Problem

Description

p-median model

Locate p facilities at the vertices of a network and allocate the demand to these facilities to reduce the distance travelled. If the facilities are not capacitated and p is fixed, then it is a p-median problem, in which all vertices are assigned to their closest facility. If p is a decision variable and the facilities are capacitated or non-capacitated, it is set as a Capacitated or Non-Capacitated Facility Location problem, respectively. These models are particularly relevant for the design of logistics and load allocation.

Cover sets

Cover sets are based on distance or maximum acceptable trip time, seeking to lessen the quantity of facilities to ensure some level of client coverage. It assumes a finite set of locations and is typically associated with a fixed budget. It is widely used to locate public services, e.g. health centres, post offices, libraries or schools.

Model centres

Model centres is a mini-max problem whose objective is to reduce the maximum distance between demand points and the nearest facility. Problem solving aims to cover all the demand trying to locate a quantity of facilities, provided that it reduces the distance covered. When the location of the facility is restricted to the network node, this is called a centre of vertex problem. If it is possible to locate the problem anywhere in the network, it is an absolute centre problem. This model is primarily applied to emergency services, e.g. fire stations and ambulance stations.