Given a group of individuals, each one with a single skill, and a social network capturing the mutual affinity among them, the Multiple Team Formation Problem (MTFP) consists in finding a set of teams, as harmonious as possible, each one comprising a given number of required skills. Dedication time of individuals can be partitioned into time fractions, thus allowing an individual to work in more than one team. In this work, we propose an Integer Linear Programming (ILP) formulation and sets of valid inequalities for the problem. Computational experiments carried out on test instances, generated according to the literature or based on real-world social networks, attest that the ILP model strengthened by valid inequalities consistently outperforms the existing quadratic formulation for MTFP.

给定一组人，每个人只有一种技能，并且需要一个社交网络来捕捉他们之间的相互亲和力，因此多团队组建问题（MTFP）在于找到尽可能和谐的一组团队，每个团队都包括一个给定的团队。所需技能的数量。可以将个人的奉献时间划分为多个时间部分，从而使一个人可以在多个团队中工作。在这项工作中，我们提出了整数线性规划（ILP）公式和该问题的有效不等式集。在测试实例上进行的计算实验（根据文献或基于现实世界的社交网络生成）证明，有效不等式加强的ILP模型始终优于现有的MTFP二次公式。