scholarly journals Scheduling jobs with an exponential sum-of-actual-processing-time-based learning effect

2010 ◽  
Vol 60 (9) ◽  
pp. 2673-2678 ◽  
Author(s):  
Ji-Bo Wang ◽  
Lin-Hui Sun ◽  
Lin-Yan Sun
Keyword(s):  
Processing Time ◽  
Learning Effect ◽  
Exponential Sum ◽  
Actual 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 Heuristic for Stochastic Online Flowshop Problem with Preemption Penalties

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Mohammad Bayat ◽  
Mehdi Heydari ◽  
Mohammad Mahdavi Mazdeh
Keyword(s):  
Standard Deviation ◽  
Processing Time ◽  
Heuristic Method ◽  
Heuristic Procedure ◽  
Release Date ◽  
Numerical Examples ◽  
Processing Times ◽  
Flowshop Problem ◽  
Expected Makespan ◽  
Actual Processing Time

The deterministic flowshop model is one of the most widely studied problems; whereas its stochastic equivalent has remained a challenge. Furthermore, the preemptive online stochastic flowshop problem has received much less attention, and most of the previous researches have considered a nonpreemptive version. Moreover, little attention has been devoted to the problems where a certain time penalty is incurred when preemption is allowed. This paper examines the preemptive stochastic online flowshop with the objective of minimizing the expected makespan. All the jobs arrive overtime, which means that the existence and the parameters of each job are unknown until its release date. The processing time of the jobs is stochastic and actual processing time is unknown until completion of the job. A heuristic procedure for this problem is presented, which is applicable whenever the job processing times are characterized by their means and standard deviation. The performance of the proposed heuristic method is explored using some numerical examples.

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.

scholarly journals A Two-Stage Three-Machine Flow Shop Assembly Problem Mixed with a Controllable Number and Sum-of-Processing Times-Based Learning Effect by Simulated Annealing Algorithms

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Shang-Chia Liu
Keyword(s):  
Simulated Annealing ◽  
Processing Time ◽  
Learning Effect ◽  
Flow Shop ◽  
Service Industries ◽  
Two Stage ◽  
Processing Times ◽  
Assembly Scheduling ◽  
Assembly Problem ◽  
Annealing Algorithms

The two-stage assembly scheduling problem is widely used in industrial and service industries. This study focuses on the two-stage three-machine flow shop assembly problem mixed with a controllable number and sum-of-processing times-based learning effect, in which the job processing time is considered to be a function of the control of the truncation parameters and learning based on the sum of the processing time. However, the truncation function is very limited in the two-stage flow shop assembly scheduling settings. Thus, this study explores a two-stage three-machine flow shop assembly problem with truncated learning to minimize the makespan criterion. To solve the proposed model, we derive several dominance rules, lemmas, and lower bounds applied in the branch-and-bound method. On the other hand, three simulated annealing algorithms are proposed for finding approximate solutions. In both the small and large size number of job situations, the SA algorithm is better than the JS algorithm in this study. All the experimental results of the proposed algorithm are presented on small and large job sizes, respectively.

A BATCHING PROBLEM WITH LEARNING EFFECT CONSIDERATIONS

2009 ◽  
Vol 26 (02) ◽  
pp. 307-317 ◽  
Author(s):  
WEN-HUA YANG
Keyword(s):  
Dynamic Programming ◽  
Completion Time ◽  
Processing Time ◽  
Learning Effect ◽  
Polynomial Function ◽  
Optimal Number ◽  
Total Completion Time ◽  
Batch Sizing ◽  
Forward Dynamic Programming ◽  
Unit Processing

Consider a batch-sizing problem, where all jobs are identical or similar, and a unit processing time (p = 1) is specified for each job. To minimize the total completion time of jobs, partitioning jobs into batches may be necessary. Learning effect from setup repetition makes small-sized batches; on the contrary, job's learning effect results in large-sized batches. With their collaborative influence, we develop a forward dynamic programming (DP) algorithm to determine the optimal number of batches and their optimal integer sizes. The computation effort required by this DP algorithm is a polynomial function of job size.

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