scholarly journals Online Batch Scheduling of Simple Linear Deteriorating Jobs with Incompatible Families

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 170 ◽  
Author(s):  
Wenhua Li ◽  
Libo Wang ◽  
Xing Chai ◽  
Hang Yuan
Keyword(s):  
Competitive Ratio ◽  
Processing Time ◽  
Online Algorithm ◽  
Deteriorating Jobs ◽  
Scheduling Problem ◽  
Starting Time ◽  
Deterioration Rate ◽  
Deteriorating Job ◽  
Incompatible Families ◽  
Actual Processing Time

We considered the online scheduling problem of simple linear deteriorating job families on m parallel batch machines to minimize the makespan, where the batch capacity is unbounded. In this paper, simple linear deteriorating jobs mean that the actual processing time p j of job J j is assumed to be a linear function of its starting time s j , i.e., p j = α j s j , where α j > 0 is the deterioration rate. Job families mean that one job must belong to some job family, and jobs of different families cannot be processed in the same batch. When m = 1 , we provide the best possible online algorithm with the competitive ratio of ( 1 + α max ) f , where f is the number of job families and α max is the maximum deterioration rate of all jobs. When m ≥ 1 and m = f , we provide the best possible online algorithm with the competitive ratio of 1 + α max .

Online Single Machine Scheduling to Minimize the Maximum Starting Time

2017 ◽  
Vol 34 (05) ◽  
pp. 1750022
Author(s):  
Lingfa Lu ◽  
Liqi Zhang
Keyword(s):  
Single Machine ◽  
Competitive Ratio ◽  
Online Algorithm ◽  
Optimal Schedule ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Scheduling Problem ◽  
Starting Time

In this paper, we consider the online single machine scheduling problem to minimize the maximum starting time of the jobs. For the non-preemptive model, we show that there is no determined or randomized online algorithm with a bounded competitive ratio. For the preemption-resume model, we show that the well-known SRPT rule yields an optimal schedule. For the preemption-restart model, we show that any determined online algorithm has a competitive ratio of at least 2 and present an online algorithm with the best-possible competitive ratio of 2.

SCHEDULING DETERIORATING JOBS ON A SINGLE MACHINE WITH RELEASE TIMES AND REJECTION

2012 ◽  
Vol 04 (02) ◽  
pp. 1250032 ◽  
Author(s):  
MING LIU ◽  
FEIFENG ZHENG ◽  
CHENGBIN CHU ◽  
YINFENG XU
Keyword(s):  
Single Machine ◽  
Processing Time ◽  
Deteriorating Jobs ◽  
Release Time ◽  
Starting Time ◽  
Release Times ◽  
Deteriorating Job ◽  
Total Penalty ◽  
Programming Algorithms ◽  
Increasing Function

This paper considers scheduling deteriorating jobs on a single machine with release times and rejection. Deteriorating job means that its actual processing time is a increasing function on its execution starting time. In this situation, jobs can be rejected by paying penalties. Each job is associated with a release time. The objective is to minimize the makespan plus the total penalty incurred by rejecting jobs. We present two dynamic programming algorithms and then design an FPTAS for the considered problem.

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 WSPT's Competitive Performance for Minimizing the Total Weighted Flow Time: From Single to Parallel Machines

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Jiping Tao ◽  
Tundong Liu
Keyword(s):  
Single Machine ◽  
Competitive Ratio ◽  
Processing Time ◽  
Online Algorithm ◽  
Parallel Machines ◽  
Flow Time ◽  
Scheduling Problem ◽  
Analysis Method ◽  
Competitive Performance ◽  
Systematic Analysis

We consider the classical online scheduling problem over single and parallel machines with the objective of minimizing total weighted flow time. We employ an intuitive and systematic analysis method and show that the weighted shortest processing time (WSPT) is an optimal online algorithm with the competitive ratio ofP+1for the case of single machine, and it is (P+(3/2)−(1/2m))-competitive for the case of parallel machines(m>1), wherePis the ratio of the longest to the shortest processing time.

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 Decomposition approaches for parallel machine scheduling of step-deteriorating jobs to minimize total tardiness and energy consumption

2021 ◽  
Author(s):  
Xiao Wu ◽  
Peng Guo ◽  
Yi Wang ◽  
Yakun Wang
Keyword(s):  
Energy Consumption ◽  
Tabu Search ◽  
Processing Time ◽  
Deteriorating Jobs ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Total Tardiness ◽  
Master Problem ◽  
Starting Time ◽  
Extra Energy

AbstractIn this paper, an identical parallel machine scheduling problem with step-deteriorating jobs is considered to minimize the weighted sum of tardiness cost and extra energy consumption cost. In particular, the actual processing time of a job is assumed to be a step function of its starting time and its deteriorating threshold. When the starting time of a job is later than its deteriorating threshold, the job faces two choices: (1) maintaining its status in holding equipment and being processed with a base processing time and (2) consuming an extra penalty time to finish its processing. The two work patterns need different amounts of energy consumption. To implement energy-efficient scheduling, the selection of the pre-processing patterns must be carefully considered. In this paper, a mixed integer linear programming (MILP) model is proposed to minimize the total tardiness cost and the extra energy cost. Decomposition approaches based on logic-based Benders decomposition (LBBD) are developed by reformulating the studied problem into a master problem and some independent sub-problems. The master problem is relaxed by only making assignment decisions. The sub-problems are to find optimal schedules in the job-to-machine assignments given by the master problem. Moreover, MILP and heuristic based on Tabu search are used to solve the sub-problems. To evaluate the performance of our methods, three groups of test instances were generated inspired by both real-world applications and benchmarks from the literature. The computational results demonstrate that the proposed decomposition approaches can compute competitive schedules for medium- and large-size problems in terms of solution quality. In particular, the LBBD with Tabu search performs the best among the suggested four methods.

SEMI-ON-LINE SCHEDULING PROBLEM FOR MAXIMIZING THE MINIMUM MACHINE COMPLETION TIME ON THREE SPECIAL UNIFORM MACHINES

2005 ◽  
Vol 22 (02) ◽  
pp. 229-237 ◽  
Author(s):  
RUN-ZI LUO ◽  
SHI-JIE SUN
Keyword(s):  
Competitive Ratio ◽  
Completion Time ◽  
Processing Time ◽  
Scheduling Problem ◽  
Uniform Machines ◽  
On Line ◽  
Special Case

In this paper, we investigate a semi-on-line version for a special case of three machines M1, M2, M3 where the processing time of the largest job is known in advance. A speed si(s1 = s2 = 1, 1 ≤ s3 = s) is associated with machine Mi. Our goal is to maximize the C min — the minimum workload of three machines. We give a C min 3 algorithm and prove its competitive ratio is [Formula: see text] and the algorithm is the best possible for 1 ≤ s ≤ 2. We also claim the competitive ratio of algorithm C min 3 is tight.

Genetic Algorithm for a Two-Agent Scheduling Problem with Truncated Learning Consideration

2014 ◽  
Vol 31 (06) ◽  
pp. 1450046 ◽  
Author(s):  
Wen-Hsiang Wu ◽  
Yunqiang Yin ◽  
Shuenn-Ren Cheng ◽  
Peng-Hsiang Hsu ◽  
Chin-Chia Wu
Keyword(s):  
Processing Time ◽  
Optimal Solution ◽  
Total Weighted Completion Time ◽  
Scheduling Problem ◽  
Learning Effects ◽  
Research Attention ◽  
Multiple Agent ◽  
Agent Scheduling ◽  
Dominance Properties ◽  
Actual Processing Time

Scheduling with learning effects has received lots of research attention lately. However, the multiple-agent setting with learning consideration is relatively limited. On the other hand, the actual processing time of a job under an uncontrolled learning effect will drop to zero precipitously as the number of the jobs already processed increases. This is rather absurd in reality. Based on these observations, this paper considers a single-machine two-agent scheduling problem in which the actual processing time of a job depends not only on the job's scheduled position, but also on a control parameter. The objective is to minimize the total weighted completion time of jobs from the first agent with the restriction that no tardy job is allowed for the second agent. A branch-and-bound algorithm incorporated with several dominance properties and lower bounds is proposed to derive the optimal solution for the problem. In addition, genetic algorithms (GAs) are also provided to obtain the near-optimal solution. Finally, a computational experiment is conducted to evaluate the performance of the proposed algorithms.

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.

scholarly journals Optimization for Due-Window Assignment Scheduling with Position-Dependent Weights

2020 ◽  
Vol 2020 ◽  
pp. 1-7 ◽  
Author(s):  
Li-Yan Wang ◽  
Dan-Yang Lv ◽  
Bo Zhang ◽  
Wei-Wei Liu ◽  
Ji-Bo Wang
Keyword(s):  
Single Machine ◽  
General Position ◽  
Processing Time ◽  
Window Size ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Scheduling Problem ◽  
Starting Time ◽  
Due Window ◽  
Due Window Assignment

This paper considers a single-machine due-window assignment scheduling problem with position-dependent weights, where the weights only depend on their position in a sequence. The objective is to minimise the total weighted penalty of earliness, tardiness, due-window starting time, and due-window size of all jobs. Optimal properties of the problem are given, and then, a polynomial-time algorithm is provided to solve the problem. An extension to the problem is offered by assuming general position-dependent processing time.

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