Integer programming to schedule a hierarchical workforce with variable demands

We consider a hierarchical workforce in which a higher qualified worker can substitute for a lower qualified one, but not vice versa. Daily labor requirements within a week may vary, but each worker must receive n off-days in the week. This problem has been considered by Hung, who discusses a necessary and sufficient condition for a labor mix to be feasible and presents a simple one-pass method that frequently gives the least cost labor mix. We show in this paper that the integer programming approach is well suited for solving this problem: the definition of the integer programming model is simple, its implementation is immediate by using, for example, the mathematical programming language and the integer programming solver XA, the computation times are low (generally a few seconds on a small microcomputer) and finally the power of the integer programming approach allows us to extend the model in two interesting directions.