One idea, one story: the simplex algorithm is in the top 10
The simplex method was picked as one of the 20th Century's top ten algorithms:
"1947: George Dantzig, at the RAND Corporation, creates the simplex method for linear programming. In terms of widespread application, Dantzig’s algorithm is one of the most successful of all time: Linear programming dominates the world of industry, where economic survival depends on the ability to optimize within budgetary and other constraints. (Of course, the “real” problems of industry are often nonlinear; the use of linear programming is sometimes dictated by the computational budget.) The simplex method is an elegant way of arriving at optimal answers. Although theoretically susceptible to exponential delays, the algorithm in practice is highly efficient—which in itself says something interesting about the nature of computation."
[Linear programming and Extensions, G. B. Dantzig, Princeton University Press, Princeton, 1963]
[The top ten algorithms of the century, in supplement to Computing in Science and Engineering,1,6,IEEE,2000]
[Linear programming, G. B. Dantzig, Operations Research, 50,1,2002,42-47]
[An Annotated Timeline of Operations Research : an informal history, Saul I. Gass, Arjang A. Assad, 2004]