Interactive volunteer schedule on my wordpress website page!

We are in need of a plugin or a custom idea that would allow our volunteers to self-schedule themselves. Currently we have about 100 volunteers and five different locations that I need to schedule them in. Because they are volunteers we want them to be able to select the times and locations they want to work so our idea was a web page that they could go to that would show the current week and the time slots for each location separately. You can view a sample here: [login to view URL] Just a simple schedule. However, were finding this isn’t so simple. Ideally the volunteers could just click on the schedule in the time slot they want and type their name. Were looking for someone who can implement this or a better idea to achieve the same result and be able to make it so that it renders good on mobile as well.