How to turn over the unit before tenant is completely moved out?

[William Glass]

BP, I've got my first tenant moving out at the end of the month and I've already begun advertising the vacancy for August 1st. I've received in under 24 hours 3 inquiries and requests to view the property. I need advice on how to best manage these different requests and ensure that I can turn the unit as quickly as possible and have a tenant lined up. The property from my initial walkthrough is in very good condition and beyond cleaning and some minor paint & touch ups, it should be a simple make-ready process. That being said there could obviously be unforeseen repairs etc. or tenant could do a number of things on the way out.

I'm requiring an application fee and background check on all prospective tenants who are serious. Do I start that process now with those that are serious prior to viewing the property? Most everyone wants to walk the property etc. How can I ensure I have the quickest turnover time and have a tenant lined up to move in ASAP?

I also realize this is a good problem to have and maybe I should be asking for higher rents...Thanks!