A simple, fast, and effective heuristic for the single-machine total weighted tardiness problem

Abstract

We consider the single-machine total weighted tardiness problem (TWT) where a set of n jobs with general weights w_1,…, w_n, integer processing times p_1,…, p_n, and integer due dates d_1,…, d_n has to be scheduled non-preemptively. If C_j is the completion time of job j then T_j = max(0, C_j - d_j) denotes the tardiness of this job. The objective is to find a schedule S^{*}_{WT} that minimizes the weighted sum of the tardiness costs of all jobs computed as \sum_{j=1}^{n} w_j T_j. This problem is known to be unary NP-hard. Our goal is to design a constructive heuristic for this problem that yields excellent feasible solutions in short computational times by exploiting the structural properties of a preemptive relaxation.