A branch and bound to minimize the number of late jobs on a single machine with release time constraints

This paper presents a branch and bound algorithm for the single machine scheduling problem 1|ri|∑Ui where the objective function is to minimize the number of late jobs. Lower bounds based on a Lagrangian relaxation and no reductions to polynomially solvable cases are proposed. Efficient elimination rules together with strong dominance relations are also used to reduce the search space. A branch and bound exploiting these techniques solves to optimality instances with up to 200 jobs, improving drastically the size of problems that could be solved by exact methods up to now.