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>

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.

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].

scholarly journals Scheduling Jobs Families with Learning Effect on the Setup

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Sergio Fichera ◽  
Antonio Costa ◽  
Fulvio Cappadonna
Keyword(s):  
Completion Time ◽  
Learning Effect ◽  
Flow Shop ◽  
Group Scheduling ◽  
Scheduling Problem ◽  
Learning Effects ◽  
Anova Analysis ◽  
Hybrid Metaheuristic ◽  
Set Up ◽  
Over Time

The present paper aims to address the flow-shop sequence-dependent group scheduling problem with learning effect (FSDGSLE). The objective function to be minimized is the total completion time, that is, the makespan. The workers are required to carry out manually the set-up operations on each group to be loaded on the generic machine. The operators skills improve over time due to the learning effects; therefore the set-up time of a group under learning effect decreases depending on the order the group is worked in. In order to effectively cope with the issue at hand, a mathematical model and a hybrid metaheuristic procedure integrating features from genetic algorithms (GA) have been developed. A well-known problem benchmark risen from literature, made by two-, three- and six-machine instances, has been taken as reference for assessing performances of such approach against the two most recent algorithms presented by literature on the FSDGS issue. The obtained results, also supported by a properly developed ANOVA analysis, demonstrate the superiority of the proposed hybrid metaheuristic in tackling the FSDGSLE problem under investigation.

scholarly journals A Competitive Online Algorithm for Minimizing Total Weighted Completion Time on Uniform Machines

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Xuyang Chu ◽  
Jiping Tao
Keyword(s):  
Completion Time ◽  
Online Algorithm ◽  
Total Weighted Completion Time ◽  
Scheduling Problem ◽  
Uniform Machines ◽  
Online Setting ◽  
Weighted Completion Time ◽  
Waiting Strategy ◽  
Machine Speed ◽  
Over Time

We consider the classic online scheduling problem on m uniform machines in the online setting where jobs arrive over time. Preemption is not allowed. The objective is to minimize total weighted completion time. An online algorithm based on the directly waiting strategy is proposed. Its competitive performance is proved to be max2smax1−1/2∑si,2smax/1+smax2.5−1/2m by the idea of instance reduction, where sm is the fastest machine speed after being normalized by the slowest machine speed.

Single Machine Two-Agent Scheduling with Deteriorating Jobs

2016 ◽  
Vol 33 (05) ◽  
pp. 1650034 ◽  
Author(s):  
Zhenyou Wang ◽  
Cai-Min Wei ◽  
Yu-Bin Wu
Keyword(s):  
Single Machine ◽  
Completion Time ◽  
Processing Time ◽  
Deteriorating Jobs ◽  
Single Machine Scheduling ◽  
Total Weighted Completion Time ◽  
Scheduling Problem ◽  
Agent Scheduling ◽  
Polynomially Solvable ◽  
Weighted Completion Time

This paper deals with the single machine scheduling problem with deteriorating jobs in which there are two distinct families of jobs (i.e., two-agent) pursuing different objectives. In this model the processing time of a job is defined as a function that is proportional to a linear function of its stating time. For the following three scheduling criteria: minimizing the makespan, minimizing the total weighted completion time, and minimizing the maximum lateness, we show that some basic versions of the problem are polynomially solvable. We also establish the conditions under which the problem is computationally hard.

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.

A SINGLE-MACHINE TWO-AGENT SCHEDULING PROBLEM BY GA APPROACH

2012 ◽  
Vol 29 (02) ◽  
pp. 1250013 ◽  
Author(s):  
SHUENN-REN CHENG
Keyword(s):  
Single Machine ◽  
Completion Time ◽  
Learning Effect ◽  
Control Parameter ◽  
Optimal Schedule ◽  
Total Weighted Completion Time ◽  
Scheduling Problem ◽  
Processing Times ◽  
Agent Scheduling ◽  
Weighted Completion Time

A single-machine two-agent scheduling problem with a truncation learning effect is being addressed in the study. The truncation learning effect means that the actual processing time of a job is a function of the sum of processing times of already scheduled jobs and a control parameter. The aim is to find an optimal schedule to minimize the total weighted completion time of jobs of the first agent under the circumstances that no tardy job is allowed for the second agent. A branch-and-bound and three heuristic-based genetic algorithms (GAs) are proposed to solve the problem. Also presented in the study are the computational results of all proposed algorithms.

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