# Facility location problems

Author: Aaron Litoff

Stewards: Dajun Yue and Fengqi You

The facility location problem deals with selecting the location of a facility from a list of integer possibilities to best meet demand wether to the next line of customers. Goal here is to most efficiently serve the constraints demanded while doing so at the lowest cost.

## Contents |

## History

The Fermat-Weber problem was one of the first facility location problems every proposed, and was done so as early as the 17th century. It was put by the French mathemetatican Fermat to the Italian physicist Torricelli as follows:

"Given three points in a plane, find a fourth point such that the sum of its distances to the three given points is as small as possible." This is the simplest continous facility location model.

A modern day engineering interpretation could be as follows:

Find the best location for a refining plant between three cities in such a way that te sum of the connections between the power plant and the cities in minimal.

## Description and Formulation

## Solution Methods

## Examples and Applications

Suppose you are a manager at a company that builds Warehouse needs to be built in a central location so that the transportation costs are minimized