I run into them seemingly all the time. My background is supply chain management, and I could fill books with just the problems I've worked on for Amazon alone.

I run into them seemingly all the time. My background is supply chain management, and I could fill books with just the problems I've worked on for Amazon alone. As an example, a particularly prestigious problem to work on there was optimization of order fulfillment across warehouses with different inventory to reduce costs for split shipments (order two things and get two boxes? That's a split shipment). It's a very difficult problem to solve, considering that there is optimization within an order but also across different orders from the same customer that are yet unfulfilled, and even across completely unrelated orders competing for the same inventory. And with hundreds of thousands of fulfillment options for even a two unit order, it can get extremely complex very quickly. That problem, by the way, is one that was worked on by a founder of instacart when he was still at Amazon. If you're really interested in IP/LP/MILP/CP with business applications, start picking up literature within the Operations Research discipline. There are plenty of great books to go around. I'd recommend Model Building in Mathematical Programming...its mostly an intro to LP techniques, but the it was the book that made things click for me in terms of identifying and translating real world problems into mathematical models.