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Two-agent flowshop scheduling to maximize the weighted number of just-in-time jobs

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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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References

  • Agnetis, A., Mirchandani, P., Pacciarelli, D., & Pacifici, A. (2000). Nondominated schedules for a job-shop with two competing users. Computational and Mathematical Organization Theory, 6(2), 191–217.

    Article  Google Scholar 

  • Agnetis, A., Mirchandani, P., Pacciarelli, D., & Pacifici, A. (2004). Scheduling problems with two competing agents. Operations Research, 42(2), 229–242.

    Article  Google Scholar 

  • Agnetis, A., Pacciarelli, D., & Pacifici, A. (2007). Multi-agent single machine scheduling. Annals of Operations Research, 150, 3–15.

    Article  Google Scholar 

  • Baker, K. R., & Smith, J. C. (2003). A multiple-criterion model for machine scheduling. Journal of Scheduling, 6, 7–16.

    Article  Google Scholar 

  • Bouzina, K. I., & Emmonss, H. (1996). Interval scheduling on identical machines. Journal of Global Optimization, 9, 379–393.

    Article  Google Scholar 

  • Carlisle, M. C., & Lloyd, E. L. (1995). On the \(k\)-coloring of intervals. Discrete Applied Mathematics, 59, 225–235.

    Article  Google Scholar 

  • Čepek, O., & Sung, S. C. (2005). A quadratic time algorithm to maximize the number of just-in-time jobs on identical parallel machines. Computers and Operations Research, 32, 3265–3271.

    Article  Google Scholar 

  • Cheng, T. C. E., Ng, C. T., & Yuan, J. J. (2006). Multi-agent scheduling on a single machine to minimize total weighted number of tardy jobs. Theoretical Computer Science, 362, 273–281.

    Article  Google Scholar 

  • Cheng, T. C. E., Ng, C. T., & Yuan, J. J. (2008). Multi-agent scheduling on a single machine with max-form criteria. European Journal of Operational Research, 188, 603–609.

    Article  Google Scholar 

  • Cheng, T. C. E., Wu, W.-H., Cheng, S.-R., & Wu, C.-C. (2011). Two-agent scheduling with position-based deteriorating jobs and learning effects. Applied Mathematics and Computation, 217, 8804–8824.

    Article  Google Scholar 

  • Choi, B. C., & Yoon, S. H. (2007). Maximizing the weighted number of just-in-time jobs in flow shop scheduling. Journal of Scheduling, 10, 237–243.

    Article  Google Scholar 

  • Chung, D. Y., & Choi, B. C. (2012). Just-in-time scheduling with multiple competing agents. Journal of the Korean Operations Research and Management Science Society, 37, 19–28.

    Article  Google Scholar 

  • Elalouf, A., Levner, E., & Tang, H. (2013). An improved FPTAS for maximizing the weighted number of just-in-time jobs in a two-machine flow shop problem. Journal of Scheduling, 16, 429–435.

    Article  Google Scholar 

  • Fan, B. Q., & Cheng, T. C. E. (2016). Two-agent scheduling in a flowshop. European Journal of Operational Research, 252, 376–384.

    Article  Google Scholar 

  • Gerstl, E., & Mosheiov, G. (2013). Scheduling problems with two competing agents to minimize weighted earliness-tardiness. Computers and Operations Research, 40, 109–116.

    Article  Google Scholar 

  • Hiraishi, K., Levner, E., & Vlach, M. (2002). Scheduling of parallel identical machines to maximize the weighted number of just-in-time jobs. Computers and Operations Research, 29(7), 841–848.

    Article  Google Scholar 

  • Hoogeveen, H., & Woeginger, G. J. (2002). Some comments on sequencing with controllable processing times. Computing, 68, 181–192.

    Article  Google Scholar 

  • Kovalyov, M. Y., Ng, C. T., & Cheng, T. C. E. (2007). Fixed interval scheduling: Models, applications, computational complexity and algorithms. European Journal of Operational Research, 178, 331–342.

    Article  Google Scholar 

  • Lann, A., & Mosheiov, G. (1996). Single machine scheduling to minimize the number of early and tardy jobs. Computers and Operations Research, 23, 765–781.

    Article  Google Scholar 

  • Leung, J. Y. T., Pinedo, M., & Wan, G. (2010). Competitive two-agent scheduling and its applications. Operations Research, 58, 458–469.

    Article  Google Scholar 

  • Leyvand, Y., Shabtay, D., Steiner, G., & Yedidsion, L. (2010). Just-in-time scheduling with controllable processing times on parallel machines. Journal of Combining Optimization, 19, 347–368.

    Article  Google Scholar 

  • Li, S. S., & Yuan, J. J. (2012). Unbounded parallel-batching scheduling with two competitive agents. Journal of Scheduling, 15, 629–640.

    Article  Google Scholar 

  • Mor, B., & Mosheiov, G. (2010). Scheduling problems with two competing agents to minimize minmax and minsum earliness measures. European Journal of Operational Research, 206, 540–546.

    Article  Google Scholar 

  • Mosheiov, G., & Shabtay, D. (2013). Maximizing the weighted number of just-in-time jobs on a single machine with position-dependent processing times. Journal of Scheduling, 16, 519–527.

    Article  Google Scholar 

  • Ng, C. T., Cheng, T. C. E., & Yuan, J. J. (2006). A note on the complexity of the problem of two-agent scheduling on a single machine. Journal of Combinatorial Optimization, 12, 387–394.

  • Perez-Gonzalez, P., & Framinan, J. M. (2014). A common framework and taxonomy for multicriteria scheduling problem with interfering and competing jobs: Multi-agent scheduling problems. European Journal of Operational Research, 235, 1–16.

    Article  Google Scholar 

  • Sahni, S. (1976). Algorithms for scheduling independent tasks. Journal of the ACM, 23(1), 116–127.

    Article  Google Scholar 

  • Shabtay, D. (2012). The just-in-time scheduling problem in a flowshop scheduling system. European Journal of Operational Research, 216(3), 521–532.

    Article  Google Scholar 

  • Shabtay, D., & Bensoussan, Y. (2012). Maximizing the weighted number of just-in-time jobs in several two-machine scheduling systems. Journal of Scheduling, 15(1), 39–47.

    Article  Google Scholar 

  • Shabtay, D., Bensoussan, Y., & Kaspi, M. (2012). A bicriteria approach to maximize the weighted number of just-in-time jobs and to minimize the total resource consumption cost in a two-machine flow-shop scheduling system. International Journal of Production Economics, 136, 67–74.

    Article  Google Scholar 

  • Shakhlevich, N., Hoogeveen, H., & Pinedo, M. (1998). Minimizing total weighted completion time in a proportionate flow shop. Journal of Scheduling, 1, 157–168.

    Article  Google Scholar 

  • Steiner, G., & Zhang, R. (2009). Approximation algorithms for minimizing the total weighted number of late jobs with late deliveries in two-level supply chains. Journal of Scheduling, 12, 565–574.

    Article  Google Scholar 

  • Sung, S. C., & Vlach, M. (2005). Maximizing weighted number of just-in-time jobs on unrelated parallel machines. Journal of Scheduling, 8, 453–460.

    Article  Google Scholar 

  • Wan, G., Vakati, S. R., Leung, J. Y.-T., & Pinedo, M. (2010). Scheduling two agents with controllable processing times. European Journal of Operational Research, 205, 528–539.

    Article  Google Scholar 

  • Wang, D., Yin, Y., Cheng, S.-R., Cheng, T. C. E., & Wu, C.-C. (2016). Due date assignment and scheduling on a single machine with two competing agents. International Journal of Production Research, 54, 1152–1169.

    Article  Google Scholar 

  • Yeung, W. K., Oguz, C., & Cheng, T. C. E. (2001). Minimizing weighed number of early and tardy jobs with a common due window involving location penalty. Annals of Operations Research, 108, 33–54.

    Article  Google Scholar 

  • Yin, Y., Cheng, S.-R., Cheng, T. C. E., Wang, D., & Wu, C.-C. (2016a). Just-in-time scheduling with two competing agents on unrelated parallel machines. Omega, 63, 41–47.

    Article  Google Scholar 

  • Yin, Y., Cheng, S.-R., Cheng, T. C. E., Wu, C.-C., & Wu, W.-H. (2012a). Two-agent single-machine scheduling with assignable due dates. Applied Mathematics and Computation, 219, 1674–1685.

    Article  Google Scholar 

  • Yin, Y., Cheng, S.-R., & Wu, C.-C. (2012b). Scheduling problems with two agents and a linear non-increasing deterioration to minimize earliness penalties. Information Sciences, 189, 282–292.

    Article  Google Scholar 

  • Yin, Y., Cheng, T. C. E., Yang, X., & Wu, C.-C. (2015). Two-agent single-machine scheduling with unrestricted due date assignment. Computers & Industrial Engineering, 79, 148–155.

    Article  Google Scholar 

  • Yin, Y., Wang, Y., Cheng, T. C. E., Wang, D. J., & Wu, C.-C. (2016b). Two-agent single-machine scheduling to minimize the batch delivery cost. Computers & Industrial Engineering, 92, 16–30.

    Article  Google Scholar 

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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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Correspondence to Yunqiang Yin or Du-Juan Wang.

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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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