scholarly journals Parallel-machine scheduling of jobs with mixed job-, machine- and position-dependent processing times

2021 ◽  
Author(s):  
Bartłomiej Przybylski
Keyword(s):  
Completion Time ◽  
Processing Time ◽  
Positive Function ◽  
Machine Scheduling ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Scheduling Problems ◽  
Processing Times ◽  
Maximum Completion Time ◽  
Machine Scheduling Problems

AbstractWe consider a number of parallel-machine scheduling problems in which jobs have variable processing times. The actual processing time of each job is described by an arbitrary positive function of the position it holds on a machine. However, the function itself may additionally depend on the job or a machine this job was assigned to. Our aim is to find a schedule that minimizes the objectives of maximum completion time or the total completion time. We present a full set of polynomial solutions for the cases of jobs with no precedence constraints. We also show that the case of single-chained jobs may be not easier in general, but some polynomial results can be obtained, too.

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 Controllable Processing Times and Impact of Deteriorating Maintenance Activities under Consideration

2016 ◽  
Vol 33 (01) ◽  
pp. 1650001 ◽  
Author(s):  
Chun-Lai Liu ◽  
Jian-Jun Wang
Keyword(s):  
Processing Time ◽  
Machine Scheduling ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Controllable Processing Times ◽  
Maintenance Activity ◽  
Processing Times ◽  
Unrelated Parallel Machine Scheduling ◽  
Deteriorating Maintenance ◽  
Maintenance Activities

In this paper, we study the problem of unrelated parallel machine scheduling with controllable processing times and deteriorating maintenance activity. The jobs are nonresumable. The processing time of each job is a linear function of the amount of a continuously divisible resource allocated to the job. During the planning horizon, there is at most one maintenance activity scheduled on each machine. Additionally, if the starting time of maintenance activity is delayed, the length of the maintenance activity required to perform will increase. Considering the total completion times of all jobs, the impact of maintenance activity in the form of the variation in machine load and the amounts of compression, we need to determine the job sequence on each machine, the location of maintenance activities and processing time compression of each job simultaneously. Accordingly, a polynomial time solution to the problem is provided.

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