Operations Research in Mathematics: A Meta-Analysis

Abstract

Operations Research (OR) represents a multidisciplinary field at the intersection of mathematics, engineering, economics, and computer science, dedicated to optimizing complex systems through advanced quantitative techniques. This meta-analysis critically examines the mathematical foundations and evolutionary trajectory of OR over the past five decades. By synthesizing findings from 113 scholarly works published between 1970 and 2022, we systematically categorize mathematical developments that have shaped modern OR practices. The analysis reveals a significant transformation from classical linear programming approaches to sophisticated computational algorithms integrated with artificial intelligence. Our review identifies three predominant research clusters: optimization theory, stochastic modeling, and decision analysis systems. Mathematical advances in convex optimization, non-linear programming, and discrete optimization have substantially expanded OR's applicability across diverse domains including supply chain management, healthcare systems, and financial risk analysis. This meta-analysis establishes a comprehensive framework for understanding the mathematical underpinnings of OR while highlighting emerging research directions requiring focused investigation in response to increasing system complexity and computational capabilities