I have not used this, but I have attended conferences where I am pretty sure it has been used. There is a Drupal distribution called COD: http://usecod.com/ and https://www.drupal.org/project/cod . The following quotes are from the usecod.com marketing page.
Sell tickets to your attendees with Drupal Commerce support ready to go
(EDIT: Dealing with sales/commerce will likely be the hardest part, but this is probably true regardless of what open source solution you choose.)
Moderate and manage session selection
Drag & Drop Scheduling
Easily schedule session across different days and rooms
The COD project itself was updated in October, so still seems under active development. Drupal as a whole has a pretty active community. It is also easy to contribute to the project (many people start by reporting issues and submitting patches).
The downside is that Drupal has a high learning curve. Using a distribution rather than starting from scratch might make the process less painful, however.