Robust minmax regret combinatorial optimization problems with a resource–dependent uncertainty polyhedron of scenarios

Abstract

A new minmax regret optimization model with a partially controllable set of uncertain parameters is studied in this paper. It is considered a combinatorial optimization problem with a vector of uncertain costs belonging to a given polyhedron. This uncertainty polyhedron allows us to model dependency relations among the unknown parameters of any possible scenario. Moreover, we will assume that we can modify the uncertainty polyhedron by investing a set of available resources in the system. Some properties of the resulting Mathematical Programming formulation are stated and a Benders decomposition algorithmic approach is experimentally analyzed through its application to a Scheduling problem with uncertain processing times.