Even though the PC helps quite a lot with the administration of the fleet and the rotation plans, there is still a human being needed who sets up the concept and framework in which the schedule will be implemented. So there is no way that a computer alone can create a schedule... it can only help to optimize the fleet utilization within a given framework!
Long haul aircraft usually don't fly only the same route back and forth. There is a detailled "rotation plan" for every single aircraft which shows the planned utilization of the fleet at any given time. Of course, due to delays, reroutings, flight cancellations there will always be ad-hoc changes to the original plan on a day-to-day basis. As Andy wrote there are many issues to observe like airport slots (usually negotiated at the IATA schedule coordination conference, the next one will take place next week in Seattle/WA btw), minimum turnaround times, curfews, maintenance and of course crew rotation.
Not too long ago, the whole scheduling process was made manually : Take a horizontal timeline of 7 days, divided into 24h each for every aircraft and draw horizontal bars in it, begin at the departure day and time, end the bar at arrival day and time. Write the flight number and dep/arr times above the bar and the origin/detination airports between these bars, then you can continue until the week is filled. Of course you have to observe the consistency of the flights, i.e. the departure airport of the next sector must always be the destination of the previous sector, except that you intend to "beam" your aircraft from one airport to the other
Once you did this process for 10 aircraft or more you will notice how helpful a Computer program is for these rotation plans
Programs are offered e.g. by Lufthansa Systems, by the Swedish company RM or by the Greek company AIMS.
Best regards,
Tom