A stability criterion for optimal solutions of a minimax problem about a partition into an arbitrary number of subsets under varying cardinality of the initial set

A stability criterion is considered for distributions of tasks between a fixed number of workers that are optimal in the minimax sense. A perturbation of the initial data may include not only a variation in the values of the cost function but also an addition or removal of tasks. The stability of a distribution is understood as the possibility to add a new element (remove or replace an existing element) to one of the subsets of the distribution with the optimality of the distribution preserved. An optimality criterion and a sufficient optimality condition are presented, the properties of optimality domains under constraints on the cost function are studied, and algorithms for constructing optimality domains are considered. The difference between optimality domains obtained by means of the criterion and by means of the sufficient condition is exemplified by a number of experiments.