Consider for example any multi-objective product mix problem in which all the products are measured in pieces or must be packed in fixed-size portions. Or, do you need an example of a specific problem.

Here is one publication, concerning a complex combinatorial problem related to a practical manufacturing problem in the automotive industry:

"Approximating the Pareto optimal set using a reduced set of objective functions"

Web page:

http://www.sciencedirect.com/science/article/pii/S0377221710004868