Obnoxious single facility location models are models that have the aim to find the best location
for an undesired facility. Undesired is usually expressed in relation to the so-called demand
points that represent locations hindered by the facility. Because obnoxious facility location
models as a rule are multimodal, the standard techniques of convex analysis used for locating
desirable facilities in the plane may be trapped in local optima instead of the desired global
optimum. It is assumed that having more optima coincides with being harder to solve. In this
thesis the multimodality of obnoxious single facility location models is investigated in order to know which models are challenging problems in facility location problems and which are
suitable for site selection. Selected for this are the obnoxious facility models that appear to be most important in literature. These are the maximin model, that maximizes the minimum
distance from demand point to the obnoxious facility, the maxisum model, that maximizes the
sum of distance from the demand points to the facility and the minisum model, that minimizes
the sum of damage of the facility to the demand points. All models are measured with the
Euclidean distances and some models also with the rectilinear distance metric. Furthermore a
suitable algorithm is selected for testing multimodality. Of the tested algorithms in this thesis, Multistart is most appropriate. A small numerical experiment shows that Maximin models have on average the most optima, of which the model locating an obnoxious linesegment has the
most. Maximin models have few optima and are thus not very hard to solve. From the Minisum
models, the models that have the most optima are models that take wind into account. In general can be said that the generic models have less optima than the weighted versions. Models that are measured with the rectilinear norm do have more solutions than the same models measured with the Euclidean norm. This can be explained for the maximin models in the numerical example because the shape of the norm coincides with a bound of the feasible area, so not all solutions are different optima. The difference found in number of optima of the Maxisum and Minisum can not be explained by this phenomenon.