The multidimensional assignment problem with application

The mathematical foundation of a special class of the symmetric multidimensional assignment problem is presented as a generalization of the well-known two-dimensional assignment model. The formulation is based on constructing a multidimensional performance index for the problem, to be optimized such that one assignment is attained at each layer. A procedure is suggested for solving such a formulation, based on modifying its elements until one independent zero component is attained in each plane. A case study of the limestone selection in a quarry for cement manufacturing is furnished to demonstrate the efficacy of the approach. It is shown that the optimal strategy, based on multidimensional assignment formulation, is effective and tends to considerably reduce the resulting fluctuations in raw material quality