Consider the classical online scheduling problem where jobs that arrive one by one are assigned to identical parallel machines with the objective of minimizing the makespan. We generalize this problem by allowing the current assignment to be changed whenever a new job arrives, subject to the constraint that the total size of moved jobs is bounded by β times the size of the arriving job. Our mai...

We present a first constant performance guarantee for preemptive stochastic scheduling to minimize the sum of weighted completion times. For scheduling jobs with release dates on identical parallel machines we derive a policy with a guaranteed performance ratio of 2 which matches the currently best known result for the corresponding deterministic online problem. Our policy applies to the recent...

In this paper, we consider the semi-online preemptive scheduling problem with known largest job sizes on two uniform machines. Our goal is to maximize the continuous period of time (starting from time zero) when both machines are busy, which is equivalent to maximizing the minimum machine completion time if idle time is not introduced. We design optimal deterministic semi-online algorithms for ...

This paper investigates semi-online scheduling problems on two parallel identical machines under a grade of service (GoS) provision. We consider two different semi-online versions where the optimal offline value of the instance is known in advance or the largest processing time of all jobs is known in advance. Respectively for two semi-online problems, we develop algorithms with competitive rat...

We present first constant performance guarantees for preemptive stochastic scheduling to minimize the sum of weighted completion times. For scheduling jobs with release dates on identical parallel machines we derive policies with a guaranteed performance ratio of 2 which matches the currently best known result for the corresponding deterministic online problem. Our policies apply to the recentl...

We explore the machine-minimizing job scheduling problem, which has a rich history in the line of research, under an online setting. We consider systems with arbitrary job arrival times, arbitrary job deadlines, and unit job execution time. For this problem, we present a lower bound 2.09 on the competitive factor of any online algorithms, followed by designing a 5.2-competitive online algorithm...

We consider the problem of minimizing the total weighted completion time on identical parallel machines when jobs have stochastic processing times and may arrive over time. We give randomized as well as deterministic online and off-line algorithms that have the best known performance guarantees in either setting, deterministic and offline or randomized and online. Our analysis is based on a nov...

We derive the first performance guarantees for a combinatorial online algorithm that schedules stochastic, nonpreemptive jobs on unrelated machines to minimize the expectation of the total weighted completion time. Prior work on unrelated machine scheduling with stochastic jobs was restricted to the offline case, and required sophisticated linear or convex programming relaxations for the assign...