A Personnel Assignment Problem

Abstract 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.