Wordpress Calendar Bidding Driver Management System

My client is looking for a driver management system. He doesnt tell his drivers when to work, they can simply come on and off shift as they like and take orders when on shift. My client needs to be sure that they are adequately covered by drivers at any one time so need to have a calendar based system, ideally in the back end of their wordpress powered site into which drivers can log on and “Bid” for days. I use the word bid because if a driver knows that they can work, for example in 5 days time, they should be able to go on the calendar and bid for first priority on that day if no other drivers have bid for this already. This would mean that they would get the first call on all work which comes in. Another driver who may wish to work on the same evening but who may not know his availability until the day before or even last minute on the day in question would log into the calendar and would see that there are drivers ahead of him in priority who had bid earlier. He might, for example end up as 4th priority when he bids. This would mean he would get handed any work which the drivers higher in priority are not able to service. The system would work on a first come first served basis in the sense that it would automatically allocate priority to drivers in the order that they bid for that day and time range. The system would enable my client to keep an eye on driver levels and recruit or support appropriately and would also enable the drivers to see which priority they would be if they worked a certain shift. I'm at a loss as to where to start. I wondered if it could be done using WP users and tying in to the Google Calendar API but it's a bit beyond me. Thanks