Min-max controllable risk problems

Abstract

A min-max controllable risk problem, defined on combinatorial structures which are either simple paths of a directed multigraph or spanning trees of an undirected multigraph, with resource dependent risk functions of the arcs or the edges, is studied. The resource amount is limited, and the objective is to distribute it between the arcs or the edges so that the maximum risk over the arcs of a simple path or the edges of a spanning tree is minimized. Two new solution approaches are presented, which are asymptotically faster than the solution approaches suggested in the literature.