Paper ID:
IJSDIP_2026_VOLUME 14_ISSUE 2_9-15
Author's Name:
Potlapuvvu Srinivasa Rao, Dr Someshwar Siddi, Mrs. Govindu Jyostna
Volume:
14
Issue:
Issue 2
Year:
2026
Pages:
9-15
Abstract
Linear Programming (LP) is a basic method of optimization that is utilized in a wide range of engineering, economics, logistics, and decision-making systems. This paper provides an in-depth overview of the classical and modern methods of solving linear programming problems in terms of their effectiveness, scalability, and relevance in real-life circumstances. The classical techniques like the Simplex technique and the graphical technique are presented as well as the modern computational techniques such as Inside the Point techniques, the metaheuristic algorithms and the machine learning-aided optimization. The paper illustrates how the increase in computing power and algorithm has greatly enhanced the accuracy and speed of solutions particularly in large scale and complicated LP models. Comparative knowledge is presented to analyze performance in terms of convergence rate, computational complexity and robustness. But there are still practical constraints such as data uncertainty sensitivity, high cost of computation of very large problems and hard to deal with dynamic or real time constraints. Moreover, certain contemporary methods demand a large amount of computing power and skills, which restrict their availability. The open research directions are hybrid optimization methods, artificial intelligence to make adaptive decisions, and designing real-time LP solvers to dynamic systems like smart healthcare and autonomous systems.
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