Abstract
We consider the scheduling problem in which two agents (agents A and B), each having its own job set (containing the A-jobs and B-jobs, respectively), compete to process their own jobs in a two-machine flowshop. Each agent wants to maximize a certain criterion depending on the completion times of its jobs only. Specifically, agent A desires to maximize either the weighted number of just-in-time (JIT) A-jobs that are completed exactly on their due dates or the maximum weight of the JIT A-jobs, while agent B wishes to maximize the weighted number of JIT B-jobs. Evidently four optimization problems can be formulated by treating the two agents’ criteria as objectives and constraints of the corresponding optimization problems. We focus on the problem of finding the Pareto-optimal schedules and present a bicriterion analysis of the problem. Solving this problem also solves the other three problems of bicriterion scheduling as a by-product. We show that the problems under consideration are either polynomially or pseudo-polynomially solvable. In addition, for each pseudo-polynomial-time solution algorithm, we show how to convert it into a two-dimensional fully polynomial-time approximation scheme for determining an approximate Pareto-optimal schedule. Finally, we conduct extensive numerical studies to evaluate the performance of the proposed algorithms.
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Acknowledgements
We thank an Editor, an Associate Editor, and anonymous referees for their helpful comments on earlier versions of our paper. This paper was supported in part by the National Natural Science Foundation of China (Nos. 11561036, 71501024, 71520107002, 71533001), and in part by the Ministry of Science Technology (MOST) of Taiwan under grant numbers MOST 105-2221-E-035-053-MY3 and MOST 103-2410-H-035-022-MY2. Cheng was supported in part by the Hong Kong Polytechnic University under the Fung Yiu King-Wing Hang Bank Endowed Professorship in Business Administration.
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Yin, Y., Cheng, T.C.E., Wang, DJ. et al. Two-agent flowshop scheduling to maximize the weighted number of just-in-time jobs. J Sched 20, 313–335 (2017). https://doi.org/10.1007/s10951-017-0511-7
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DOI: https://doi.org/10.1007/s10951-017-0511-7