Three general forms of matrix factoring are allowed and operate only on the internal matrix:
1) Factoring Individual Cells within Selected Areas:
where f is a user-defined factor and the cells which are factored may either constitute the entire matrix or a selected subset (i.e. an “area”)
2) Row or Column Specific Factoring:
or
where Ai/Bj are row/column specific factors set by the user.
3) Singly - or Doubly-Constrained Furnessing:
where the row and/or column balancing factors are chosen such that
where the row and column sums Oi and Dj are user input. (Under a singly - constrained model only one set of constraints is applied as under 2); under doubly - constrained, both are. Note that singly constrained Furnessing is effectively equivalent to row/column factoring, the only difference being that the required trip ends are defined under Furness as opposed to the trip end factors; e.g. Oi as opposed to Oi / oi.)
All three forms are available through a combination of interactive commands and/or data from external ascii control files. The choice of the form and the mode of control is made both in the “top” menu within FACTOR and in the next sub-menu; e.g. if you choose Furness at the top menu the choice of single/double constraints and/or input mode is made at the next menu.
Note as well that, under doubly-constrained Furness, it is implicitly assumed that the sum of all the row totals should equal the sum of all the column totals. If this condition is not satisfied various options to correct are offered; e.g., factoring up all row constraints so that they equal the column totals
Since factoring in transport applications is mostly applied to trip matrices the documentation below refers for simplicity to ‘origins’ and ‘destinations’ and ‘trip ends’ instead of ‘row totals’ or ‘column totals’, although the actual factoring operations are applicable to any type of matrix.