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Polynomial time algorithm for minmax scheduling with common due-window and proportional-linear shortening processing
Xue Jia1, Jing Xue1, Shi-Yun Wang1
1School of Science, Shenyang Aerospace University, Shenyang, China.
This study introduces an optimal polynomial algorithm for single-machine scheduling problems with due-window assignments. It minimizes the maximum cost, considering earliness, tardiness, and due-window parameters.
Area of Science:
- Operations Research
- Scheduling Theory
Background:
- Addresses single-machine scheduling challenges.
- Incorporates proportional-linear shortening processing times.
- Focuses on due-window assignment optimization.
Purpose of the Study:
- Determine optimal schedules and due-window parameters.
- Minimize the maximum cost (minmax objective).
- Minimize costs including earliness, tardiness, start time, and due-window length.
Main Methods:
- Analysis of optimal properties for the scheduling problem.
- Development of a polynomial-time algorithm.
- Minmax cost optimization framework.
Main Results:
- Identified optimal properties of the scheduling problem.
- Proposed an efficient polynomial algorithm for optimal solutions.
- Successfully minimized the worst-case cost.
Conclusions:
- The developed algorithm provides an optimal solution for the specified scheduling problem.
- Efficiently determines optimal schedules, start times, and due-window sizes.
- Offers a practical approach to minimize complex scheduling costs.
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