Thus far, we have been exploring problems where the solution space consists of real-valued vectors. However, in some contexts, like in Chapter 6 and Chapter 7, it is sensible to imagine that fractional or irrational solutions may not make sense in the real-world contexts of those problems. It’s also not a stretch to imagine more classical production-type problems where only integral units would be possible.
In the cases where real valued and integer valued optimal solutions may differ, some care must be taken to solve for the optimal integer valued solution. In Section 8.1, we explore one potential algorithm which is algebraically driven, and in Section 8.2, we discuss an alternative algorithm which is geometrically focused.
