Here is a great video by Sommer Gentry and Dorry Segev explaining their work on operations research models (integer optimization and graph theory) for the kidney exchange problem. [Disclosure: I know Sommer from graduate school. We graduated from MIT within a few months of each other.]
This problem arises when friends or relatives of someone in need of a transplant want to donate their kidney but find out their loved one is not a match. If someone else's would-be donor is a match, the kidneys can be "swapped" and both patients in need of a kidney can receive one. In order to find compatible matches, the whole transplant centers have to work together when deciding who matches with whom, in order to maximize the number of transplants.
The short documentary does a fantastic job explaining operations research to the general public. I loved Sommer's definition of OR in the video as "the discipline of applying advanced analytical methods to make better decisions", and hopefully the engaging format and wonderful animations (they make graph theory and optimization seem so simple!) will help better convey to non-specialists what OR really does.
Dorry and Sommer are a husband-and-wife team based in Baltimore - Dorry as a transplant surgeon at Johns Hopkins and Sommer an Associate Professor at the United States Naval Academy. When they are not optimizing kidney exchanges, both are well-known in the lindy hop community for their dancing skills and their popular classes at the Mobtown Ballroom. Learn more about them at OptimizedMatch.com or in the Baltimore Sun magazine.