A better online algorithm for the parallel machine scheduling to minimize the total weighted completion time

2014 ◽  
Vol 43 ◽  
pp. 215-224 ◽  
Author(s):  
Jiping Tao
Keyword(s):  
Completion Time ◽  
Online Algorithm ◽  
Machine Scheduling ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Total Weighted Completion Time ◽  
Weighted Completion Time

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].

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 Two Parallel-Machine Scheduling Problems with Function Constraint

2020 ◽  
Vol 2020 ◽  
pp. 1-6 ◽  
Author(s):  
Chia-Lun Hsu ◽  
Jan-Ray Liao
Keyword(s):  
Completion Time ◽  
Machine Scheduling ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Total Completion Time ◽  
Scheduling Problems ◽  
Worst Case ◽  
Time Problem ◽  
Constraint Problem ◽  
Machine Scheduling Problems

The objective of this paper is to minimize both the makespan and the total completion time. Since parallel-machine scheduling which contains the function constraint problem has been a new issue, this paper explored two parallel-machine scheduling problems with function constraint, which refers to the situation that the two machines have a same function but one of the machines has another. We pointed out that the function constraint occurs not only in the manufacturing system but also in the service system. For the makespan problem, we demonstrated that it is NP-hard in the ordinary sense. In addition, we presented a polynomial time heuristic for this problem and have proved its worst-case ratio is not greater than 5/4. Furthermore, we simulated the performance of the algorithm through computational testing. The overall mean percent error of the heuristic is 0.0565%. The results revealed that the proposed algorithm is quite efficient. For the total completion time problem, we have proved that it can be solved in On4 time.

Unrelated Parallel-Machine Scheduling with Deteriorating Jobs and Rejection

2012 ◽  
Vol 263-266 ◽  
pp. 655-659 ◽  
Author(s):  
Chou Jung Hsu ◽  
Chia Wen Chang
Keyword(s):  
Completion Time ◽  
Deteriorating Jobs ◽  
Machine Scheduling ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Unrelated Parallel Machine ◽  
Absolute Deviation ◽  
Total Load ◽  
Unrelated Parallel Machine Scheduling ◽  
Total Penalty

This paper aimed to investigate the unrelated parallel-machine scheduling with deteriorating jobs and rejection. The objective is to find the rejected jobs, the non-rejected jobs, and the optimal non-rejected job sequence so that the cost function that includes the weighted of total load, total completion time, and total absolute deviation of completion time plus the total penalty of the rejected jobs would be minimized. Results showed that the problem is polynomial time solvable when the number of machine is fixed.

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