Operations research

This third special issue of 2020, which appears on schedule despite the tragic events of the year, is dedicated to Operations Research. The Tangente team thanks the two learned societies, ROADEF and GDR RO, which were deeply involved in its writing. Thanks to the members of the Scientific Committee, and in particular to Nadia Brauner, who devoted a lot of time to the success of this issue.

A million-dollar problem: finding a solution, is it as easy as verifying it? Written in the form 'P = NP?', this problem remains open for now. Thus, showing that a schedule satisfies the imposed constraints is easy, but finding one that works? If one must enumerate them one by one to test them, one risks spending more time than the age of the Sun, whereas we would like to have the solution in five minutes or twenty-four hours. We first seek to identify problems that we know how to solve quickly. For the others, we will use if possible intelligent tree searches, efficient exact algorithms of the combinatorial path-finding type, or approximate methods (metaheuristics).

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…

From electoral redistricting to the organization of a hospital service, through the protection of biodiversity or the use of renewable energies, the applications of operations research concern very varied, sometimes unexpected, domains where its modeling methods and tools help humans in their decision-making. The goal: finding an optimal solution (or at least "not too bad") among a large number of possibilities. O.R. enables the design, configuration and operation of complex systems that are of great importance for businesses or for local authorities.