Abstarct: In discrete location problems (in particular, the p-median problems), there are ”n” customers with given weight which goal is to find the location of ”p” supplier (median) such that the sum of weighted distances from customers to the nearest supplier get minimized. But the inverse discrete location problems (in particular, the inverse p-median problems) consist in changing the parameters of a p-median problem at minimum cost such that a set of ”p” prespecified suppliers becomes the p-median. The costs are proportional to the increase or decrease of the corresponding parameters. These parameters are the lenght of edges and the weight of vertices. Every parameter can only be changed between a lower bound and an upper bound. In this thesis, first we consider the inverse 1-median problem with variable vertices weight on tree and cycle and finally the inverse conditional core problem on tree is considered, that the core problem on tree is in fact a path that sum of weighted distances from all vertices to this path is minimized.