Modeling question, mixture between set covering and cutting stocksproblem

Hello everybody,

I have a modeling problem coming from a small printing company: fixed-
sized sheets of paper contain eight equal-sized cells to be filled
with different content; after the content has been decided a printing
plate is set-up and a couple of hundred sheets to a few thousand are
printed which are then finally cut into its eight cells. Setting up
the printing plates costs time and money, but once they are made, the
printing is comparatively cheap.

There are two decisions to make: assigning content to plates and
deciding the number of sheets to print from each plate. There is an
order list of content and desired quantity to be produced. The
problem is to find an assignment of content to printing plates and
quantity of sheets to produce from each plate such that the cost
needed for the plates and the total overproduction is minimized.

(There are other constraints but we ignore them for now.)

Right now, I use a mixture between a set covering formulation and
"reverse cutting stock" formulation as follows. Decision variables
are binary and select a set of printing plates from a large candidate
set of N platters. Each content k corresponds to a row in the
constraint system and b_k units must be produced. per
content is measured by slack_k, and a single unit overproduced costs
c_slack. A printing plate costs c_use to setup. For the problem
data, b_k are roughly in the same range, (min_k(b_k)/max_k(b_k)) >
0.1, and c_use = 20000*c_slack, that is 20000 overproduced cell-
contents equal one printing plate setup cost. Columns in the
constraint system contain 8 non-zero entries. For example, a column
A_j=[0, 1200, 0, 1200, 2400, 0, 0, 1200, 1200, 0, 0, 1200, 0, 0, 0,
1200]' says that content (2, 4, 5, 5, 8, 9, 12, 16) are on this
platter (5 occurs in two cells) and the platter is printed 1200 times.

min_{x,slack} \sum_{k=1}^{K} c_slack slack_k + \sum_{n=1}^{N} c_use
x_n
sb.t. \sum_{n=1}^{N} a_{k,n} x_n - slack_k = b_k, for all k=1,,K
x_n \in {0, 1} binary, for all n=1,,N
slack_k >= 0, for all k=1,,K

Right now I generate a few thousand platters by a naive heuristic and
the resulting problem is solved using the CINR Cbc MILP solver.

Here are my questions:
1. I would like to apply branch-and-price to this formulation as it
looks similar to set covering formulations used for airline crew
scheduling. However, the pricing problem is somewhat ill-posed
because the columns of A scale arbitrarily large. How to formulate a
meaningful pricing problem for the situation where A_{i,j} can be
chosen as well?

2. Has anyone of you encountered similar models before and has a
pointer to the literature?

Thanks a lot,
Sebastian