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

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 | ∑ C j ⩽ B | ∑ w j C j ) for which we propose a ( 2 , 1 ) -approximation algorithm. We also address the problem 1 | ∑ c j C j ⩽ B | ∑ w j C j 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 + ɛ ) , 1 ) (respectively ( 2 ( 1 + ɛ ) , 2 ) )-approximate Pareto curve for the problem 1 ‖ ( ∑ C j , ∑ w j C j ) (respectively 1 ‖ ( ∑ c j C j , ∑ w j C j ) ).