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In this paper, we consider the single-machine earliness-tardiness (E-T) scheduling problem with distinct release dates, due dates, and E-T costs. The problem is formulated using dynamic programming. The solution procedure embodies a new hybrid optimization approach called generalized dynamic programming (GDP), which incorporates techniques from two methodologies: dynamic programming and branch-and-bound. An assignment-based lower bound is employed in branch-and-bound. We test 135 random instances with up to 30 jobs to evaluate the algorithm's performance. It shows that the GDP approach achieves much better results than linear programming-based branch-and-bound algorithms such as those included in the commercial package, CPLEX.