scholarly journals Single Machine Problem with Multi-Rate-Modifying Activities under a Time-Dependent Deterioration

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
M. Huang ◽  
Huaping Wu ◽  
Vincent Cho ◽  
W. H. Ip ◽  
Xingwei Wang ◽  
...  
Keyword(s):  
Branch And Bound ◽  
Heuristic Algorithm ◽  
Single Machine ◽  
Single Machine Scheduling ◽  
Branch And Bound Algorithm ◽  
Time Dependent ◽  
Reasonable Time ◽  
Special Cases ◽  
Short Time ◽  
Error Percentage

The single machine scheduling problem with multi-rate-modifying activities under a time-dependent deterioration to minimize makespan is studied. After examining the characteristics of the problem, a number of properties and a lower bound are proposed. A branch and bound algorithm and a heuristic algorithm are used in the solution, and two special cases are also examined. The computational experiments show that, for the situation with a rate-modifying activity, the proposed branch and bound algorithm can solve situations with 50 jobs within a reasonable time, and the heuristic algorithm can obtain the near-optimal solution with an error percentage less than 0.053 in a very short time. In situations with multi-rate-modifying activities, the proposed branch and bound algorithm can solve the case with 15 jobs within a reasonable time, and the heuristic algorithm can obtain the near-optimal with an error percentage less than 0.070 in a very short time. The branch and bound algorithm and the heuristic algorithm are both shown to be efficient and effective.

scholarly journals Note on a Single-Machine Scheduling Problem with Sum of Processing Times Based Learning and Ready Times

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Shang-Chia Liu ◽  
Wei-Ling Hung ◽  
Chin-Chia Wu
Keyword(s):  
Branch And Bound ◽  
Heuristic Algorithm ◽  
Single Machine ◽  
Learning Effect ◽  
Optimal Solution ◽  
Single Machine Scheduling ◽  
Branch And Bound Algorithm ◽  
Release Time ◽  
Average Error ◽  
Processing Times

In the recent 20 years, scheduling with learning effect has received considerable attention. However, considering the learning effect along with release time is limited. In light of these observations, in this paper, we investigate a single-machine problem with sum of processing times based learning and ready times where the objective is to minimize the makespan. For solving this problem, we build a branch-and-bound algorithm and a heuristic algorithm for the optimal solution and near-optimal solution, respectively. The computational experiments indicate that the branch-and-bound algorithm can perform well the problem instances up to 24 jobs in terms of CPU time and node numbers, and the average error percentage of the proposed heuristic algorithm is less than 0.5%.

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