In addition to this remarks of the sibling comment, we don't always have a well-understood objective function. For example, how much is lunchtime worth compared

In addition to this remarks of the sibling comment, we don't always have a well-understood objective function. For example, how much is lunchtime worth compared with time outside normal hours? What we can say is that there is a certain 'badness' to it, which should increase exponentially or polynomially as we thread further outside of our preferred domain. These are known as soft constraints. A fundamental problem with soft constraints in MIP is that we cannot create cuts in the conflict graph. Technically, everything conflicts with everything else, but at very high badness. So, we then have to decompose the problem in a preconceived way, such as on geographical boundaries, time boundaries or using heuristics. This engineering can be challenging, especially given that MIP is often hard to debug. So, like the sibling comment: I prefer meta-heuristics over constraint logic programming in many cases, but I do not deny that CLP/MIP can be very useful as well.