Scheduling identical parallel machines with fixed delivery dates to minimize total tardiness

This paper addresses the problem of minimizing the total tardiness of a set of jobs to be scheduled on identical parallel machines where jobs can only be delivered at certain fixed delivery dates. Scheduling problems with fixed delivery dates are frequent in industry, for example when a manufacturer has to rely on the timetable of a logistics provider to ship its products to customers. We develop and empirically evaluate both optimal and heuristic solution procedures to solve the problem. As the problem is NP-hard, only relatively small instances can be optimally solved in reasonable computational time using either an efficient mathematical programming formulation or a branch-and-bound algorithm. Consequently, we develop a tabu search and a hybrid genetic algorithm to quickly find good approximate solutions for larger instances.