Linear Programming Runs Logistics

Every time Amazon decides which warehouse ships which package — or an airline schedules a flight crew — a linear programming problem is being solved. The math: maximize or minimize a linear quantity subject to dozens or thousands of inequality constraints.

George Dantzig invented the simplex algorithm in 1947 while working for the US Air Force, and it revolutionized operations research. Modern versions solve problems with millions of variables in seconds. The core idea is pure inequality geometry: each constraint carves a flat region in high-dimensional space, and the optimal answer sits at a vertex where several inequalities meet. A multi-billion-dollar industry rests on what looks like high-school algebra.