Linear Programming in Operations Research and Decision Making: A Systematic Review of Methods, Applications, and Research Trends

Volume: 11    Issue: 2

Year of Publication: 2026

Pages: 31-43

Authors: Yamin Swe, Khin Myo Myo Minn, Hlaing Htake Khaung Tin

DOI: https://doi.org/10.5281/zenodo.23018808

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Abstract

Linear Programming (LP) continues to represent an essential tool for optimization in operations research and decision-making especially for resource-scarce situations, conflicting activities, and operational constraints. This systematic review provides a summary of literature regarding the evolution, solution procedures, applications, extensions, and new directions of research for LP. The review includes foundational work on simplex method, duality, sensitivity analysis, and mathematical modeling along with developments in the interior point approach and large-scale optimization. The expansion of LP into Integer Linear Programming, Mixed-Integer Linear Programming, Multi-Objective and Goal Programming, Fuzzy and Uncertainty-aware Optimization and Hybrid LP are also discussed. From the literature reviewed, it is clear that there are many applications of LP in areas such as production planning, transportation and logistics, supply chains, agriculture, finance, energy, healthcare, scheduling and many others. In addition, from recent literature, it is evident that LP continues to be a relevant field for large scale optimization as well as hybridization with decomposition, cutting-plane, column generation, data analytics, and machine learning techniques. There are many ongoing challenges such as the problem of parameter uncertainty, conflicting objectives like economics and sustainability, scalability, reproducibility, and prediction-driven optimization.From the analysis, it can be seen that LP is not just a conventional method of optimization, but rather a continuously evolving platform that continues to aid in current-day decision making. The future research should focus on optimization that is robust and sustainable, real-time decision making, integration of LP with artificial intelligence, and optimization transparency.

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Keywords

Linear Programming, Operations Research, Optimization, Decision Making, Resource Allocation, Mathematical Programming, Systematic Review, Optimization Methods