Exact Resolution of the Team Formation Problem via Binary Quadratic Programming
The Team Formation Problem (TFP) has become a well-known problem in the Operations Research field over the last few years. The problem consists of: given a collaborative social network expressed as a graph, where each node represents a person, and a set of jobs which must be executed, the goal is to find a subgraph which satisfies certain requisites. In terms of computational complexity, the TFP is NP-hard. To make the problem more suitable to the reality of scheduling people in projects, we propose the Project TFP (PTFP) as a generalization of the original problem, where dynamic formation of times is represented. In this work, we extend some definitions found in literature of the TFP, define an objective function to the PTFP, describe an instance generator to the problem and propose a model based on binary quadratic programming to solve to optimality instances of the PTFP. We executed computational experiments in order to assess the proposed model. These preliminary experiments demonstrate that the results are promising.