Given Krakow's size and its industrial base, I don't think it would be a stretch to find working printing tools and machines to make ration cards or tickets.
Paper is easy to recycle and use if you access to hot water. I would guess that most materials in Krakow would recycle so why not ration cards
The cards could be a simple card design print on white with a few colour dots as an anti-counterfeiting measure the dots would be applied before distribution and would be random and changed weekly. Old cards would change for new ones at certain times with only one card per person being exchanged.
We did this in Afghanistan for soldiers beer cards. I printed them off and some else applied a marker colour dot.
Also the Mount Pony facility in Culpeper, VA housed a Federal Reserve Board which operated a 140,000 square foot radiation hardened facility. Dedicated on 10 December 1969, the 400 foot long bunker is built of steel-reinforced concrete a foot thick. Lead-lined shutters can be dropped to cover the windows of the semi-recessed facility, which is covered by 2 to 4 feet of dirt and surrounded by barbed-wire fences and guard posts. The seven computers at the facility, operated by the Federal Reserve Bank of Richmond, are the central node for all American electronic funds transfer activities. Until July 1992 the bunker also served as a Continuity of Government facility. With a peacetime staff of 100, the facility was designed to support an emergency staff of 540 for 30 days. But only 200 beds were provided in the men's and women's dormintories, which would be shared on a "hot-bunk" basis by the staff, working around the clock. Until 1988 the facility stored a $1 billion stock of currency to be used to reactivate the American economy following a nuclear attack.
https://fas.org/nuke/guide/usa/c3i/mt_pony.htm