Greedy randomised dispatching heuristics for the single machine scheduling problem with quadratic earliness and tardiness penalties

In this paper, we present greedy randomised dispatching heuristics for the single-machine scheduling problem with quadratic earliness and tardiness costs and no machine idle time. The several heuristic versions differ, on the one hand, on the strategies involved in the construction of the greedy randomised schedules. On the other hand, these versions also differ on whether they employ only a final improvement step or perform a local search after each greedy randomised construction. The proposed heuristics were compared with existing procedures as well as with optimum solutions for some instance sizes. The computational results show that the proposed procedures clearly outperform their underlying dispatching heuristic, and the best of these procedures provide results that are quite close to the optimum. The best of the proposed algorithms is the new recommended heuristic for large instances as well as a suitable alternative to the best existing procedure for the larger of the middle-sized instances.