On-line simultaneous maximization of the Size and the Weight for degradable intervals schedules

Abstract

We consider the problem of scheduling on-line a sequence of degradable intervals in a set of k identical machines. Our objective is to find a schedule that maximizes simultaneously the Weight (equal to the sum of processing times) and the Size (equal to the number) of the scheduled intervals. We propose a bicriteria algorithm that uses the strategies of two monocriteria algorithms (GOL [7], maximizing the Size and LR [4], maximizing the Weight) and yields two simultaneous constant competitive ratios. This work is an extension of [2] (COCOON'04), where the same model of degradable intervals was investigated in an off-line context and the two objectives were considered separately. © Springer-Verlag Berlin Heidelberg 2005.