Heuristics for the single machine scheduling problem with early and quadratic tardy penalties

In this paper, we consider the single machine scheduling problem with linear earliness and quadratic tardiness costs, and no machine idle time. We propose several dispatching heuristics, and analyse their performance on a wide range of instances. The heuristics include simple scheduling rules, as well as a procedure that takes advantage of the strengths of these rules. We also consider linear early / quadratic tardy dispatching rules, and a greedy-type procedure. Extensive experiments were performed to determine appropriate values for the parameters required by some of the heuristics. The computational tests show that the best results are given by the linear early / quadratic tardy dispatching rule. This procedure is also quite efficient, and can quickly solve even very large instances.