. Hitchcock, “The distribution of a product from several sources to numerous localities,” J. Math. Phys., vol. 20, pp. 224–230 (1941).
[3] K. B. Haley, “New methods in mathematical programming: The solid transportation problem,” Oper. Res., vol. 10, no. 4, pp. 448–463 (1962).
[4] W. C. Healy, “Multiple choice programming (A procedure for Linear programming with zero one variables),” Oper. Res., vol. 12, no. 1, pp. 122–138 (1964).
[5] M. A. El. Sayed and I. A. Baky, “Multi-choice fractional stochastic multi-objective transportation problem,” Soft Comput., vol. 27, pp. 11551–11567 (2023).
[6] V. D. Joshi, K. Agarwal, and J. Singh, “Goal programming approach to solve linear transportation problems with multiple objectives,” J. Comput. Anal. Appl., vol. 31, pp. 127–139 (2023).
[7] H. Bhatia, “Solid transportation problem in linear fractional programming,” J. Oper. Res., Stat., Comput. Sci., vol. 18, pp. 35–50 (1978).
[8] R. Saini, V. D. Joshi, and J. Singh, “Multi-objective linear fractional transportation problem under uncertainty,” in Advances in Mathematical Modelling, Applied Analysis and Computation, Cham: Springer, pp. 475–487 (2023).
[9] V. D. Joshi, J. Singh, R. Saini, and K. S. Nisar, “Solving multi-objective linear fractional transportation problem under neutrosophic environment,” J. Interdiscip. Math., vol. 25, no. 1, pp. 123–136 (2022).
[10] V. D. Joshi and N. Gupta, “Linear fractional transportation problem with varying demand and supply,” Le Matematiche, vol. 66, pp. 3–12 (2011).
[11] M. P. Biswal and S. Acharya, “Solving multi-choice linear programming problems by interpolating polynomials,” Math. Comput. Model., vol. 54, pp. 1405–1412 (2013).
[12] J. B. Scarborough, Numerical Mathematical Analysis, Baltimore: Johns Hopkins Univ. Press (1950).
[13] V. D. Joshi, P. Agarwal, and A. Kumar, “Fuzzy transportation planning: A goal programming tactic for navigating uncertainty and multi-objective decision making,” Int. J. Interact. Des. Manuf. (2023).
[14] V. D. Joshi, M. Sharma, and J. Singh, “Solving multi-choice solid stochastic multi objective transportation problem with supply, demand and conveyance capacity involving Newton divided difference interpolations,” J. Comput. Anal. Appl., vol. 33, pp. 372–395 (2024).
[15] S. K. Roy, “Lagrange’s Interpolating Polynomial Approach to Solve Multi-choice Transportation Problem,” Int. J. Appl. Comput. Math., vol. 1, pp. 639–649 (2015).
[16] V. D. Joshi, M. Sharma, and H. Alsaud, “Solving a multi-choice solid fractional multi objective transportation problem: involving the Newton divided difference interpolation approach,” AIMS Math., vol. 9, no. 6, pp. 16031–16060 (2024).
[17] S. Acharya and M. P. Biswal, “Solving multi-choice multi-objective transportation problem,” Int. J. Math. Oper. Res., vol. 8, no. 4, pp. 509–527 (2016).
[18] V. D. Joshi, M. Sharma, Reem K. Alhefthi and Mahesh Purohit, “Optimal route planning for multi-level multi-choice transportation problem with uncertain parameters using Lagrange’s interpolating polynomial’’. vol. 46, no. 3, pp. 761-766 (2025).
