The initial method used for calculating takeoff performance was based on model tables, a takeoff program looked up the answer on the appropriate model table. It worked quite quickly but was a tad conservative.
Enter Airbus with the A340, they decided that they could get better answers by calculating the takeoff performance rather than using model tables. This became known as the "First Principle Method". The calculation is quite slow but the resulting takeoff performance is usually worth the wait!
For example, B747-400 from J'burg will get approximately 8000 kgs more takeoff weight when the calculation is based on the first principle method.
Mutt.