# On Finding Stable and Efficient Solutions for the Team Formation Problem

arXiv: https://arxiv.org/abs/1804.00309 · HTML: https://mlsanity.com/paper/1804.00309/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Apr 2018.

## Built on by (most cited first, 1 of 1)

- [ULTRA: A Data-driven Approach for Recommending Team Formation in Response to Proposal Calls](https://mlsanity.com/paper/2201.05646/) (2022)

## Abstract (arXiv)

The assignment of personnel to teams is a fundamental and ubiquitous managerial function, typically involving several objectives and a variety of idiosyncratic practical constraints. Despite the prevalence of this task in practice, the process is seldom approached as a precise optimization problem over the reported preferences of all agents. This is due in part to the underlying computational complexity that occurs when quadratic (i.e., intra-team interpersonal) interactions are taken into consideration, and also due to game-theoretic considerations, when those taking part in the process are self-interested agents. Variants of this fundamental decision problem arise in a number of settings, including, for example, human resources and project management, military platooning, sports-league management, ride sharing, data clustering, and in assigning students to group projects. In this paper, we study a mathematical-programming approach to "team formation" focused on the interplay between two of the most common objectives considered in the related literature: economic efficiency (i.e., the maximization of social welfare) and game-theoretic stability (e.g., finding a core solution when one exists). With a weighted objective across these two goals, the problem is modeled as a bi-level binary optimization problem, and transformed into a single-level, exponentially sized binary integer program. We then devise a branch-cut-and-price algorithms and demonstrate its efficacy through an extensive set of simulations, with favorable comparisons to other algorithms from the literature.