Shift bidding is a relatively new phenomenon found only in hospitals as far as I can determine. It has come about due to the nursing shortage, and was instituted primarily to save hospitals money although it has the additional effect of giving nurses a sense of empowerment over their work schedules and wages. The way it works is this: nurses go to their computers, and, after logging in to the hospital's web page, view the shifts that are still available for the coming week. They then decide what shifts they would like to work and place a bid for their hourly wage for that shift. The hospital administrator then surveys the total number of bids and accepts the lowest bid informing that nurse by email that the shift is hers.
Typically, bids will start above the nurse's regular hourly wage. For example, if a regular shift wage is $35. an hour, nurses will bid on unfilled shifts with rates of $40. to $50. an hour. This works out good for the hospital since, if they have to call the agency to fill unfilled shifts, it will charge $60. an hour. Part of that is the agency's fee, so the nurse they supply will typically make $45. an hour. Therefore, if the hospital can fill the shift with one of their own nurses, they can save $10. or $15. an hour, and the nurse will make approximately what the agency nurse would make. It's a win-win situation for the hospital and the nurses.
Nurses like the flexibility of being able to pick and choose their shifts as well as the possibility of making more money than they would on a regular shift. They can work part time if they so desire. They can also pick the department or area of the hospital in which they would like to work thereby expanding their skills and experience. Of course they must have the necessary qualifications for any assignment. As it got closer to the time, if there were any unfilled shifts, the maximum rate at which nurses could bid might be raised in order to avoid having to go to the agency. Hospitals prefer their own nurses to agency nurses since they consider them to be more dedicated. For more information on how shift bidding works, you can go here and here and here and here and here and here.
Shift bidding is a rudimentary form of Preferensism. If the concept of shift bidding is extended in such a way that each nurse can submit a range of preferences for work and wage schedules instead of submitting just one wage per shift, then nurses can be matched to shifts in such a way as to give, insofar as is possible, every nurse their highest preference. In a Preferensist approach a total budget would be set over all shifts instead of the hospitals' trying to minimize the outlay per shift. Then the final assignment of nurses to shifts would have to be brought in under budget rather than each shift's budget being minimized. There would be a constraint on the overall process instead of each shift.