Hello, thanks for your post!
Obviously there a lot of "unknowns" in your profile since you're a few years away from applying. A lot will depend on the quality of your work experience and how well you do so really try to take advantage of every opportunity to take on leadership, work on solving new problems, and work in diverse teams. Seek out mentors too who can provide you with feedback and possibly serve as recommenders when it comes time. Also if it's possible to broaden your exposure beyond supply chain or to spend some time working in another country, that experience might serve you well too. Especially if you're thinking about transitioning to consulting or general mangement post-MBA.
Only having 2 years experience will definitely be on the low end when you do apply so make sure you demonstrate that you've really thought through why it makes sense for you to get your MBA at that point. Do some thinking (never too early to start!) about your specific long-term career goals, what you need to be successful in those goals, and how the MBA will help you get there.
As for specific schools, INSEAD is quite competitive but I wouldn't rule it out, especially if you can get some international work experience and have really strong recommendations and essays when you do apply. I think Booth has an option for early career candidates but most programs tend to seek 3-5 years experience. You can take a look at our 2016 Class Profile Infographic (though keep in mind these numbers could change in the next 2 years!) -
https://www.mbamission.com/blog/2014/12/ ... fographic/. As you begin to research schools, take a look at our program selection guide too (
https://info.mbamission.com/Selecting-Yo ... ram-E-Book).
Hope this helps and keep us posted if we can help down the road!