Researched
Linear Optimization (Simplex)
Dantzig invents the simplex method in 1947, the standard way to get the best result from scarce resources in logistics, flights and production.
Open in the interactive tree →George Dantzig was looking for optimal deployment plans for the US Air Force and developed a method that solves large systems of inequalities. Karmarkar's interior-point method followed in 1984. Optimization now sits inside supply chains, power grids, markets and the training of neural networks.
Prerequisites
- Zero, Decimals & Algebra~820
- Linear Algebra & Matrices1858The simplex method works by pivoting on systems of linear equations
- Programmable Computer1941
- Game Theory1944Von Neumann linked linear-programming duality to the minimax theorem of games
Unlocks
- Complexity Theory & NP1971Karp's NP-complete list includes integer programming, the hard cousin of simplex LP
- AI Forecasting & Supply Twins2020-2026