My task is to find a way of filling the capacity of a printing machine as efficiently as possible.

The machine has a printing width of 310mm. The print jobs that it produces are coils of labels which are of widths that can be run either 4 across the machine width or 5 across.
The print jobs will be sorted into 5 across groups and 4 across groups. These groups will be run separately on the machine. (No mixed widths)
The different jobs will be of different run lengths, and here lies the problem to be solved.
If coil 1 on the machine is 1000 labels long, so must the other 3 be. However, the ordered job lengths are likely to be different
For instance we might have 6 different jobs of the 4 across width
Job a 4000 labels
Job b 4000 labels
Job c 2000 labels
Job d 2000 labels
Job e 5000 labels
Job f 3000 labels
We need 1). the minimum number of print runs
2). The minimum over run of labels

There are some constraints on the coils of labels
1. No joins
2. Min length 1000 labels per coil
3. Max length 2000 labels per coil
A possible solution for this case is
RUN 1st coil 2nd coil 3rd coil 4th coil
1 5000 of a 5000 0f b 5000 of e 5000 of f
2 1000 of c 1000 of c 1000 of d 1000 of d
This will give an overrun of 1000 of a, 1000 of b and 2000 of f
Another possible solution is
RUN 1st coil 2nd coil 3rd coil 4th coil
1 2000 of a 2000 of a 2000 of b 2000 of b
2 2000 of c 2000 of d 2000 of f 2000 of f
3 1250 of e 1250 of e 1250 of e 1250 of e
This gives an overrun of 1000 of f but it requires 3 runs of the press
There will be many other possibilities.
There would be a cost associated with overruns and with extra runs and this would decide which was best.
I am not expecting some kind soul to solve this for me , but I am at a loss as to how to start and would welcome some ideas and pointers as to possible ways forward.
I am hoping that I can devise a mathematical way to produce solutions and then use SOLVER to choose the best one.
John