A general approach to studying the stability of a Pareto optimal solution of a vector integer linear programming problem

We consider a multicriteria integer linear programming problem with a finite set of admissible solutions. With the use of Minkowski–Mahler inequality, we obtain a bound for the domain in the space of parameters of the problem equipped with some norm where the Pareto optimality of the solution is still retained. In the case of a monotone norm, we give a formula for the stability radius of the solution. As a corollary we obtain the formula for the stability radius in the case of the Hölder norm and, in particular, the Chebyshev norm in the space of parameters of a vector criterion.