Bloomberg, available on select computers in the Business Library, has data (when available) on a company's suppliers and customers. Use the SPLC function for a specific company.  For example, to find Merck's suppliers, customers, and peers, you would type: MRK <Equity> SPLC <GO>.

You could also look for articles from trade publications which may mention a company's chain. Use ABI/INFORM Global and Business Source Complete. Search supply chain AND [your company's name].