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Cyclic Scheduling of Identical Parts in a Robotic Cell

Author

Listed:
  • Yves Crama

    (Université de Liège, Liège, Belgium)

  • Joris van de Klundert

    (Maastricht University, Maastricht, The Netherlands)

Abstract

We consider a robotic flowshop in which one type of product is to be repeatedly produced, and where transportation of the parts between the machines is performed by a robot. The identical parts cyclic scheduling problem is then to find a shortest cyclic schedule for the robot; i.e., a sequence of robot moves that can be infinitely repeated and that has minimum cycle time. This problem has been solved by Sethi et al. (Sethi, S. P., C. Sriskandarajah, G. Sorger, J. Blazewicz, W. Kubiak. 1992. Sequencing of parts and robot moves in a robotic cell. Internat. J. Flexible Manufacturing Systems 4 331–358.) when m ≤ 3. In this paper, we generalize their results by proving that the identical parts cyclic scheduling problem can be solved in time polynomial in m , where m denotes the number of machines in the shop. In particular, we present a dynamic programming approach that allows us to solve the problem in O ( m 3 ) time. Our analysis relies heavily on the concept of pyramidal permutation, a concept previously investigated in connection with the traveling salesman problem.

Suggested Citation

  • Yves Crama & Joris van de Klundert, 1997. "Cyclic Scheduling of Identical Parts in a Robotic Cell," Operations Research, INFORMS, vol. 45(6), pages 952-965, December.
    • Handle: RePEc:inm:oropre:v:45:y:1997:i:6:p:952-965
    DOI: 10.1287/opre.45.6.952
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    Citations

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    Cited by:

    1. Hall, Nicholas G. & Kamoun, Hichem & Sriskandarajah, Chelliah, 1998. "Scheduling in robotic cells: Complexity and steady state analysis," European Journal of Operational Research, Elsevier, vol. 109(1), pages 43-65, August.
    2. Agnetis, A., 2000. "Scheduling no-wait robotic cells with two and three machines," European Journal of Operational Research, Elsevier, vol. 123(2), pages 303-314, June.
    3. Milind Dawande & Chelliah Sriskandarajah & Suresh Sethi, 2002. "On Throughput Maximization in Constant Travel-Time Robotic Cells," Manufacturing & Service Operations Management, INFORMS, vol. 4(4), pages 296-312, August.
    4. Neil Geismar, H. & Dawande, Milind & Sriskandarajah, Chelliah, 2005. "Approximation algorithms for k-unit cyclic solutions in robotic cells," European Journal of Operational Research, Elsevier, vol. 162(2), pages 291-309, April.
    5. Milind Dawande & Michael Pinedo & Chelliah Sriskandarajah, 2009. "Multiple Part-Type Production in Robotic Cells: Equivalence of Two Real-World Models," Manufacturing & Service Operations Management, INFORMS, vol. 11(2), pages 210-228, February.
    6. Drobouchevitch, Inna G. & Sethi, Suresh P. & Sriskandarajah, Chelliah, 2006. "Scheduling dual gripper robotic cell: One-unit cycles," European Journal of Operational Research, Elsevier, vol. 171(2), pages 598-631, June.
    7. Irina N. Lushchakova & Alan J. Soper & Vitaly A. Strusevich, 2009. "Transporting jobs through a two‐machine open shop," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(1), pages 1-18, February.
    8. Brauner, Nadia & Finke, Gerd, 2001. "Optimal moves of the material handling system in a robotic cell," International Journal of Production Economics, Elsevier, vol. 74(1-3), pages 269-277, December.
    9. W Zahrouni & H Kamoun, 2011. "Transforming part-sequencing problems in a robotic cell into a GTSP," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(1), pages 114-123, January.
    10. Drobouchevitch, Inna G. & Neil Geismar, H. & Sriskandarajah, Chelliah, 2010. "Throughput optimization in robotic cells with input and output machine buffers: A comparative study of two key models," European Journal of Operational Research, Elsevier, vol. 206(3), pages 623-633, November.
    11. Tharanga Rajapakshe & Milind Dawande & Chelliah Sriskandarajah, 2011. "Quantifying the Impact of Layout on Productivity: An Analysis from Robotic-Cell Manufacturing," Operations Research, INFORMS, vol. 59(2), pages 440-454, April.
    12. Hichem Kamoun & Nicholas G. Hall & Chelliah Sriskandarajah, 1999. "Scheduling in Robotic Cells: Heuristics and Cell Design," Operations Research, INFORMS, vol. 47(6), pages 821-835, December.
    13. Xin Li & Richard Y. K. Fung, 2016. "Optimal K-unit cycle scheduling of two-cluster tools with residency constraints and general robot moving times," Journal of Scheduling, Springer, vol. 19(2), pages 165-176, April.
    14. Che, Ada & Chu, Chengbin, 2009. "Multi-degree cyclic scheduling of a no-wait robotic cell with multiple robots," European Journal of Operational Research, Elsevier, vol. 199(1), pages 77-88, November.
    15. Chelliah Sriskandarajah & Inna Drobouchevitch & Suresh P. Sethi & Ramaswamy Chandrasekaran, 2004. "Scheduling Multiple Parts in a Robotic Cell Served by a Dual-Gripper Robot," Operations Research, INFORMS, vol. 52(1), pages 65-82, February.
    16. Zhichao Feng & Milind Dawande & Ganesh Janakiraman, 2021. "On the Capacity of a Process with Batch Processing and Setup Times," Production and Operations Management, Production and Operations Management Society, vol. 30(11), pages 4273-4287, November.
    17. Milind Dawande & Zhichao Feng & Ganesh Janakiraman, 2021. "On the Structure of Bottlenecks in Processes," Management Science, INFORMS, vol. 67(6), pages 3853-3870, June.
    18. Janny M. Y. Leung & Guoqing Zhang & Xiaoguang Yang & Raymond Mak & Kokin Lam, 2004. "Optimal Cyclic Multi-Hoist Scheduling: A Mixed Integer Programming Approach," Operations Research, INFORMS, vol. 52(6), pages 965-976, December.
    19. Imai, Akio & Yamakawa, Yukiko & Huang, Kuancheng, 2014. "The strategic berth template problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 72(C), pages 77-100.
    20. Gultekin, Hakan & Akturk, M. Selim & Karasan, Oya Ekin, 2006. "Cyclic scheduling of a 2-machine robotic cell with tooling constraints," European Journal of Operational Research, Elsevier, vol. 174(2), pages 777-796, October.

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