Evaluation of greedy, myopic and less-greedy heuristics for the single machine, total tardiness problem

Simple, yet highly effective modifications to the net benefit of relocation (NBR) heuristic of Holsenback and Russell provide significant improvements in solution quality without any increase in computational effort by tempering the greedy nature of the original NBR heuristic. Two lemmas reduce the size of the search while adhering to optimality conditions. Experimentation compares the modified NBR heuristic (M-NBR) with the two leading heuristics of the literature. Testing on 25, 50 and 100-job problems over a wide range of due dates and tardiness factors shows the M-NBR algorithm to be the best single-pass heuristic to date. We show that a composite heuristic, employing the better of the M-NBR and another leading heuristic solution, consistently produces near-optimal solutions with negligible CPU requirements.