As has been covered in parts above, it depends greatly on what stage of the planning you are at. Planning can be broken up into long-term, seasonal (IATA seasons), short term and operational horizons.
This is more the 18 month + horizon, and focuses on high level route requirements and long term fleet issues (lease, buy, divest, renew leases, etc..). It will also be in this planning that new routes would be added or non-performing routes written out of the plan.
This breaks the planning down into IATA seasons (2 per year), which are literally daylight saving and non-daylight saving times. Most airlines plan 3 seasons out, creating a base schedule for each. A base schedule is a weeks snapshot of the schedule to be put in place, allocating aircraft type, flight numbers, frequency and times to the route network (but not actual tail numbers). This is often what the published timetables are generated from, which is why they are nearly always wrong.
Airlines also often create sub-seasons within seasons to cater for periods of different travel patterns (such as Christmas-New Year).
This is where things start to get a bit more detailed. A short-term schedule may represent a months flying, and is a modification of the base schedule for that period. A months flying would be worked on about three months in advance.
The purpose of this planning horizon is to cater for any specific demand patters that might be evident, and adjusting the base schedule accordingly (down to an individual day if necessary). It is also when the planning introduces heavy maintenance requirements and crewing rosters, which means actual tail numbers are being used at this stage.
This is when everything you have done to this point goes out the window and things start happening in real time. The schedule is handed over to operations about a week before the operating date, where they can do the last minute changes for maintenance or day-of-operation requirements. This is supposed to be performed without destroying the integrity of the original schedule (he laughs uncontrollably)
As mentioned above, sometimes airlines have a fleet of one aircraft type but with different specs within the fleet type (eg. You may have 20 B737-800's but only 8 are ETOPS). Most scheduling systems will allow the planner to create a sub-fleet for these differences so that you don't need to schedule by tail number months out from the operation (for example, B738 used for the standard and, say, B73E for the ETOPS ones).
For the computer systems, small airlines can get away with desktop applications, but larger airlines need much larger equipment. The larger airlines would use mainframe or Unix platforms to house their scheduling systems, not just for the size and grunt, but the physical coverage, flexibility, and communicative aspects of the system. For large airlines, the scheduling system usually needs to be accessed at multiple location, and be able to interface with reservations, crewing, yield management and complex forecasting applications.
Oh, LMML - Yield Managers would like to think that they and their systems call the shots on the schedule, but fortunately they don't
. You will find that schedules planning would gather the information to perform capacity management during the various stages of schedule preparation. It is then up to the poor buggers in yield management using the yield management system to determine how the hell they are going to fill the aircraft, whilst at the same time maximizing revenue.
Hope this helps without confusing the hell out of you.