Characterization of all ρ-approximated sequences for some scheduling problems

Some scheduling problems present the peculiarity to be solvable in polynomial time and to have a huge number of optimal solutions. In the disturbed environment of a production manufacturing system, where the forecasted schedule is going to change because of unexpected events or uncertainties, it can be interesting not only to know one or several optimal sequences, but the characteristics of `good´ sequences. In this paper, we focus on the characterization of all the ρ-approximated sequences, which are solutions of a scheduling problem with a performance not worse than a given distance from the value of the optimal solution. With the support of the lattice of permutations, we define the characteristics of the optimal sequences for some particular scheduling problems. We present a method which is able, for some specific scheduling problems, to give the characteristics of all the ρ-approximated sequences. A computational experience is carried out to evaluate the performance of the proposed method.