### Filling free space

Initially, each imposition is computed so as to reach the exact minimum quantities. Thereafter, the empty spaces will be filled using the allowable surplus per article (typically 10%). The articles which  have not reached the 110%, will be placed first, so that as many articles as possible are invoiceable.

Rule 1: start from the given optimal solution with its computed run length.

Rule 2: add only replicas until 110% is reached. Don’t fill more than that.

Rule 3: add each replica individually, and each time try to add that replica which is maximally invoiceable.

As an example, we examine a case whereby all articles should be punched and whereby the solution consists of three impositions. Since all articles have a punch form, they should be arranged across in a stroke with a minimum band length of 30cm (or 12 inches, see “cutting into strokes”). In this case there are empty spaces, which can be used to demonstrate the filling process.

Imposition 1, run length=2500sheet, surplus=0%

Imposition 2, run length=1250 sheet, surplus=0%

Imposition 3, run length=5000 sheet, surplus=0%

Allowing a surplus of 10% we obtain:

Imposition 1, run length=2500, surplus=10%

Imposition 2, run length=1250, surplus=10%

Imposition 3, run length=5000, surplus=10%

Remark: since the articles 1a and 1b have a different punch form compared with 5e and 5f, the filling occurs with the articles 5e and 5f. Doing so, the  30 cm condition, as required for punching, will be met. The 30cm condition is always prioritised in the filling process.

Considering the 10%-solution, it is still possible to add to imposition 2, by allowing a surplus of 20% or more.

Imposition 2, run length=1250, surplus=20%

Note that the surplus is only used to fill empty places. The run length does not change at all. It is not so that a 20% surplus will lead to a 20% overproduction overall. What happens is that some articles allow for a 20% overproduction, if and only if this helps in filling up empty spaces. When there are no empty spaces in the optimal solution, nothing will change.