Simplex Algorithm
The simplex algorithm is a method for solving linear programming problems. It iteratively moves along the edges of a polytope to find the optimal vertex solution, and while it has exponential worst-case complexity, it performs efficiently in practice.
Background
- The simplex algorithm is the classic method for solving linear programming problems — mathematical models where you need to maximize or minimize a linear objective (e.g., profit) subject to a set of linear constraints (e.g., limited resources). It was developed by George Dantzig in 1947.
- "Linear programming" does not mean computer programming; it is a branch of optimization used widely in operations research, logistics, manufacturing, finance, and many engineering fields.
- The algorithm works by moving along the edges of a geometric shape (a polytope) in high-dimensional space, checking corner points until it finds the optimal solution. It is famously efficient in practice, though its worst-case theoretical performance is exponential.
- Understanding the simplex algorithm is key to grasping why linear programming became a foundational tool in supply chain management, airline scheduling, portfolio optimization, and other domains where constrained decision-making is required.