Range-Approval Hybrid Voting has been previously discussed . It could be applied to more than just political voting scenarios e.g. to shift bidding . Shift bidding is something that is already happening in hospitals today. The way it works is nurses go to their computers and specify the hourly amounts they would be willing to work for based on the particular day and the shift. Obviously the midnight shift is less desirable so nurses will probably bid a higher amount to work it than for a daytime shift. Then the hospital takes the bids and minimizes its labor costs making sure all shifts are covered. So if Nurse A bid $40 an hour for Thursday's midnight shift and Nurse B bid $30. an hour, the hospital would take Nurse B's bid.
Notice that this system works to the advantage of the hospital in that it minimizes labor costs, but it also works to the advantage of the nurses in that it allows them to pick and choose the slots that work for them and probably results in nurses who work less desirable shifts making more money. A refinement would be to allow the nurse to specify the maximum number of shifts she is willing to work in any given time period.
However, shift bidding does not maximize individual or social utility among the nurses. Visualize a system in which the nurses rate each shift and hourly pay rate according to its utility to them and the hospital tries to maximize social utility among the nurses. So each nurse would specify a series of hourly amounts and utility ratings for each shift. Range-Approval Hybrid Voting could be used which guarantees (I think) that each nurse could rate each shift according to its utility to her without fear of manipulation (even with prior knowledge of other's proclivities) or voting system anomalies and the hospital assigns shifts in such a way as to maximize social utility. This system would be subject to the restriction of an overall budget set by the hospital which would restrain the pay rates specified by the nurses. So a nurse who assigned a high utility to an outlandish pay rate would probably not be considered for that particular shift.
This would seem to me to be a great improvement over shift bidding for the nurses and also for the hospital in that it would set an overall budget whereas with shift bidding the hospital's budget would be variable and subject to manipulation because the hospital would have to make sure that all shifts were adequately covered regardless of labor costs.