A Relax-and-fix Heuristic for Multiple Team Formation Problem

The multi-functional team formation problem (TFP) aims to construct an appropriate team balancing the coverage gains of the skills set and the cost such as communication and individual cost. Existing works focus on optimizing these objectives separately although they impact the team gain together. In this paper, we study a new problem that considers multiple projects and aims to minimize the total cost of communication and individual team member. The problem is named after the Team Formation Problem for multiple projects (TFP-MP). The problem is firstly formulated as a constrained quadratic set covering problem, which is further equivalently transformed to a mixed integer programming (MIP) model. To solve the problem, we propose a relax-and-fix heuristic by exploring the model structure and we evaluate the computational performances by solving different problem instances based randomly generated data. The computational experiment results show that the proposed relax-and-fix heuristic algorithm can solve large instances.