A general branch-and-bound algorithm for fair division problems

In this paper, we introduce a branch-and-bound algorithm for solving fair division problems with indivisible items. Unlike similar algorithms for this problem, our algorithm is applicable to a wide class of possible fairness criteria. Computational results show that the algorithm exhibits very good performance for a considerable number of problem instances. Main applications of the algorithm are seen in computational studies of fairness criteria and fair division problems. In these problems, a relatively small number of items is considered, so an exact algorithm can be used even though the problem is a generalization of the set partitioning problem, which is NP-complete. An exemplary study comparing Max–min and Nash bargaining solutions to the fair division problem illustrates the use of the algorithm.