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The best way to find a new position is by looking into companies where you might want to work. You won't find many posted internships in logistics or supply chain management, but these are areas where companies could often use extra help.
Once you have a short list of target companies, then try reaching out to potential hiring managers, telling them a little about yourself and why you are looking to gain experience in supply chain / logistics and letting them know that you are interested in an internship with their company. Be sure to be clear about what hours and days you are available. LinkedIn is your friend -- you can do searches on keywords like "supply chain" and find people in your field who might be good to network with. The best way to approach people at first is to try to set up an "informational interview" to learn more about their company and understand more about what they do. Many if not most people will be willing to take the time to talk to a student who wants to learn more about their field.