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Flowshop scheduling with interstage job transportation

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Abstract

There are a variety of joint job production and transportation scheduling problems that arise in modern manufacturing systems. In this paper, we study two such problems that arise in a flowshop environment where there are two processing stages and a single transporter that is available to deliver the finished jobs from the first stage to the second. In the first problem, there is a single machine in each of the two flowshop stages and jobs have different sizes when loaded onto the transporter. In the second problem, there are two parallel machines in the first stage and a single machine in the second stage, and the transporter can carry only one job in each shipment. The objective of both problems is to minimize the makespan, i.e., the completion time of the last job in the second stage. The two problems are both strongly NP-hard. For each problem, we propose a fast heuristic and show that the heuristic has a tight worst-case bound of 2.

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References

  • Chen, B. (1995). Analysis of classes of heuristics for scheduling two-stage flow shop with parallel machines at one stage. Journal of the Operational Research Society, 46, 234–244.

    Article  Google Scholar 

  • Chen, Z.-L. (2010). Integrated production and outbound distribution scheduling: Review and extensions. Operations Research, 58, 130–148.

    Article  Google Scholar 

  • Dósa, G. (2007). The tight bound of first fit decreasing bin-packing algorithm is \(\text{ FFD(I) } \le 11/9\text{ OPT(I) } + 6/9\). Lecture Notes of Computer Science, 4614, 1–11.

    Article  Google Scholar 

  • Gong, H., & Tang, L. (2011). Two-machine flowshop scheduling with intermediate transportation under job physical space consideration. Computers & Operations Research, 38, 1267–1274.

    Article  Google Scholar 

  • Graham, R. L. (1966). Bounds for certain multiprocessing anomalies. The Bell System Technical Journal, 45, 1563–1581.

    Article  Google Scholar 

  • Gupta, J. N. D. (1988). Two-stage, hybrid flowshop scheduling problem. Journal of the Operational Research Society, 39, 359–364.

    Article  Google Scholar 

  • Gupta, J. N. D., & Tunc, E. A. (1991). Schedules for a two-stage hybrid flowshop with parallel machines at the second stage. International Journal of Production Research, 29, 1489–1502.

    Article  Google Scholar 

  • Hoogeveen, J. A., Lenstra, J. K., & Veltman, B. (1996). Preemptive scheduling in a two-stage multiprocessor flow shop is NP-hard. European Journal of Operational Research, 1, 172–175.

    Article  Google Scholar 

  • Hurink, J., & Knust, S. (2001). Makespan minimization for flow-shop problems with transportation times and a single robot. Discrete Applied Mathematics, 112, 199–216.

    Article  Google Scholar 

  • Johnson, S. M. (1954). Optimal two- and three-machine production schedules with setup times included. Naval Research Logistics, 1, 61–68.

    Article  Google Scholar 

  • Karuno, Y., & Nagamochi, H. (2003). A better approximation for the two-machine flowshop scheduling problem with time lags. 14th annual international symposium on algorithms and computation (pp. 309–318). Kyoto, Japan.

  • Langston, M.-A. (1987). Interstage transportation planning in the deterministic flow-shop environment. Operations Research, 35, 556–564.

    Article  Google Scholar 

  • Lee, C. Y., & Chen, Z.-L. (2001). Machine scheduling with transportation considerations. Journal of Scheduling, 4, 3–24.

    Article  Google Scholar 

  • Lee, C. Y., & Strusevich, V. A. (2005). Two-machine shop scheduling with an uncapacited interstage transporter. IIE Transaction, 37, 725–736.

    Article  Google Scholar 

  • Lee, C. Y., & Vairaktarakis, G. L. (1998). Performance comparision of some classes of flexible flow shops and job shops. International Journal of Flexible Manufacturing Systems, 10, 379–405.

    Article  Google Scholar 

  • Maggu, P. L., & Das, G. (1980). On \(2\times n\) sequencing problem with transportaion times of jobs. Pure and Applied Mathematika Sciences, 12, 1–6.

    Google Scholar 

  • Mendoza, A., Ventura, J., & Huang, K.-L. (2010). A flowshop scheduling problem with transportation times and capacity constraints. 11th international material handling research colloquium (pp. 296–304).

  • Naderi, B., Zandieh, M., & Shirazi, M. A. H. A. (2009). Modeling and scheduling a case of flexible flowshops: Total weighted tardiness minimization. Computers & Industrial Engineering, 57, 1258–1267.

    Article  Google Scholar 

  • Oğuz, C., Ercan, M. F., Cheng, T. E. C., & Fung, Y. F. (2003). Heuristic algorithms for multiprocessor task scheduling in a two-stage hybrid flow-shop. European Journal of Operational Research, 149, 390–403.

    Article  Google Scholar 

  • Oulamara, A., & Soukhal, A. (2001). Flow shop scheduling problems with transportation and capacity constraints. IEEE International Conference on Systems, Man, and Cybernetics, 4, 2540–2545.

    Google Scholar 

  • Panwalker, S. (1991). Scheduling of a two-machine flow shop with travel time between machines. Journal of the operational Research Society, 42, 609–613.

    Article  Google Scholar 

  • Ruiz, R., & Vázquez-Rodríguez, J. A. (2010). The hybrid flow shop scheduling problem. European Journal of Operational Research, 205, 1–18.

    Article  Google Scholar 

  • Sriskandarajah, C., & Sethi, S. P. (1989). Scheduling algorithms for flexible flowshops: Worst and average case performance. European Journal of Operational Research, 43, 143–160.

  • Stern, H. I., & Vitner, G. (1990). Scheduling parts in a combined production-transportation work cell. Journal of the Operational Research Society, 41, 625–632.

    Article  Google Scholar 

  • Tang, L., & Liu, P. (2009). Flowshop scheduling problems with transportation or deterioration between the batching and single machines. Computers & Industrial Engineering, 56, 1289–1295.

    Article  Google Scholar 

  • Veltman, B. (1993). Multiprocessor scheduling with communicaiton Delays. PhD Thesis, CWI, Amsterdam, The Netherlands.

  • Xuan, H., & Tang, L. (2007). Scheduling a hybrid flowshop with batch production at the last stage. Computers & Operations Research, 34, 2718–2733.

    Article  Google Scholar 

  • Yu, W., Hoogeven, J. A., & Lenstra, J. K. (2005). Minimizing makespan in a two-machine flow shop with delays and unit-time operations is NP-hard. Journal of Scheduling, 7, 333–348.

    Article  Google Scholar 

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Acknowledgments

The authors would like to thank three anonymous referees for their constructive comments on the earlier version of the paper. The first author was supported by the National Natural Science Foundation of China Grants (No. 11301327 ).

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Authors and Affiliations

  1. Department of Business Administration, School of Management, Shanghai University, Shanghai, 200444, People’s Republic of China

    Weiya Zhong

  2. Department of Decision, Operations, and Information Technologies, Robert H. Smith School of Business, University of Maryland, College Park, MD, 20742-1815, USA

    Zhi-Long Chen

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  1. Weiya Zhong
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  2. Zhi-Long Chen
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Correspondence to Weiya Zhong.

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Zhong, W., Chen, ZL. Flowshop scheduling with interstage job transportation. J Sched 18, 411–422 (2015). https://doi.org/10.1007/s10951-014-0409-6

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  • DOI: https://doi.org/10.1007/s10951-014-0409-6

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