You could start as a Manager in any Third Party Logistics Company, there are plenty of these 3PLs needed nowadays because of the Ecommerce phenomenon because many physical product manufacturers want to focus only on their product and don't want to deal with the distribution part of their business. You can work your way up from there.
You could start as a manager for a company like Amazon or DHL or UPS.
Or even more challenging and exciting get into a consulting company that focuses on Supply Chain business, helping the 3PLs and Distributors deploy systems, spend about 5 years learn the business and start your own technology startup or a consulting practice. Supply Chain is one area where all these innovations that we are seeing in the consumer space has not made it through, so it will be exciting and of course challenging to bring those innovations into Supply Chain. There are plenty of opportunities if you are open to be creative, don't mind doing something challenging and open to taking a little bit of risk.
The latest thing that is happening is deploying wearables and even drones in Supply Chain, think about what will happen if manufacturing comes back to the US fully, Supply Chain will be even more significant.
Also think about what IOT and Data Proliferation and Analytics could do to Supply Chain. You could pick a Supply Chain that focuses on sustainable aspects with the sustainable part of your degree.
Also check out my book Puga Sankara's Supply Chain Blog - that is a must read before spending Hundreds & Thousands of $$$ on your MBA or Masters Degree to get the best ROI or before starting your Entrepreneurial journey.