Abstract
We consider the scheduling problems arising when two agents, each with a family of jobs, compete to perform their respective jobs on a single machine. A setup time is needed for a job if it is the first job to be processed on the machine or its processing on the machine follows a job that belongs to another family. Each agent wants to minimize a certain cost function, which depends on the completion times of its jobs only. The aim is to find a schedule for all the jobs of the two agents that minimizes the objective of one agent while keeping the objective of the other agent being bounded by a fixed value \(Q\). Polynomial-time and pseudo-polynomial-time algorithms are designed to solve the problem involving various combinations of regular scheduling objective functions.
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Acknowledgments
The authors would like to thank the associate editor and one anonymous reviewer for their helpful comments and suggestions on an earlier version of our paper. Li was supported in part by National Natural Science Foundation of China (Nos. 11326191, 11401605 and 11171313), and the Education Department of Henan Province Natural Science Research Program (No. 14A110027). Feng was in part by National Natural Science Foundation of China (11401604), NSF of Henan Province (No. 132300410392).
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Li, SS., Chen, RX. & Feng, Q. Scheduling two job families on a single machine with two competitive agents. J Comb Optim 32, 784–799 (2016). https://doi.org/10.1007/s10878-015-9902-x
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DOI: https://doi.org/10.1007/s10878-015-9902-x