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The assignment of personnel to teams is a fundamental and ubiquitousmanagerial function, typically involving several objectives and a variety ofidiosyncratic practical constraints. Despite the prevalence of this task inpractice, the process is seldom approached as a precise optimization problemover the reported preferences of all agents. This is due in part to theunderlying computational complexity that occurs when quadratic (i.e.,intra-team interpersonal) interactions are taken into consideration, and alsodue to game-theoretic considerations, when those taking part in the process areself-interested agents. Variants of this fundamental decision problem arise ina number of settings, including, for example, human resources and projectmanagement, military platooning, sports-league management, ride sharing, dataclustering, and in assigning students to group projects. In this paper, westudy a mathematical-programming approach to "team formation" focused on theinterplay between two of the most common objectives considered in the relatedliterature: economic efficiency (i.e., the maximization of social welfare) andgame-theoretic stability (e.g., finding a core solution when one exists). Witha weighted objective across these two goals, the problem is modeled as abi-level binary optimization problem, and transformed into a single-level,exponentially sized binary integer program. We then devise abranch-cut-and-price algorithms and demonstrate its efficacy through anextensive set of simulations, with favorable comparisons to other algorithmsfrom the literature.

On Finding Stable and Efficient Solutions for the Team Formation Problem