In many simulation studies involving networks there is the need to rely on a sample network to perform the simulation experiments. In many cases, real network data is not available due to privacy concerns. In that case we can recourse to synthetic data sets with similar properties to the real data. In this paper we discuss the problem of generating synthetic data sets for a certain kind of online social network, for simulation purposes. Some popular online social networks, such as LinkedIn and ResearchGate, allow user endorsements for specific skills. For each particular skill, the endorsements give rise to a directed subgraph of the corresponding network, where the nodes correspond to network members or users, and the arcs represent endorsement relations. Modelling these endorsement digraphs can be done by formulating an optimization problem, which is amenable to different heuristics. Our construction method consists of two stages: The first one simulates the growth of the network, and the second one solves the aforementioned optimization problem to construct the endorsements.