A greedy heuristic for the mean tardiness sequencing problem

The mean tardiness problem involves sequencing a set of jobs on a single processor so as to minimize the average tardiness. Tardiness is the difference between the completion time of a job and its due date if the job is late, and zero otherwise. Optimal algorithms such as branch and bound or dynamic programming are effective for small problems; consequently, a variety of heuristics have been proposed. Several research studies have shown that the Wilkerson-Irwin heuristic is attractive both in terms of computational time and deviation from optimality. An extremely simple construction heuristic is proposed that is based on recursively identifying the most promising job to sequence in the last open position. This heuristic is compared to the Wilkerson-Irwin procedure on classes of test problems that have been previously shown to be difficult to solve. Rigorous statistical analysis confirms that the new heuristics is significantly better than Wilkerson-Irwin and that it performs increasingly better as problem size increases. This procedure can be embedded in more complex hybrid procedures such as those investigated by Potts and Van Wassenhove in 1991, or within optimum-seeking approaches such as branch and bound.