FACILITY LOCATION PROBLEM

Facility location problems can be commonly found in many industries, including logistics and telecommunications. In this example, we’ll show you how to tackle a facility location problem that involves determining the number and location of warehouses that are needed to supply a group of supermarkets. We’ll demonstrate how to construct a mixed-integer programming (MIP) model of this problem, implement this model in the Gurobi Python API, and then use the Gurobi Optimizer to find an optimal solution.

The study of facility location problems - also known as "location analysis" [1] - is a branch of operations research and computational geometry concerned with the optimal placement of facilities to minimize transportation costs while considering factors like safety (e.g. by avoiding placing hazardous materials near housing) and the location of competitors' facilities.

##Applications

Facility location problems have applications in a wide variety of industries. For supply chain management and logistics, this problem can be used to find the optimal location for stores, factories, warehouses, etc. Other applications range from public policy (e.g. positioning police officers in a city), telecommunications (e.g. cell towers in a network), and even particle physics (e.g. separation distance between repulsive charges). Another application of the facility location problem is to determine the locations for natural gas transmission equipment. Finally, facility location problems can be applied to cluster analysis.