A Branch-and-Bound Algorithm for the Prize-Collecting Single-Machine Scheduling Problem with Deadlines and Total Tardiness Minimization

We study a prize-collecting single-machine scheduling problem with hard deadlines, where the objective is to minimize the difference between the total tardiness and the total prize of the selected jobs. This problem is motivated by industrial applications, both as a stand-alone model and as a pricing subproblem in column-generation algorithms for parallel machine scheduling problems. A preprocessing rule is devised to identify jobs that cannot belong to any optimal schedule. The resulting reduced problem is solved to optimality by a branch-and-bound algorithm and two integer linear programming formulations. The algorithm and the formulations are experimentally compared on randomly generated benchmark instances.