Call Center Scheduling Software

I need a scheduling program that is able to automatically create schedules for between 40 and 250 employees based off of each employee's availability. We would also need the ability to add requests off. We need to be able to define staffing levels by hour. A visual representation or 'drag and drop' interface would be a plus. My goal as a scheduler is to fill as many seats as possible at all times; we currently have 18 seats to fill but will be expanding to 60 within the next few months. Not having to define shifts would be great. I need the ability to add restraints like, no shifts longer than eight hours, an employee a cannot work more than 20 hours a week, an employee cannot work more than 5 days in a row, an employee cannot work more than 5 days a week. I would also like the ability to define certain people's entire schedules in some cases. It may also be important to note that we are not an inbound call center and as a result do not need forecasting functionality.