The following personnel assignment problem is considered. Let (T, ≤) be a linearly ordered set where T is a set (of people), and let (P, ≤) be a partially ordered set where P, a set of positions of two types, is of the same cardinality as T. Each person i in T is to be assigned to a position. A feasible assignment of personnel to positions is an embedding of (P, ≤) in (T, ≤). Given measures of each person's effectiveness in both types of positions, an optimal assignment maximizes the total measure of effectiveness. The general assignment problem is shown to be NP-complete. O(n log n) algorithms for two special cases of the problem are presented.
ASJC Scopus subject areas
- Control and Optimization
- Computational Mathematics
- Computational Theory and Mathematics