Discrete location problems with uncertainty

Discrete facility location problems consist in finding the best set of facilities over a finite set of potential sites so that a certain service is provided: goods delivered from a warehouse, emergency vehicles that provide first aid or take sick people to hospitals, shops that are near the potential customers, etc. Although when these problems were introduced in the literature, exact and precise information on the data was assumed, it is nowadays clear that this is rarely true. Therefore, models that account for uncertainty are required. In this chapter we will survey three of the most important families of problems in discrete facility location: the single-source capacitated facility location problem, covering problems, and hub location problems. The main contributions and solution methods in the area are reviewed for these problems, including formulations for some of the models and solution methods.