Choosing a print size in the hardest possible way

I have a cat, who I have taken many many pictures of over the years, but I do not have pictures of the cat displayed anywhere. To the disappointment of my wife, we also have a Paris-themed collage frame which we have consistently failed to travel to Paris in pursuit of pictures for. In the interest of re-use, I’m going to fill the frame with pictures of our cat.

The frame is a varied arrangement of photo sizes and orientations split evenly between 4x6s and 3½x5s in a mix of landscape and portraits. We’re also going to get an 8x10 printed to add to our family photos collection in another part of the house.

I do most of my photo-printing at CostCo’s PhotoCentre; they’re fast, convenient, and affordable in addition to having a very acceptable finished product in a number of sizes printed on color-profiled printers.

In case you don’t have a CostCo account, I’ve shamelessly copy-pasted their pricing for you. They offer a decent range of prints, but if you look at the pricing you’ll notice it’s somewhat of a staircase with multiple sizes at the same per-print price (e.g. 5x5 and 5x7 prints). The naive interpretation of this is reasonably correct, some sizes are just cut-down versions of others. Not immediately visible, but 16x20 and 24x36 prints are done on different equipment and paper while 12x18s are just very uncommon and are priced as such.

Since we’re already committed to cutting the prints, let’s look at the cheapest options we have for printing. Fairly quick math gives us the raw cost per square-inch for full-sheet prints at any of the options. It’s very evident that 4x6 prints have dramatically lower cost (because they’re really common but also because they’re printed on dedicated equipment which is really fast at them).

Once we move past “one print per page”, there’s an optimization problem in the arrangement of prints on a given set of pages. It’s not a hard problem, but it would be nice if it was already solved. If you imagine it’s sheets of plywood instead of sheets of photo-paper, we can use the free CutList.

CutList takes a list of parts and then a list of supply pieces to cut them out of, depending on a couple of constraints, it then finds the “optimal” way to cut them from the supply pieces — where optimal is a configurable choice of “least waste from cut-pieces, fewest waste pieces, and largest waste pieces”. There are also constraints on the part orientation and the directions of “cuts” required to separate the parts, but those don’t really apply. The program takes the kerf of the cut into account when fitting pieces, which is helpful for saw blades, but doesn’t really apply to scissors and paper cutters, annoyingly 0 cut width isn’t an option, so I had to add a small amount of “margin” to each supply piece.

Given the per-area pricing, I ran through a few obvious scenarios:

1. “Exact” fits — 8x10 on an 8x10, 4x6s on 4x6s, and 3½x5s doubled-up on 5x7s. This generates 0 waste and minimal cuts.
2. Cheap 4x6s (except for the 8x10).
3. All on 8x10s — yes 8x12 are cheaper but it doesn’t make a difference.

Doing the math on each option, even with the extra waste of printing a 3½x5 on a 4x6, the 4x6 option ha the lowest total cost. That said, cutting 3½x5s from 4x6s is annoying and for an extra 30¢, I’m happy to pick the “exact fit” scenario and make only two cuts to split the 5x7s.

Yes, this was just an excuse to post Cat photos, sorry.