Logistics

optimal delivery routes (TSP)

Amazon, Flipkart and Zomato solve millions of vehicle-routing optimisations daily — minimise total distance subject to capacity constraints.

ML

gradient descent trains every neural network

Every neural-network training run is gradient-descent optimisation: minimise loss(W) by moving W in the negative-gradient direction.

Finance

portfolio allocation

Portfolio optimisation (Markowitz) maximises expected return for a fixed risk — a quadratic-programming problem solved daily by every fund.

Manufacturing

production scheduling

Linear programming schedules production lines to maximise throughput within machine-time and material constraints — born at WWII Pentagon.

Energy

power grid load balancing

Power grids run optimal-power-flow solvers every 5 minutes to dispatch the cheapest generation that meets demand and respects line limits.

Sports analytics

lineup optimisation

IPL teams optimise auction bids and batting orders using mixed-integer programming — "spend the budget for max expected wins".