Abstract
In this paper, we study stacking policies for containers at an automated container terminal. It is motivated by the increasing pressure on terminal performance put forward by the increase in the size of container ships. We consider several variants of category stacking, where containers can be exchanged during the loading process. The categories facilitate both stacking and online optimization of stowage. We also consider workload variations for the stacking cranes.
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References
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Acknowledgements
The authors would like to thank A. Nagel, F.J.A.M. Nooijen, and R.Th. van der Ham (ECT) for assistance during the research. The authors also thank the referees for useful comments, which helped to improve the paper.
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Appendices
Appendix A
Experiments
- A0:
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This is a reference experiment that uses random stacking without exchanges.
- A:
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This experiment considers category stacking for all modalities.
- B:
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Category stacking without exchangeability for short-sea/feeder and truck containers.
- C:
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Same as the previous experiment, with an added preference for ground locations in the random part of the algorithm.
- D:
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Experiment C with 29 lanes instead of 27.
- E:
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Experiment D, with the workload control variable set to 80% rather than 88.9%.
- F:
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Experiment E with alternative reefer stacking policy (no workload control variable for reefer containers though).
- G:
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Experiment F, with reefer containers also subject to the workload control feature with a limit of 80%.
- H:
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Experiment G with the closest transfer point feature. This feature selects an empty pile closest to the transfer point at which the container will leave the stack.
- I:
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This setup is based on experiment H: We allow the stacking of regular containers in the third part of the stack (this part is usually reserved for reefer containers).
- J:
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In this modification of experiment I, we exclude import containers from the closest transfer point rule.
- K:
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Experiment I, with the option of exchanges between different lanes. Exchanges are considered whenever the ASC workload of the selected lane exceeds 80%. Feasible exchange locations are limited to the top containers of each pile and are located using a random search approach.
- L:
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Same as experiment K, with the expected departure time rule: a container can only be stacked on top of other containers if the new container has an expected departure time less than 3 h after the expected departure time of the current topmost container in the pile.
- M:
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Experiment L, but the expected departure time of the new container must be before or equal to the expected departure time of the topmost container of the pile.
- N:
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Experiment K with the ASC workload feature for incoming containers, for which multiple uniform piles in different lanes have been located.
- O:
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Experiment N, with the addition of the ASC workload feature for outgoing, regular (i.e., nonreefer) containers.
Appendix B
Numerical results of the experiments
Experiment | A0 | A | B | C | D | E | F | G | H | I | J | k | L | M | N | O |
Reshuffle occasions | ||||||||||||||||
Total | 60.9 | 31.0 | 31.0 | 16.1 | 13.3 | 13.4 | 11.4 | 11.4 | 10.4 | 6.9 | 7.1 | 6.8 | 6.2 | 7.0 | 6.8 | 6.9 |
Jumbo | 67.8 | 12.4 | 18.5 | 10.2 | 8.5 | 8.3 | 4.3 | 4.1 | 3.6 | 2.1 | 2.3 | 2.1 | 1.8 | 2.4 | 2.0 | 1.4 |
Deep-sea | 55.9 | 12.3 | 19.5 | 11.4 | 9.4 | 9.5 | 5.0 | 4.8 | 4.1 | 2.2 | 2.5 | 2.2 | 2.4 | 2.8 | 2.3 | 2.3 |
Short-sea/feeder | 62.8 | 71.5 | 58.6 | 31.5 | 26.1 | 26.6 | 26.3 | 26.6 | 24.5 | 17.3 | 17.5 | 17.2 | 15.2 | 16.9 | 17.1 | 17.9 |
Export | 55.9 | 35.1 | 34.2 | 18.7 | 15.5 | 15.6 | 12.9 | 12.9 | 11.8 | 8.0 | 8.2 | 7.9 | 7.1 | 8.1 | 7.9 | 8.0 |
Truck | – | 68.0 | 58.4 | 32.3 | 26.7 | 26.4 | 26.5 | 26.6 | 26.0 | 16.2 | 16.3 | 14.9 | 12.5 | 14.9 | 16.1 | 16.1 |
Rail | – | 9.5 | 14.7 | 3.8 | 3.0 | 3.2 | 2.7 | 3.1 | 2.5 | 1.3 | 1.2 | 1.1 | 1.5 | 1.5 | 1.3 | 1.0 |
Barge | – | 8.8 | 13.8 | 3.9 | 2.8 | 2.9 | 2.8 | 2.9 | 2.4 | 1.4 | 1.4 | 1.1 | 1.5 | 1.6 | 1.2 | 1.3 |
Import | – | 19.2 | 21.8 | 8.7 | 7.0 | 7.1 | 6.9 | 7.0 | 6.5 | 3.9 | 3.9 | 3.5 | 3.4 | 3.8 | 3.8 | 3.7 |
Reshuffles performed | ||||||||||||||||
Total | 89.3 | 46.1 | 41.8 | 23.0 | 19.0 | 19.0 | 16.0 | 16.2 | 14.8 | 9.7 | 9.9 | 9.5 | 8.8 | 9.6 | 9.5 | 9.8 |
Jumbo | 99.7 | 15.7 | 23.5 | 13.4 | 11.3 | 10.8 | 5.5 | 5.3 | 4.7 | 2.8 | 3.0 | 2.8 | 2.0 | 2.8 | 2.6 | 1.8 |
Deep-sea | 81.8 | 16.4 | 25.4 | 15.3 | 13.0 | 13.1 | 6.1 | 5.8 | 5.0 | 2.7 | 3.0 | 2.6 | 2.8 | 3.1 | 2.7 | 2.7 |
Short-sea/feeder | 92.1 | 112.2 | 82.2 | 47.0 | 38.5 | 39.0 | 38.3 | 39.3 | 36.0 | 24.7 | 25.1 | 24.7 | 23.0 | 24.1 | 24.5 | 26.1 |
Export | 81.9 | 52.9 | 46.6 | 26.8 | 22.2 | 22.3 | 18.3 | 18.5 | 16.8 | 11.2 | 11.5 | 11.2 | 10.3 | 11.1 | 11.0 | 11.4 |
Truck | – | 103.5 | 83.9 | 49.0 | 40.2 | 39.2 | 39.4 | 39.5 | 39.1 | 24.0 | 24.3 | 22.6 | 20.1 | 22.7 | 24.2 | 24.8 |
Rail | – | 10.8 | 17.0 | 4.3 | 3.4 | 3.7 | 3.0 | 3.5 | 2.8 | 1.4 | 1.4 | 1.2 | 1.6 | 1.6 | 1.4 | 1.1 |
Barge | – | 9.8 | 15.9 | 4.5 | 3.2 | 3.4 | 3.2 | 3.3 | 2.7 | 1.5 | 5.4 | 1.2 | 1.6 | 1.6 | 1.4 | 1.3 |
Import | – | 26.2 | 27.9 | 12.1 | 9.6 | 9.6 | 9.4 | 9.6 | 9.0 | 5.3 | 9.9 | 4.9 | 4.8 | 5.2 | 5.3 | 5.3 |
No position (per 100,000) | ||||||||||||||||
For new container | 0 | 0 | 0 | 96 | 1 | 3 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | – |
For reshuffle | 74 | 40 | 28 | 42 | 25 | 25 | 0 | 0 | 0 | 15 | 23 | 18 | 24 | 36 | 18 | – |
Ground locations: maximum | ||||||||||||||||
Overall | 84.5 | 75.3 | 79.9 | 91.1 | 89.2 | 89.1 | 88.7 | 87.8 | 89.4 | 95.2 | 94.7 | 95.7 | 96.4 | 96.5 | 95.1 | 95.2 |
Part 1 of the stack | 89.6 | 80.8 | 86.3 | 98.7 | 97.7 | 97.5 | 97.5 | 97.4 | 99.4 | 98.4 | 97.8 | 98.9 | 99.6 | 99.8 | 98.4 | 98.3 |
Part 2 of the stack | 50.6 | 50.2 | 51.4 | 48.6 | 48.1 | 46.7 | 58.2 | 58.2 | 58.2 | 58.2 | 58.2 | 58.2 | 57.9 | 57.9 | 58.2 | 58.2 |
Part 3 of the stack | 68.9 | 50.4 | 50.6 | 53.5 | 42.2 | 40.2 | 22.4 | 22.2 | 14.4 | – | – | – | – | – | – | – |
Ground locations: average | ||||||||||||||||
Overall | 77.4 | 64.7 | 70.3 | 81.3 | 79.0 | 79.0 | 78.3 | 78.2 | 79.4 | 83.9 | 83.5 | 84.0 | 85.1 | 85.3 | 83.9 | 84.3 |
Part 1 of the stack | 83.5 | 69.6 | 76.5 | 89.0 | 87.5 | 87.4 | 87.4 | 87.4 | 89.3 | 87.6 | 87.1 | 87.7 | 88.9 | 89.0 | 87.5 | 88.0 |
Part 2 of the stack | 38.7 | 38.9 | 38.6 | 39.2 | 37.5 | 38.1 | 38.7 | 38.7 | 38.7 | 38.7 | 38.7 | 38.6 | 38.7 | 38.6 | 38.6 | 38.7 |
Part 3 of the stack | 47.1 | 36.0 | 31.4 | 36.5 | 24.5 | 24.8 | 13.6 | 13.3 | 8.8 | – | – | – | – | – | – | – |
Workload ASC: overall | ||||||||||||||||
Maximum (%) | 301.9 | 312.6 | 289.4 | 270.4 | 302.5 | 260.8 | 246.5 | 287.8 | 220.2 | 278.9 | 258.9 | 259.1 | 193.6 | 238.1 | 214.0 | 367.3 |
Average (%) | 31.2 | 27.0 | 26.8 | 25.4 | 23.3 | 23.4 | 23.3 | 23.3 | 22.5 | 22.3 | 22.3 | 22.3 | 22.3 | 22.4 | 22.1 | 22.0 |
Percentage >80% | 10.3 | 7.3 | 7.1 | 6.1 | 5.1 | 4.7 | 4.6 | 4.6 | 3.9 | 3.7 | 3.7 | 3.1 | 3.1 | 3.2 | 2.6 | 2.0 |
Percentage >90% | 7.7 | 5.3 | 5.1 | 4.4 | 3.5 | 2.8 | 2.7 | 2.7 | 2.2 | 2.1 | 2.1 | 1.2 | 1.2 | 1.3 | 1.0 | 0.9 |
Percentage >100% | 5.7 | 3.8 | 3.6 | 3.1 | 2.4 | 1.7 | 1.6 | 1.6 | 1.2 | 1.1 | 1.1 | 0.5 | 0.5 | 0.5 | 0.3 | 0.4 |
Percentage >110% | 4.1 | 2.7 | 2.5 | 2.2 | 1.6 | 1.0 | 1.0 | 1.0 | 0.7 | 0.6 | 0.6 | 0.2 | 0.2 | 0.2 | 0.1 | 0.2 |
Percentage >120% | 3.0 | 1.9 | 1.7 | 1.5 | 1.1 | 0.6 | 0.6 | 0.6 | 0.4 | 0.3 | 0.4 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 |
Workload ASC: jumbo | ||||||||||||||||
Maximum (%) | – | 312.6 | 289.4 | 270.4 | 302.5 | 260.8 | 246.5 | 225.3 | 220.2 | 278.9 | 258.9 | 259.1 | 193.6 | 218.0 | 214.0 | 367.3 |
Average (%) | – | 59.5 | 60.4 | 57.6 | 53.2 | 53.2 | 53.0 | 52.9 | 50.0 | 49.6 | 49.8 | 49.5 | 49.4 | 49.8 | 49.4 | 49.0 |
Percentage >80% | – | 28.4 | 28.6 | 25.9 | 22.2 | 21.3 | 21.1 | 20.7 | 17.7 | 16.8 | 17.3 | 14.5 | 14.6 | 15.3 | 12.7 | 9.5 |
Percentage >90% | – | 22.3 | 22.0 | 19.8 | 16.5 | 13.3 | 13.1 | 12.8 | 10.5 | 9.8 | 10.4 | 5.9 | 6.0 | 6.3 | 4.8 | 4.4 |
Percentage >100% | – | 17.1 | 16.5 | 14.7 | 11.8 | 8.3 | 8.0 | 7.8 | 6.3 | 5.6 | 5.9 | 2.3 | 2.3 | 2.6 | 1.7 | 1.9 |
Percentage >110% | – | 13.0 | 12.3 | 10.8 | 8.4 | 5.2 | 5.0 | 5.0 | 3.7 | 3.2 | 3.3 | 1.0 | 1.0 | 1.1 | 0.7 | 0.9 |
Percentage >120% | – | 9.6 | 8.8 | 7.8 | 5.9 | 3.1 | 3.1 | 3.0 | 2.1 | 1.8 | 1.9 | 0.5 | 0.4 | 0.5 | 0.3 | 0.5 |
Workload ASC: deep-sea | ||||||||||||||||
Maximum (%) | – | 266.3 | 242.7 | 239.8 | 226.5 | 190.9 | 199.0 | 287.8 | 206.5 | 204.3 | 197.9 | 176.6 | 159.6 | 238.1 | 213.4 | 205.8 |
Average (%) | – | 39.7 | 40.1 | 38.3 | 35.2 | 35.3 | 35.1 | 35.0 | 33.2 | 33.0 | 33.1 | 33.0 | 33.1 | 33.2 | 32.9 | 32.5 |
Percentage >80% | – | 11.8 | 11.8 | 10.1 | 8.1 | 7.3 | 7.0 | 7.0 | 5.7 | 5.4 | 5.4 | 4.2 | 4.4 | 4.3 | 3.3 | 2.8 |
Percentage >90% | – | 8.0 | 8.2 | 6.8 | 5.1 | 4.0 | 4.0 | 4.0 | 2.9 | 2.9 | 2.8 | 1.7 | 1.8 | 1.6 | 1.2 | 1.2 |
Percentage >100% | – | 5.4 | 5.4 | 4.4 | 3.2 | 2.2 | 2.2 | 2.2 | 1.6 | 1.5 | 1.4 | 0.6 | 0.7 | 0.6 | 0.4 | 0.5 |
Percentage >110% | – | 3.5 | 3.5 | 2.9 | 2.0 | 1.3 | 1.2 | 1.2 | 0.8 | 0.7 | 0.7 | 0.2 | 0.3 | 0.3 | 0.2 | 0.2 |
Percentage >120% | – | 2.3 | 2.2 | 1.8 | 1.1 | 0.7 | 0.7 | 0.7 | 0.4 | 0.4 | 0.4 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 |
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Dekker, R., Voogd, P. & van Asperen, E. Advanced methods for container stacking. OR Spectrum 28, 563–586 (2006). https://doi.org/10.1007/s00291-006-0038-3
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DOI: https://doi.org/10.1007/s00291-006-0038-3