Single Facility Location Problem

Abstract

This chapter will focus on the simplest types of location problems, single facility location problem. These problems occur on a regular basis when working, layout problems (e.g., we may need to locate a machine in a shop, or items inside a warehouse). Also, on a larger scale, they can occur in, say, choosing the location of a warehouse to serve customers to whom goods must be delivered.

The models shall be studied as being “quick and dirty.” They are “quick” in the sense that they can be used quickly and easily, and “dirty” in the send that they are approximate. The use of these models should be considered particularly when some location decision must be made quickly and with limited resource available for decision analysis.

When we wish to locate a single new facility in the plane, we often would like to minimize an objective function involving Euclidean or rectilinear distances between the new facility and a collection of existing facilities having known planar locations. The first objective function we consider is that of total travel distance, or total travel cost.