A final note on the ones assignment method and its variants: they do not work

Eric Landquist, Curtis Reigle and Francis J. Vasko

International Journal of Industrial and Systems Engineering, 2018, vol. 29, issue 3, 405-412

Abstract: A recent paper presented a new algorithm, called the ones assignment method, for solving the assignment problem. This method is similar to the Hungarian method, but seeks to create, through division, ones in each row and column (instead of zeros as in the Hungarian method) of the assignment matrix. Subsequent steps are analogous to the Hungarian method. Several other researchers have suggested modifications to the ones assignment method in an effort to overcome flaws in the original method. In this brief paper, we provide a trivial assignment problem and show that neither the ones assignment method nor any of its variants are able to find the optimal solution to this problem which is obvious on inspection. We further argue that any further modifications to this or any similar method will likewise prove to be ineffective.

Keywords: assignment problem; Hungarian method; auction algorithm; ones assignment method; optimisation; linear programming; algorithm; sub-optimal; counterexample; additive strategy; multiplicative strategy. (search for similar items in EconPapers)
Date: 2018
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