Optimal set partitioning is the problem to find an (unlabeled) partition of a finite set of real numbers which minimizes a total cost, assumed to be the sum of costs contributed by the component subsets. Possibly the problem is constrained to partitions consisting of a fixed number k of subsets (k-partitioning) or to partitions with fixed shape, i.e. the subsets must have fixed cardinalities. A partition is called ordered if the intervals defined by each of the subsets are disjoint (the subsets are then naturally ordered). Optimal ordered partitions are easily constructed in \(O(n^ 2)\) time, which is not the case for general optimal partitions. Therefore it is of interest to determine whether for some set partitioning problem there always exists an optimal partition which is ordered. This is the question addressed in this paper. The authors introduce several types of set functions, such as minimum- ordered and superadditive functions, and show the corresponding set partitioning problem to have this desirable property. Several examples demonstrate how such functions arise in reliability, scheduling and clustering problems.