Covid Group Testing
Covid-19 has created a serious testing situation where existing resources are not sufficient for testing each individual. One solution is group testing where multiple people can be tested using resources usually needed for a single person. Once samples are collected, the model determines what group testing strategy each lab should use and how the samples should be allocated from centers to labs, obtaining as many correctly processed kits as possible. This is implemented using GAMS/MIRO. Users can run the model on default data, view the results, then change data to generate a new scenario, comparing two saved scenarios in the comparison tool.
Gerrymandering in Wisconsin
Gerrymandering refers to a strategy where politicians try to maximize the votes they get by redistricting and manipulating district boundaries. The term gerrymandering got its first appearance in 1810s with Elbridge Gerry, the Governer of Massachusetts at that time, signing a bill that created a partisan distict in the Boston area that was compared to the shape of a mythological salamander.The traveling salesman problem is a standard use for discrete optimization. We consider fairness objectives while constructing a new district assignment strategy. Such fairness includes population bounds (i.e. all districts should have roughly the same population), contiguity constraints (i.e. all unit assigned to a district should be connected), and the pursuit of compactness (districts that are not elongated).
The Traveling Salesman Problem
The traveling salesman problem is a standard use for discrete optimization. The problem is known to be NP-Hard, and is often used to demonstrate techniques that might be viable for large scale instances. There are heuristics that are also used. The approach here shows how to use cutting planes that are generated "on-the-fly" to solve a problem visiting all the state capitols in the United States.