Facility location problem

Authors: Liz Cantlebary, Lawrence Li (CHEME 6800 Fall 2020)

Stewards: Allen Yang, Fengqi You

The Facility Location Problem (FLP) is a classic optimization problem that determines the best location for a factory or warehouse to be placed based on geographical demands, facility costs, and transportation distances. However, FLP can be further broken down into capacitated and uncapacitated problems, depending on whether the facilities in question have a maximum capacity or not.

Weber Problem

The Weber Problem is a simple FLP. It is based on the premise of minimizing transportation costs from a point on a plane to various destinations, where each destination has a different associated cost per unit distance. Solving this problem is generally equivalent to finding the geometric minimum between three points with different weights. The formulation of the Weber problem is⁽¹⁾

${\underset {x,y}{min}}\{W(x,y)=\sum _{t=1}^{N}w_{i}d_{i}(x,y)\}$

where

$d_{i}(x,y)={\sqrt {(x-a_{i})^{2}+(y-b_{i})^{2}}}$

References

1. http://www.pitt.edu/~lol11/ie1079/notes/ie2079-weber-slides.pdf