A greedy reduction algorithm for setup optimization

A reduction algorithm for setup optimization in general ordered sets is proposed. Moreover, the class of weakly cycle-free orders is introduced. All orders in this class are Dilworth optimal. Cycle-free orders and bipartite Dilworth optimal orders are proper subclasses. The algorithm allows greedy setup optimization in cycle-free orders and coincides with the algorithm of Syslo et al. [5] in the class of bipartite orders.