[currymj]

if you have a license for a good fast solver already for some reason, it can be very effective to reduce some NP-hard problems to integer programming.

also, one interesting application related to data science is to embed a machine learning model (usually regression, maybe decision tree or neural network) inside the integer program, and then maximize over its inputs. this can let you characterize worst-case behavior, or answer questions like "how must a user change their features to flip the prediction?".

solvers are so expensive that MIPs will probably never become part of mainstream data science, but they can be very powerful beyond classic OR problems.