A note on scheduling to meet two min-sum objectives

International audienceWe 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 y > 1, there is no (x, y)-approximation with 1 < x < 1 + (1/γ) and 1 < y < 1 + (γ - 1)/(2 + y)

A Note on Scheduling to Meet Two Min-Sum Objectives

We consider the problem of scheduling a set of independent jobs on a single machine where a solution is evaluated with respect to two min-sum objective functions: the sum of completion times and the sum of weighted completion times. In particular, we are interested in (; )- approximation schedules, i.e., schedules which are simultaneously at most times from the optimum for the first objective, and times from the optimum for the second objecive. We propose a simple (1 + ; 1 + )-approximation algorithm which for any &gt; 0 always outputs (1 + ; 1 + )-approximation schedules in polynomial time. In addition, we show that for 0 &lt; 1, there is an instance such that no (x; y)-schedule with x &lt; 1 + and y &lt; 1 + 1 2+1 exists