Great solved problems
Some large optimization problems have an efficient algorithmic solution. This is the case when it comes to finding the shortest path among an immense number of possibilities, to make a flow (of electricity, water, information…) transit through a network or to solve a "linear" program, not requiring enumerating all potential solutions. These questions have the good taste of belonging to the P class of problems that can be solved in "reasonable" time (sometimes polynomial). The associated algorithms, some of which, like the simplex, are ranked among the ten most important of the 20th century, have engraved the name of their discoverer in the history of computer science: Dijkstra, Ford and Fulkerson, Bellman…
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Coming to grips with randomness
Stochastic optimization problems are specifically characterized by uncertainty in the data. The modeler has only imperfect knowledge of the data relating to the system under consideration or how it will evolve. Their values can, however, be characterized by probability distributions.
Fair optimization
Decisions made within organizations often affect several individuals, whose interests must be considered fairly. Fair optimization finds efficient solutions while maintaining a balance among the individuals’ levels of satisfaction.
Scheduling: Mathematical planning | Tangente
Deciding when to carry out the tasks needed to achieve a goal sometimes calls for imagination—or abstraction. Yet all such situations can draw on scheduling theory, a field of operations research that has been highly active for over a century.
Network flows, transport and cuts | Tangente
Many transport problems can be modelled using "flows". One example is the transmission of electricity discussed in this article. Other classic applications involve transporting fluids (gas, water, oil, etc.) as well as people or goods (by truck, train, ship, etc.).