Skip to main content
SpringerLink
Log in

Approximation algorithms for the twin robot scheduling problem

  • Published:
Journal of Scheduling Aims and scope Submit manuscript

Abstract

We consider the \(\mathscr {NP}\)-hard twin robot scheduling problem, which was introduced by Erdoğan et al. (Naval Res Logist (NRL) 61(2):119–130, 2014). Here, two moving robots positioned at the opposite ends of a rail have to perform automated storage and retrieval jobs at given positions along the gantry rail with a non-crossing constraint. The objective is to minimize the makespan. We extend the original problem by considering pickup and delivery times and present exact and approximation algorithms with a performance ratio of \(\approx \,1.1716\) for large instances. Further, we compare the presented algorithms in a comprehensive numerical study.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  • Boysen, N., Briskorn, D., & Emde, S. (2015). A decomposition heuristic for the twin robots scheduling problem. Naval Research Logistics (NRL), 62(1), 16–22.

    Article  Google Scholar 

  • Boysen, N., Briskorn, D., & Meisel, F. (2017). A generalized classification scheme for crane scheduling with interference. European Journal of Operational Research, 258(1), 343–357.

    Article  Google Scholar 

  • Bozer, Y. A., & White, J. A. (1984). Travel-time models for automated storage/retrieval systems. IIE Transactions, 16(4), 329–338.

    Article  Google Scholar 

  • Briskorn, D., Emde, S., & Boysen, N. (2016). Cooperative twin-crane scheduling. Discrete Applied Mathematics, 211, 40–57.

    Article  Google Scholar 

  • Briskorn, D., Jaehn, F., & Wiehl, A. (2019). A generator for test instances of scheduling problems concerning cranes in transshipment terminals. OR Spectrum, 41, 45–69.

    Article  Google Scholar 

  • Bürgy, R., & Gröflin, H. (2016). The blocking job shop with rail-bound transportation. Journal of Combinatorial Optimization, 31(1), 152–181.

    Article  Google Scholar 

  • Carlo, H. J., & Martínez-Acevedo, F. L. (2015). Priority rules for twin automated stacking cranes that collaborate. Computers and Industrial Engineering, 89, 23–33.

    Article  Google Scholar 

  • Ehleiter, A., & Jaehn, F. (2016). Housekeeping: Foresightful container repositioning. International Journal of Production Economics, 179, 203–211.

    Article  Google Scholar 

  • Erdoğan, G., Battarra, M., & Laporte, G. (2014). Scheduling twin robots on a line. Naval Research Logistics (NRL), 61(2), 119–130.

    Article  Google Scholar 

  • Gademann, A. N., et al. (1999). Optimal routing in an automated storage/retrieval system with dedicated storage. IIE Transactions, 1(5), 407–415.

    Google Scholar 

  • Hu, Z.-H., Sheu, J.-B., & Luo, J. X. (2016). Sequencing twin automated stacking cranes in a block at automated container terminal. Transportation Research Part C: Emerging Technologies, 69, 208–227.

    Article  Google Scholar 

  • Jaehn, F., & Kress, D. (2018). Scheduling cooperative gantry cranes with seaside and landside jobs. Discrete Applied Mathematics, 242, 53–68.

    Article  Google Scholar 

  • Kim, K. H., & Kim, K. Y. (1999). An optimal routing algorithm for a transfer crane in port container terminals. Transportation Science, 33(1), 17–33.

    Article  Google Scholar 

  • Kim, K. Y., & Kim, K. H. (1997). A routing algorithm for a single transfer crane to load export containers onto a containership. Computers and Industrial Engineering, 33(3–4), 673–676.

    Article  Google Scholar 

  • Kress, D., Dornseifer, J., & Jaehn, F. (2019). An exact solution approach for scheduling cooperative gantry cranes. European Journal of Operational Research, 273(1), 82–101.

    Article  Google Scholar 

  • Kuhn, H. W. (1955). The hungarian method for the assignment problem. Naval Research Logistics (NRL), 2(1–2), 83–97.

    Article  Google Scholar 

  • Kung, Y., Kobayashi, Y., Higashi, T., & Ota, J. (2012). Motion planning of two stacker cranes in a large-scale automated storage/retrieval system. Journal of Mechanical Systems for Transportation and Logistics, 5(1), 71–85.

    Article  Google Scholar 

  • Kung, Y., Kobayashi, Y., Higashi, T., Sugi, M., & Ota, J. (2014). Order scheduling of multiple stacker cranes on common rails in an automated storage/retrieval system. International Journal of Production Research, 52(4), 1171–1187.

    Article  Google Scholar 

  • Lieberman, R., & Turksen, I. (1981). Crane scheduling problems. AIIE Transactions, 13(4), 304–311.

    Article  Google Scholar 

  • Roodbergen, K. J., & Vis, I. F. (2009). A survey of literature on automated storage and retrieval systems. European Journal of Operational Research, 194(2), 343–362.

    Article  Google Scholar 

  • Speer, U., & Fischer, K. (2016). Scheduling of different automated yard crane systems at container terminals. Transportation Science, 51(1), 305–324.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Management Science and Operations Research, Helmut-Schmidt-University, Holstenhofweg 85, 22043, Hamburg, Germany

    Florian Jaehn

  2. Stettenstraße 28, 86150, Augsburg, Germany

    Andreas Wiehl

Authors
  1. Florian Jaehn
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andreas Wiehl
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Florian Jaehn.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This work has been supported by the German Science Foundation (DFG) through the grant “Scheduling mechanisms for rail mounted gantries with respect to crane interdependencies” (JA 2311/2-1)

Appendix

Appendix

See Table 7.

Table 7 Number of Jobs—4 * 1540 instances
Full size table

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jaehn, F., Wiehl, A. Approximation algorithms for the twin robot scheduling problem. J Sched 23, 117–133 (2020). https://doi.org/10.1007/s10951-019-00631-9

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10951-019-00631-9

Keywords

Search

Navigation