this talk considers the problem of constructing optimal designs for regression models when there are several independent variables and some of them are not under the control of the experimenter. a variable that is not under control can have known values before the experiment is realized. the first case is briefly discussed in the literature. the aim of this work is to provide equivalence theorems for the second case and the mixture of both cases. iterative algorithms for generating approximate optimal designs are given and a real case of lung cancer is discussed. assuming an optimal design was carried out and then a new patient arrives the marginal design changes. thus, we want to find the optimal joint design with this new restriction. different approaches are considered to deal with this typical situation.