Single Facility Location: Multi-Objective Euclidean Distance Location

The problem of single facility location can be stated as follows: Determine the location of a single new facility with respect to a number of existing facilities that minimizes an appropriate defined total cost function which is chosen to be proportional to distance. Typical examples are the location of a new:

• machine in a manufacturing facility;

• warehouse relative to production;

• pump in chemical operations;

• well in an oil field development.

A generalization of this problem involves the multifacility location-allocation problem, [5]. A mathematical formulation of the single-facility problem is as follows: m existing facilities are located at known distinct points P ₁,..., P _m , a new facility is to be located at a point X, costs of ‘transportation’ nature are incurred and are directly proportional to an appropriately defined distance between the new facility and the existing ones. Let d(X, P _i ) represent the distance between points X and P _i and let w _i represent the cost of...