> It's amazing how often someone finds an NP-Complete problem and doesn't even attempt to try and solve it.
Just out of curiosity, how are you coming across these? I've dabbled in integer programming with both Gurobi and SAS (once for hobby purposes, and twice to solve some pretty major problems for work). For some reason, I've found it to be some of the most enjoyable work I've done to date - perhaps because of the satisfaction of being able to say "this is (one of) the best possible solution(s) to this problem."
I'm constantly looking for new problems to play around with (particularly those with business applications), but I don't find too many. In fact, just yesterday, I was commuting home running through business models and trying to imagine likely unsolved problems where you'd be minimizing/maximizing something subject to constraints...
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.
Just out of curiosity, how are you coming across these? I've dabbled in integer programming with both Gurobi and SAS (once for hobby purposes, and twice to solve some pretty major problems for work). For some reason, I've found it to be some of the most enjoyable work I've done to date - perhaps because of the satisfaction of being able to say "this is (one of) the best possible solution(s) to this problem."
I'm constantly looking for new problems to play around with (particularly those with business applications), but I don't find too many. In fact, just yesterday, I was commuting home running through business models and trying to imagine likely unsolved problems where you'd be minimizing/maximizing something subject to constraints...