Online Scheduling of Incompatible Family Jobs with Equal Length on an Unbounded Parallel-Batch Machine with Job Delivery

2018 ◽  
Vol 35 (04) ◽  
pp. 1850026
Author(s):  
Qijia Liu ◽  
Jinjiang Yuan
Keyword(s):  
Competitive Ratio ◽  
Completion Time ◽  
Online Algorithm ◽  
Online Scheduling ◽  
Equal Length ◽  
Batch Machine ◽  
Job Delivery ◽  
Over Time

In this paper, we consider the online scheduling of incompatible family jobs with equal length on an unbounded parallel-batch machine with job delivery. The jobs arrive online over time and belong to [Formula: see text] incompatible job families, where [Formula: see text] is known in advance. The jobs are first processed in batches on an unbounded parallel-batch machine and then the completed jobs are delivered in batches by a vehicle with infinite capacity to their customers. The jobs from distinct families cannot be processed and delivered in the same batch. The objective is to minimize the maximum delivery completion time of the jobs. For this problem, we present an online algorithm with the best competitive ratio of [Formula: see text].

scholarly journals Online Scheduling with Delivery Time on a Bounded Parallel Batch Machine with Limited Restart

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Hailing Liu ◽  
Long Wan ◽  
Zhigang Yan ◽  
Jinjiang Yuan
Keyword(s):  
Positive Solution ◽  
Competitive Ratio ◽  
Online Algorithm ◽  
Online Scheduling ◽  
Equal Length ◽  
Delivery Time ◽  
Batch Machine ◽  
Time Scheduling ◽  
Work Done ◽  
Over Time

We consider the online (over time) scheduling of equal length jobs on a bounded parallel batch machine with batch capacitybto minimize the time by which all jobs have been delivered with limited restart. Here, “restart” means that a running batch may be interrupted, losing all the work done on it, and jobs in the interrupted batch are then released and become independently unscheduled jobs, called restarted jobs. “Limited restart” means that a running batch which contains some restarted jobs cannot be restarted again. Whenb=2, we propose a best possible online algorithmH(b=2)with a competitive ratio of1+α, whereαis the positive solution of2α(1+α)=1. Whenb≥3, we present a best possible online algorithmH(b≥3)with a competitive ratio of1+β, whereβis the positive solution ofβ(1+β)2=1.

A BEST POSSIBLE ONLINE ALGORITHM FOR SCHEDULING TO MINIMIZE MAXIMUM FLOW-TIME ON BOUNDED BATCH MACHINES

2014 ◽  
Vol 31 (04) ◽  
pp. 1450030 ◽  
Author(s):  
CHENGWEN JIAO ◽  
WENHUA LI ◽  
JINJIANG YUAN
Keyword(s):  
Competitive Ratio ◽  
Completion Time ◽  
Online Algorithm ◽  
Unit Length ◽  
Maximum Flow ◽  
Flow Time ◽  
Release Time ◽  
Batch Machine ◽  
The Difference ◽  
Over Time

We consider online scheduling of unit length jobs on m identical parallel-batch machines. Jobs arrive over time. The objective is to minimize maximum flow-time, with the flow-time of a job being the difference of its completion time and its release time. A parallel-batch machine can handle up to b jobs simultaneously as a batch. Here, the batch capacity is bounded, that is b < ∞. In this paper, we provide a best possible online algorithm for the problem with a competitive ratio of [Formula: see text].

ONLINE SCHEDULING OF MIXED CPU-GPU JOBS

2014 ◽  
Vol 25 (06) ◽  
pp. 745-761 ◽  
Author(s):  
LIN CHEN ◽  
DESHI YE ◽  
GUOCHUAN ZHANG
Keyword(s):  
Competitive Ratio ◽  
Completion Time ◽  
Online Algorithm ◽  
Online Scheduling ◽  
Scheduling Problem ◽  
Competitive Algorithm ◽  
Processing Times ◽  
Special Cases ◽  
Identical Machines ◽  
The One

We consider the online scheduling problem in a CPU-GPU cluster. In this problem there are two sets of processors, the CPU processors and the GPU processors. Each job has two distinct processing times, one for the CPU processor and the other for the GPU processor. Once a job is released, a decision should be made immediately about which processor it should be assigned to. The goal is to minimize the makespan, i.e., the largest completion time among all the processors. Such a problem could be seen as an intermediate model between the scheduling problem on identical machines and unrelated machines. We provide a 3.85-competitive online algorithm for this problem and show that no online algorithm exists with competitive ratio strictly less than 2. We also consider two special cases of this problem, the balanced case where the number of CPU processors equals to that of GPU processors, and the one-sided case where there is only one CPU or GPU processor. For the balanced case, we first provide a simple 3-competitive algorithm, and then a better algorithm with competitive ratio of 2.732 is derived. For the one-sided case, a 3-competitive algorithm is given.

scholarly journals Online Scheduling on a Single Machine with Grouped Processing Times

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Qijia Liu ◽  
Long Wan ◽  
Lijun Wei
Keyword(s):  
Single Machine ◽  
Competitive Ratio ◽  
Processing Time ◽  
Online Algorithm ◽  
Arrival Time ◽  
Online Scheduling ◽  
Scheduling Problem ◽  
Processing Times ◽  
Over Time

We consider the online scheduling problem on a single machine with the assumption that all jobs have their processing times in[p,(1+α)p], wherep>0andα=(5-1)/2. All jobs arrive over time, and each job and its processing time become known at its arrival time. The jobs should be first processed on a single machine and then delivered by a vehicle to some customer. When the capacity of the vehicle is infinite, we provide an online algorithm with the best competitive ratio of(5+1)/2. When the capacity of the vehicle is finite, that is, the vehicle can deliver at mostcjobs at a time, we provide another best possible online algorithm with the competitive ratio of(5+1)/2.

scholarly journals A best possible algorithm for an online scheduling problem with position-based learning effect

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Ran Ma ◽  
Lu Zhang ◽  
Yuzhong Zhang
Keyword(s):  
Single Machine ◽  
Completion Time ◽  
Processing Time ◽  
Learning Effect ◽  
Online Algorithm ◽  
Online Scheduling ◽  
Release Time ◽  
Scheduling Problem ◽  
Over Time ◽  
Actual Processing Time

<p style='text-indent:20px;'>In this paper, we focus on an online scheduling problem with position-based learning effect on a single machine, where the jobs are released online over time and preemption is not allowed. The information about each job <inline-formula><tex-math id="M1">\begin{document}$ J_j $\end{document}</tex-math></inline-formula>, including the basic processing time <inline-formula><tex-math id="M2">\begin{document}$ p_j $\end{document}</tex-math></inline-formula> and the release time <inline-formula><tex-math id="M3">\begin{document}$ r_j $\end{document}</tex-math></inline-formula>, is only available when it arrives. The actual processing time <inline-formula><tex-math id="M4">\begin{document}$ p_j' $\end{document}</tex-math></inline-formula> of each job <inline-formula><tex-math id="M5">\begin{document}$ J_j $\end{document}</tex-math></inline-formula> is defined as a function related to its position <inline-formula><tex-math id="M6">\begin{document}$ r $\end{document}</tex-math></inline-formula>, i.e., <inline-formula><tex-math id="M7">\begin{document}$ p_j' = p_j(\alpha-r\beta) $\end{document}</tex-math></inline-formula>, where <inline-formula><tex-math id="M8">\begin{document}$ \alpha $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M9">\begin{document}$ \beta $\end{document}</tex-math></inline-formula> are both nonnegative learning index. Our goal is to minimize the sum of completion time of all jobs. For this problem, we design a deterministic polynomial time online algorithm <i>Delayed Shortest Basic Processing Time</i> (DSBPT). In order to facilitate the understanding of the online algorithm, we present a relatively common and simple example to describe the execution process of the algorithm, and then by competitive analysis, we show that online algorithm DSBPT is a best possible online algorithm with a competitive ratio of 2.</p>

A Best Possible Online Algorithm for the Parallel-Machine Scheduling to Minimize the Maximum Weighted Completion Time

2015 ◽  
Vol 32 (04) ◽  
pp. 1550030 ◽  
Author(s):  
Wenjie Li
Keyword(s):  
Lower Bound ◽  
Competitive Ratio ◽  
Completion Time ◽  
Processing Time ◽  
Online Algorithm ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Identical Machines ◽  
Weighted Completion Time ◽  
Over Time

In this paper, we consider the online scheduling on m identical machines in which jobs arrive over time. The goal is to determine a nonpreemptive schedule that minimizes the weighted makespan, i.e., the maximum weighted completion time of jobs. When m = 1, we first present a lower bound 2, and then provide an online algorithm with a competitive ratio of 3. For the case in which m ≥ 1, and all jobs have a common processing time p > 0, we obtain a best possible online algorithm with a competitive ratio of [Formula: see text].

SEMI-ONLINE MACHINE COVERING

2007 ◽  
Vol 24 (03) ◽  
pp. 373-382 ◽  
Author(s):  
SHENG-YI CAI
Keyword(s):  
Competitive Ratio ◽  
Completion Time ◽  
Online Algorithm ◽  
Parallel Machines ◽  
Identical Parallel Machines ◽  
Processing Times ◽  
First Case ◽  
Machine Covering

This paper investigates two different semi-online versions of the machine covering, which is the problem of assigning a set of jobs to a system of m(m ≥ 3) identical parallel machines so as to maximize the earliest machine completion time. In the first case, we assume that the largest processing times is known in advance. In the second case, we assume that the total processing times of all jobs is known in advance. For each version we propose a semi-online algorithm and investigate its competitive ratio. The competitive ratio of each algorithm is [Formula: see text], which is shown to be the best possible competitive ratio for each semi-online problem.

Online-List Scheduling on a Single Bounded Parallel-Batch Machine to Minimize Makespan

2015 ◽  
Vol 32 (04) ◽  
pp. 1550028
Author(s):  
Wenhua Li ◽  
Jie Gao ◽  
Jinjiang Yuan
Keyword(s):  
Lower Bound ◽  
Competitive Ratio ◽  
Online Algorithm ◽  
Positive Root ◽  
List Scheduling ◽  
Batch Machine

In this paper, we consider the online-list scheduling on a single bounded parallel-batch machine to minimize makespan. In the problem, the jobs arrive online over list. The first unassigned job in the list should be assigned to a batch before the next job is released. Each batch can accommodate up to b jobs. For b = 2, we establish a lower bound 1 + γ of competitive ratio and provide an online algorithm with a competitive ratio of [Formula: see text], where γ is the positive root of γ(γ + 1)2 = 1. For b = 3, we establish a lower bound 1 + α of competitive ratio and provide an online algorithm with a competitive ratio of 2, where α is the positive root of the equation (1 + α)(1 + α2) = 2.

An Improved Online Algorithm for the Online Preemptive Scheduling of Equal-Length Intervals on a Single Machine with Lookahead

2015 ◽  
Vol 32 (06) ◽  
pp. 1550047
Author(s):  
Wenjie Li ◽  
Jinjiang Yuan
Keyword(s):  
Lower Bound ◽  
Single Machine ◽  
Operations Research ◽  
Competitive Ratio ◽  
Processing Time ◽  
Online Algorithm ◽  
Equal Length ◽  
Preemptive Scheduling ◽  
Time Segment ◽  
Time Point

This paper studies the online preemptive scheduling of equal-length intervals on a single machine with lookahead. Let [Formula: see text] be the length (processing time) of all intervals. In the problem, at every time point [Formula: see text], online algorithms can foresee all the intervals that will arrive in the time segment [Formula: see text] for a certain [Formula: see text]. When [Formula: see text], Zheng et al. [Comput- ers & Operations Research, 2013] established a lower bound of [Formula: see text] and provided an online algorithm with a competitive ratio of 3. In this paper, we provide for this problem an improved online algorithm with a competitive ratio of 2.

Best-Possible Online Algorithms for Single Machine Scheduling to Minimize the Maximum Weighted Completion Time

2018 ◽  
Vol 35 (06) ◽  
pp. 1850048
Author(s):  
Xing Chai ◽  
Lingfa Lu ◽  
Wenhua Li ◽  
Liqi Zhang
Keyword(s):  
Online Algorithms ◽  
Single Machine ◽  
Competitive Ratio ◽  
Completion Time ◽  
Online Algorithm ◽  
Optimal Schedule ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Asia Pacific ◽  
Weighted Completion Time

In this paper, we consider the online single machine scheduling problem to minimize the maximum weighted completion time of the jobs. For the preemptive problem, we show that the LW (Largest Weight first) rule yields an optimal schedule. For the non-preemptive problem, Li [Li, W (2015). A best possible online algorithm for the parallel-machine scheduling to minimize the maximum weighted completion time. Asia-Pacific Journal of Operational Research, 32(4), 1550030 (10 pages)] presented a lower bound 2, and then provided an online algorithm with a competitive ratio of 3. In this paper, we present two online algorithms with the best-possible competitive ratio of [Formula: see text] for the non-preemptive problem.

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