Volume 54, Number 2, March-April 2020
|Page(s)||307 - 323|
|Published online||27 February 2020|
A three-agent scheduling problem for minimizing the flow time on two machines
Department of Statistics, Feng Chia University, 40724 Taichung, Taiwan, R.O.C.
2 Department of Computer Science and Information Management, Hungkuang University, 43302 Taichung, Taiwan, R.O.C.
* Corresponding author: email@example.com
Accepted: 6 September 2019
This study introduces a two-machine three-agent scheduling problem. We aim to minimize the total tardiness of jobs from agent 1 subject to that the maximum completion time of jobs from agent 2 cannot exceed a given limit and that two maintenance activities from agent 3 must be conducted within two maintenance windows. Due to the NP-hardness of this problem, a genetic algorithm (named GA+) is proposed to obtain approximate solutions. On the other hand, a branch-and-bound algorithm (named B&B) is developed to generate the optimal solutions. When the problem size is small, we use B&B to verify the solution quality of GA+. When the number of jobs is large, a relative deviation is proposed to show the gap between GA+ and another ordinary genetic algorithm. Experimental results show that the proposed genetic algorithm can generate approximate solutions by consuming reasonable execution time.
Mathematics Subject Classification: 90C05 / 90-08
Key words: Multi-agent scheduling / maintenance scheduling / branch-and-bound algorithm / genetic algorithm / solution quality
© EDP Sciences, ROADEF, SMAI 2020
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