A branch-and-bound algorithm for single machine scheduling with quadratic earliness and tardiness penalties

► We study the single machine problem with quadratic earliness and tardiness costs. ► The problem, for the first time, is optimally solved for problems up to 30 jobs. ► Lower and upper bounds have higher efficiency in comparison with previous studies. ► The proposed heuristic method has an overall optimality gap less than 1.3 percent.