Sticker Printing Optimization

Easily minimize total printed pages while meeting sticker demands using OR-Tools CP-SAT. This approach helps define up to N layouts—each with a limited capacity—and decides how many copies of each sticker to include per layout.

Problem Overview

• You have multiple stickers (each identified by a name) with a required demand (i.e., how many copies of that sticker are needed).
• You want to place these stickers into up to a certain number of layouts (printing plates), each layout having a limited capacity (a maximum number of sticker spots).
• For each layout you define, you can print it multiple times, producing as many copies of the included stickers as needed.
• Goal: Minimize the total number of printed pages (i.e., how many times each layout is printed), while meeting or exceeding the demand for each sticker.
• Constraints:
  • Each layout can hold at most layout_capacity stickers in total (sum of copies of all sticker types in that layout). You have a maximum of max_layouts layouts you can define.
  • Each sticker’s demand must be met or exceeded by the total prints of the layouts that include it.
  • Every sticker must appear in at least one layout.

Key Features

• Reduce Printing Costs: Minimizes the total number of printed pages.
• Meet or Exceed Demand: Ensures every sticker’s required amount is fulfilled.
• Flexible Layouts: Define up to max_layouts, each with configurable layout_capacity.
• Fast Optimization: Powered by Google’s OR-Tools CP-SAT solver.

Example output

Used layouts: [0, 1]
Total pages (layouts printed): 6063

Layout 0: printed 1037 times.
  Distribution (sticker_name -> copies_per_page):
    Sticker 7 => 2
    Sticker 11 => 2
    ...

Layout 1: printed 5026 times.
  Distribution (sticker_name -> copies_per_page):
    Sticker 13 => 6
    Sticker 16 => 5
    ...

Demand checks:
  Sticker 13: printed=30156, required=29100, met=True
  Sticker 16: printed=25130, required=24300, met=True
  ...

Other

For questions or feedback, open an issue in the repository or email marcin@sobczak.me