Abstract
We address cumulative deterioration scheduling in which two agents compete to perform their respective jobs on a single machine. By cumulative deterioration we mean that the actual processing time of any job of the two agents is a linear increasing function of the total normal processing times of already processed jobs. Each agent desires to optimize some scheduling criterion that depends on the completion times of its own jobs only. We study several scheduling problems arising from different combinations of some regular scheduling criteria, including the maximum cost (embracing lateness and makespan as its special cases), the total completion time, and the (weighted) number of tardy jobs. The aim is to find an optimal schedule that minimizes the objective value of one agent while maintaining the objective value of the other agent not exceeding a fixed upper bound. For each problem under study, we design either a polynomial-time or a pseudo-polynomial-time algorithm to solve it.
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Acknowledgements
The authors are grateful to the Associate editor, one anonymous referee and Prof. Jinjiang Yuan for their useful comments which helped us to improve the paper. This research was supported in part by National Natural Science Foundation of China under Grant Numbers (11401605, 11501279 and 11701595).
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Chen, RX., Li, SS. Two-agent single-machine scheduling with cumulative deterioration. 4OR-Q J Oper Res 17, 201–219 (2019). https://doi.org/10.1007/s10288-018-0388-0
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DOI: https://doi.org/10.1007/s10288-018-0388-0