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Planar 3-index Assignment Problem

Problem formulation

Multi-index assignment problems were introduced by Pierskalla in 1968 as a natural extension of linear assignment problems. For a long time only 3-index assignment problems have been considered, while in recent years problems with more than 3 indices have been investigated, mainly in the context of multi-target tracking and data association problems by Poore in 1994.

The planar 3-index assignment problem (planar 3AP) can be stated in the following way. Let $n^3$ cost coefficients $c_{ijk}$ for $i,j,k = 1, \ldots , n$ be given. We can write this problem as an integer linear program:

Mathematical formulation

References

  • R. Burkard, M. Dell’Amico, S. Martello, Assignment Problems, 2009, DOI
  • W.P. Pierskalla. The multidimensional assignment problem. Oper. Res., 16:422–431, 1968, DOI
  • A.B. Poore. Multidimensional assignment formulation of data association problems arising from multitarget and multisensor tracking. Computational Opt. Appl., 3:27–57, 1994, DOI