Approximation results for a bicriteria job scheduling problem on a single machine without preemption

Authors:
Eric Angel;Evripidis Bampis;Laurent Gourvès
Affiliations:
LaMI, Université d'Évry, Tour Évry 2, 523 Place des terrasses de l'agora, 91000 Évry Cedex, France;LaMI, Université d'Évry, Tour Évry 2, 523 Place des terrasses de l'agora, 91000 Évry Cedex, France;LaMI, Université d'Évry, Tour Évry 2, 523 Place des terrasses de l'agora, 91000 Évry Cedex, France
Venue:
Information Processing Letters
Year:
2005

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Abstract

We study the problem of minimizing the average weighted completion time on a single machine under the additional constraint that the sum of completion times does not exceed a given bound B (1|Σ Cj ≤ B|ΣwjCj) for which we propose a (2, 1)-approximation algorithm. We also address the problem 1|ΣcjCj ≤ B|ΣwjCj for which we present a (2, 2)- approximation algorithm. After showing that the problem of minimizing two different sums of weighted completion times is intractable, we present an algorithm which computes a (2(1 + ε), 1) (respectively (2(1 + ε), 2))-approximate Pareto curve for the problem 1||(ΣCj, ΣwjCj) (respectively 1||(ΣcjCj, ΣwjCj)).