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

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 !Cj B !wjCj) for which we propose a 2 1 -approximationalgorithm. We also address the problem1 !c jCj B !wjCj 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 " 1 (resp. 2 1 " 2 )-approximate Pareto curve for the problem 1 !Cj !wjCj (resp. 1 !c jCj !wjCj ).