A column generation approach for the team formation problem

Abstract

We address a cooperative multi-team formation problem where there are multiple teams in an organization, and teams can be reformed by exchanging members among each other. We formulate this problem as a nonlinear integer programming model, by later reformulating it, which prescribes the optimal exchange decisions for all teams that maximizes the minimum resulting team value across all teams. For this problem, in order to obtain tighter dual bounds, we propose a column generation approach where each column represents specific exchange decisions of a team pair, and at each iteration, a set of attractive exchange patterns for all team pairs are generated by a series of subproblems. We implement a parallel processing scheme to solve all subproblems in order to further accelerate the procedure. In addition, to obtain near-optimal solutions, we propose a column generation-based methodology, where at the last iteration, the restricted master problem is solved as an integer programming model with all generated columns. Our results show that the column generation procedure provides dual bound improvements ranging between 2.44% and 5.31%, on average, over the linear programming relaxation of the original model for our generated instances. In addition, the proposed column generation-based methodology yields near-optimal, and in most cases, optimal solutions by providing CPU savings ranging from 71.6% to 89.2%, on average, over the CPU times of the original integer model.