Lex Schrijver, who led a team redesigning the Dutch railway schedule, has a course in Combinatorial Optimization with a number of applications (although usually not at a very concrete level). I'm not always happy with the level of detail in the proofs in the text, but keep in mind that these are lecture notes and they're free. He also has a number of other texts on his website; it's a treasure trove.
This, of course, is "Hungarian" combinatorics. As for enumerative and algebraic combinatorics, I don't know of a source giving many applications (but then again, who needs applications if you can have universal properties?...).