The multiple team formation problem using sociometry

© 2016 The Authors. Published by Elsevier Ltd. The Team Formation problem (TFP) has become a well-known problem in the OR literature over the last few years. In this problem, the allocation of multiple individuals that match a required set of skills as a group must be chosen to maximise one or several social positive attributes. Specifically, the aim of the current research is two-fold. First, two new dimensions of the TFP are added by considering multiple projects and fractions of people's dedication. This new problem is named the Multiple Team Formation Problem (MTFP). Second, an optimisation model consisting in a quadratic objective function, linear constraints and integer variables is proposed for the problem. The optimisation model is solved by three algorithms: a Constraint Programming approach provided by a commercial solver, a Local Search heuristic and a Variable Neighbourhood Search metaheuristic. These three algorithms constitute the first attempt to solve the MTFP, being a variable neighbourhood local search metaheuristic the most efficient in almost all cases. Applications of this problem commonly appear in real-life situations, particularly with the current and ongoing development of social network analysis. Therefore, this work opens multiple paths for future research.