The choice of optimisation criterion in the uniform assignment problem

V. S. Rublev ; N. B. Chaplygina

Diskretnaya Matematika, Tome 17 (2005) no. 4, pp. 150-157

Résumé

In many optimisation problems, an optimisation criterion is introduced whose part may be played by a numerical functional which has to be maximised or minimised. The situation is rather common where several functionals may be put for the part of criterion. As a rule, the choice of criterion is a result of certain intuitive reasons and influences the way of solving the problem. Considering a problem with different criteria, one can get different solutions, so a need for additional studies arises in order to make the best choice among optimisation criteria. In the uniform assignment problem, any symmetric functional which has the properties of a norm can be taken as the uniformity criterion. But the solutions which minimise a particular criterion, namely, the square deviation of the number of jobs of a worker from the average, minimise all other criteria as well, and it is reasonable to choose precisely this functional as the optimisation criterion.