Single-shift off-day scheduling of 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. Such a workforce structure exists in many practical situations (e.g. nursing staff and military staff). Daily labor requirements within a week may vary, but each worker must receive n (n = 2, 3, 4 for 5-day, 4-day, and 3-day workweeks respectively) off-days in the week. We discuss the necessary and sufficient conditions for a labor mix to be feasible. We then present a simple one-pass method that frequently gives the least cost labor mix.