In this paper, we propose an optimization framework to retrieve an optimal group of experts to perform a multi-aspect task. While a diverse set of skills are needed to perform a multi-aspect task, the group of assigned experts should be able to collectively cover all these required skills. We consider three types of multi-aspect expert group formation problems and propose a unified framework to solve these problems accurately and efficiently. The first problem is concerned with finding the top k experts for a given task, while the required skills of the task are implicitly described. In the second problem, the required skills of the tasks are explicitly described using some keywords but each expert has a limited capacity to perform these tasks and therefore should be assigned to a limited number of them. Finally, the third problem is the combination of the first and the second problems. Our proposed optimization framework is based on the Facility Location Analysis which is a well known branch of the Operation Research. In our experiments, we compare the accuracy and efficiency of the proposed framework with the state-of-the-art approaches for the group formation problems. The experiment results show the effectiveness of our proposed methods in comparison with state-of-the-art approaches.