An optimal online algorithm for single-processor scheduling problem with learning effect

Abstract

This paper deals with the canonical single-processor online scheduling problem with the position-based learning effect. Specially speaking, a round of jobs arriving online over time will be processed on a single processor. Noticeably, in this model, for each job Jk, the actual processing time pkl is defined as a power function of its position l, i.e., pkl=pklβ, where pk indicates its normal processing time and β≤0 is the learning index. Our goal is to make the sum of completion times as small as possible. For this problem, we testify that there is no online algorithm with a competitive ratio of less than 2. Most notably, we design an online algorithm entitled as Delayed Shortest Normal Processing Time (DSNPT), matching the lower bound proposed by us, and hence DSNPT is optimal.