Semi-online scheduling with “end of sequence” information

Abstract

We study a variant of classical scheduling, which is called scheduling with "end of sequence" information. It is known in advance that the last job has the longest processing time. Moreover, the last job is marked, and thus it is known for every new job whether it is the final job of the sequence. We explore this model on two uniformly related machines, that is, two machines with possibly different speeds. Two objectives are considered, maximizing the minimum completion time and minimizing the maximum completion time (makespan). Let s be the speed ratio between the two machines, we consider the competitive ratios which are possible to achieve for the two problems as functions of s. We present algorithms for different values of s and lower bounds on the competitive ratio. The proposed algorithms are best possible for a wide range of values of s. For the overall competitive ratio, we show tight bounds of φ + 1 ≈ 2.618 for the first problem, and upper and lower bounds of 1.5 and 1.46557 for the second problem.

Semi-online scheduling: A survey

“…Related Machines: Last Job. Epstein and Ye [51] followed the work of [26] and considered LL as the known EPI in their study of semi-online scheduling on 2-related machines with min-max and max-min optimality criteria. They considered S 1 = 1 s and S 2 =1, where s ≥ 1.…”

“…-Algorithm Fastest Last(FL) was proposed by Epstein and Ye [51] for P 2 |LL|C min . Algorithm FL schedules an incoming job J i on the slowest machine M 1 if and only if l 2 + p i > α(S)(l 1 + S • p i ), else J i is scheduled on the fastest machine M 2 .…”

A better semi-online algorithm for Q3/s1 = s2≤ s3/Cmin with the known largest size

“…Several semi-online algorithms on two uniform machines are also presented by [2,4,5,8]. Luo and Sun [7] gave a complicated semi-online algorithms for Q3/1 = s 1 = s 2 ≤ s 3 = s, max /C min with the competitive ratio max{2, 3s+2 s+2 }.…”

Online scheduling with a buffer on related machines

“…Some relevant models are as follows. Zhang and Ye [20] studied a model, in which it is known in advance that the largest job is last, and the scheduler is notified when this last job arrives (see also [9]). Some models assume a priori knowledge on the input already in the beginning of the input sequence, such as the total size of all jobs [15,2,3], bounds on possible job sizes [14], the cost of an optimal schedule [4,6], or other properties of the sizes, e.g., an arrival in a sorted order [13,17,7].…”