Lower bounds on the approximation ratios of leading heuristics for the single machine total tardiness problem

Federico Della Croce (1) , Andrea Grosso (2) , Vangelis Th. Paschos (3)

1 DAI
2 Département d'Informatique [Université de Turin]
3 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision

The weakly NP- hard machine total scheduling tardiness problem has been extensively studied in the last decades. Various heuristics have been proposed to efficiently solve in practice a problem for which a fully polynomial time approximation scheme exists (though with complexity polynomial 0(n7/ε)). In this note we show that all known constructive heuristics for the problem, namely MDD, PSK, WI, COVERT, AU, NBR, present arbitrarily bad approximation ratio. Same behavior is shown by the decomposition heuristics DEC/EDD, DEC/MDD, DEC/PSK and DEC/WI

Mots clés: Scheduling; total tardiness; approximation algorithm; approximation ratio; NP-complete problem

Domaines: Mathématique discrète [cs.DM]; Complexité [cs.CC]

Federico Della Croce, Andrea Grosso, Vangelis Th. Paschos. Lower bounds on the approximation ratios of leading heuristics for the single machine total tardiness problem. 2005. ⟨hal-00004213⟩