scholarly journals Group Scheduling Problems with Time-Dependent and Position-Dependent DeJong’s Learning Effect

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Li Sun ◽  
Lei Ning ◽  
Jia-zhen Huo
Keyword(s):  
Polynomial Time ◽  
Completion Time ◽  
Learning Effect ◽  
Time Dependent ◽  
Total Weighted Completion Time ◽  
Group Scheduling ◽  
Scheduling Problems ◽  
Scheduling Model ◽  
Proposed Model ◽  
Weighted Completion Time

In this paper, we introduce a group scheduling model with time-dependent and position-dependent DeJong’s learning effect. The objectives of scheduling problems are to minimize makespan, the total completion time, and the total weighted completion time, respectively. We show that the problems remain solvable in polynomial time under the proposed model.

SCHEDULING PROBLEMS WITH THE EFFECTS OF DETERIORATION AND LEARNING

2007 ◽  
Vol 24 (02) ◽  
pp. 245-261 ◽  
Author(s):  
JI-BO WANG ◽  
T. C. EDWIN CHENG
Keyword(s):  
Performance Measures ◽  
Single Machine ◽  
Completion Time ◽  
Flow Shop ◽  
Machine Scheduling ◽  
Total Weighted Completion Time ◽  
Scheduling Problems ◽  
Processing Times ◽  
Weighted Completion Time ◽  
Machine Scheduling Problems

This paper deals with the machine scheduling problems with the effects of deterioration and learning. In this model the processing times of jobs are defined as functions of their starting times and positions in a sequence. We introduce polynomial solutions for some single machine problems and flow shop problems. The performance measures include makespan, total completion time, total weighted completion time, and maximum lateness.

scholarly journals Transportation and Batching Scheduling for Minimizing Total Weighted Completion Time

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 819 ◽  
Author(s):  
Hongjun Wei ◽  
Jinjiang Yuan ◽  
Yuan Gao
Keyword(s):  
Computational Complexity ◽  
Approximation Algorithm ◽  
Polynomial Time ◽  
Completion Time ◽  
Total Weighted Completion Time ◽  
Single Vehicle ◽  
Weighted Completion Time ◽  
Np Hardness

We consider the coordination of transportation and batching scheduling with one single vehicle for minimizing total weighted completion time. The computational complexity of the problem with batch capacity of at least 2 was posed as open in the literature. For this problem, we show the unary NP-hardness for every batch capacity at least 3 and present a polynomial-time 3-approximation algorithm when the batch capacity is at least 2.

Scheduling with Rejection and a Deteriorating Maintenance Activity on a Single Machine

2017 ◽  
Vol 34 (02) ◽  
pp. 1750010 ◽  
Author(s):  
Shi-Sheng Li ◽  
Ren-Xia Chen
Keyword(s):  
Polynomial Time ◽  
Single Machine ◽  
Completion Time ◽  
Single Machine Scheduling ◽  
Total Weighted Completion Time ◽  
Scheduling Problems ◽  
Maintenance Activity ◽  
Polynomial Time Algorithms ◽  
Deteriorating Maintenance ◽  
The Impact

We study single-machine scheduling problems with job rejection and a deteriorating maintenance activity, where the impact of performing this activity is reflected in a reduction of the job processing times. The duration of the maintenance activity is a linear increasing function of its starting time. The aim is to determine the location of the maintenance activity and the job sequence of the accepted jobs so as to minimize scheduling cost of the accepted jobs plus total penalty of the rejected jobs. When the scheduling measures are the makespan, total completion time and combination of earliness, tardiness and due date cost, we provide polynomial time algorithms to solve these problems, respectively. When the scheduling measures are the maximum tardiness and total weighted completion time under the agreeable ratio assumption, we introduce pseudo-polynomial time algorithms to solve these [Formula: see text]-hard problems, respectively.

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.

scholarly journals Minimizing Total Weighted Completion Time on Single Machine with Past-Sequence-Dependent Setup Times and Exponential Time-Dependent and Position-Dependent Learning Effects

2009 ◽  
Vol 2009 ◽  
pp. 1-10 ◽  
Author(s):  
Kaibiao Sun ◽  
Hongxing Li
Keyword(s):  
Single Machine ◽  
Completion Time ◽  
Processing Time ◽  
Setup Times ◽  
Time Dependent ◽  
Total Weighted Completion Time ◽  
Learning Effects ◽  
Exponential Time ◽  
Weighted Completion Time ◽  
Dependent Learning

This paper addresses a single-machine problem in which the past-sequence-dependent (p-s-d) setup times and exponential time-dependent and position-dependent learning effects are considered. By the exponential time-dependent learning effect, it means that the processing time of a job is defined by an exponent function of the total actual processing time of the already processed jobs. The setup times are proportional to the length of the already processed jobs. The aim is to minimize the total weighted completion time, this is an NP-hard problem. Under certain conditions, it is shown that the classical WSPT rule is optimal for the problem.

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