Scheduling is probably the most obvious example of a real problem. You’ve got a space that has many different ways of being bounded and need to efficiently search that space.

Physical design systems (modeling possible boat hulls, say—not the physics itself but the interaction of numerous variables) and resource allocation (drafting a baseball team, say) seem like other likely areas, though I’ve got no idea if constraint tools are the best option or whether they’re even used.

Broadly: if a multivariate problem can’t be modeled, a constraint-based search strategy is the(/one) next-best tool.

Dependency management is a common example; e.g. we want A; A depends on B and C; B depends on D or E; C conflicts with D; etc. These are all constraints, and we can ask a system like MiniZinc to find a set of packages which don't conflict (in that example {A, B, C, E} satisfy the constraints).

I don't think MiniZinc itself is used by any package-management tools, although some use competing tools/libraries. Personally I've used MiniZinc for a related problem: finding a subset of dependencies (of a given size, say 10), which satisfy the most outputs.

Edit: Another constraint modelling problem I've tackled (although I didn't use MiniZinc to solve it) is seating allocation on public transport: if the scheduled vehicle is unavailable, and the replacement has a different seating layout, how can we best assign the reserved seats (taking into account ticket class, seat direction, window/aisle, amenities, etc.)?

Examples from the software domain: Dependency resolution in package managers (packages with version requirements) may use constraint solving. Or type checking may be implemented using constraint solving. Though often if the application is well understood enough, it may jump over generic modelling language like MiniZinc and generate instructions for a boolean satisfaction solver directly.

Solving sudoku and other kinds of logical "puzzles".

Let Me GPT That For You! -> https://gprivate.com/65ubk

My GPT answer was: Imagine you have a big box of colorful building blocks, and you want to create something specific, like a house or a car. But you have some rules or constraints that you need to follow in order to complete your creation. Constraint modeling is like playing with those building blocks, but with rules. It helps you figure out how to build something while following certain restrictions. These restrictions could be things like the size or shape of the blocks you can use, how they can fit together, or even how many blocks you have to use. So, constraint modeling is like a game where you have to solve puzzles using your building blocks, but you have to follow certain rules to complete the puzzle. It helps you think logically and creatively to build something amazing!