Lexicographic bottleneck problems

Abstract

We study combinatorial optimization problems with bottleneck objective function, where any feasible solution has the same number of elements. In addition to minimizing the largest element of a feasible solution we are interested in minimizing also the second largest element, the third largest element, and so on. For this version of the bottleneck problem two generic solution procedures are developed and analyzed. The first is based on scaling the cost elements. In the second approach an optimal solution is constructed iteratively. Both methods have polynomial running time, provided the underlying sum optimization problem is polynomially solvable.