Optimal facility location

Optimal facility location(OFL), also called location analysis, is a class of optimization problems. In all these problems, the goal is to decide where to locate some facility (e.g. a school, a gas station, a factory, etc.), in a way that optimizes some pre-specified criteria. Some examples are:

• "Decide where to locate a new school, given the locations of the students, such that the sum of daily transportation costs of all students to the school will be as small as possible."
• "Decide where to locate a new factory, given the locations of citizens, such that the minimum distance between the factory and a citizen house is as large as possible".

OFL is studied in operations research, computational geometry (a branch of computer science), and location theory (a branch of economics). Some techniques used for OFL also apply to cluster analysis.

There are various kinds of OFL problems. They differ in their objective function (e.g. sum of distances or minimum distance), in the optimization direction (maximization vs. minimization), in the number of facilities (one vs. many), and more.