A note on scheduling to meet two min-sum objectives

Abstract

We consider a single machine scheduling problem with two min-sum objective functions: the sum of completion times and the sum of weighted completion times. We propose a simple polynomial time ( 1 + ( 1 / γ ) , 1 + γ ) -approximation algorithm, and show that for γ > 1 , there is no ( x , y ) -approximation with 1 < x < 1 + ( 1 / γ ) and 1 < y < 1 + ( γ - 1 ) / ( 2 + γ ) .