Software product line (SPL) engineering manages families of software products that share common features. However, cost-effective test case generation for an SPL is challenging. Applying existing test case generation techniques to each product variant separately may test common code in a redundant way. Moreover, it is difficult to share the test results among multiple product variants. In this paper, we propose the use of centralization, which combines multiple product variants from the same SPL and generates test cases for the entire system. By taking into account all variants, our technique generally avoids generating redundant test cases for common software components. Our case study on three SPLs shows that compared with testing each variant independently, our technique is more efficient and achieves higher test coverage.