Abstract
The operational performance of automated RMGC systems is to a large extent determined by the planning strategies applied for container stacking, crane scheduling and crane routing. In the present chapter, these operational planning problems are addressed in depth. It is started with the container-stacking problem. After reviewing and classifying existing stacking strategies, a new stacking approach is presented, which allows for a weighted combination of different stacking strategies, and a procedure for generating and scheduling housekeeping moves is introduced. Thereafter, the crane-scheduling problem is addressed. After this problem is discussed and an overview on known solution approaches is given, some new scheduling strategies are presented which are based on priority rules, integer programming, enumeration and genetic algorithms. Finally, the problem of routing RMGCs is introduced, relevant literature for that problem is discussed and different claiming-based routing strategies are presented.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The kinematic equations for the computation of driving, acceleration and deceleration times as well as for acceleration and deceleration distances (Hering et al. 2009) can be used to compute the time duration for movements of a steadily accelerated/decelerated portal, trolley and spreader between two positions as
$$m = \frac{v} {a} + \frac{1} {v} \times \left (l -\frac{{v}^{2}} {2a} -\frac{{v}^{2}} {2b}\right ) + \frac{v} {b},$$where the time for acceleration to the maximum velocity, the driving time with the maximum velocity and the time for deceleration to the stop are given by the first, second and third terms of the sum. Simplifying this equation yields
$$m = \frac{l} {v} + \frac{v} {2a} + \frac{v} {2b}.$$
References
Aydin, C. (2007). Improved Rehandling Strategies for Container Retrieval Process. Master Thesis, Graduate School of Engineering and Natural Sciences, Sabanci University, Istanbul.
Bohrer, P. (2010). Crane scheduling in container terminals: mathematical models, heuristics and algorithms. Saarbrücken: VDM Verlag Dr. Müller.
Borgman, B., van Asperen, E., & Dekker, R. (2010). Online rules for container stacking. OR Spectrum, 32(3), 687–716.
Böse, J. W., Reiners, T., Steenken, D., & Voß, S. (2000). Vehicle dispatching at seaport container terminals using evolutionary algorithms. In Proceedings of the 33rd Hawaii international conference on system sciences (pp. 1–10).
Briskorn, D., Drexl, A., & Hartmann, S. (2006). Inventory-based dispatching of automated guided vehicles on container terminals. OR Spectrum, 28(4), 611–630.
Cao, Z., Lee, D.-H., & Meng, Q. (2008). Deployment strategies of double-rail-mounted gantry crane systems for loading outbound containers in container terminals. International Journal of Production Economics, 115(1), 221–228.
Carlo, H. J., & Vis, I. F. A. (2008). Routing new types of stacking crane configurations at container terminals. In K. Ellis, R. Meller, M. K. Ogle, B. A. Peter, G. D. Taylor, & J. S. Usher (Eds.), Progress in material handling reserach (pp. 55–70). Charlotte: Material Handling Institute.
Caserta, M., Voß, S., & Sniedovich, M. (2011). Applying the corridor method to a blocks relocation problem. OR Spectrum, 33(4), 885–914.
Chen, T. (1999). Yard Operations in the Container Terminal –A Study in the ’Unproductive Moves’. Maritime Policy & Management, 26(1), 27–38.
Chen, T., Lin, K., & Juang, Y.-C. (2000). Empirical studies on yard operations part 2: quantifying unproductive moves undertaken in quay transfer operations. Maritime Policy & Management, 27(2), 191–207.
Choe, R., Park, T., Seung, M. O., & Kwang, R. R. (2007). Real-time scheduling for non-crossing stacking cranes in an automated container terminal. In M. A. Orgun & J. Thornton (Eds.), AI 2007: Advances in artificial intelligence, Vol. 4830 of Lecture notes in computer science (pp. 625–631). Berlin: Springer.
Croce, F. D., Tadei, R., & Volta, G. (1995). A genetic algorithm for the job shop problem. Computers & Operations Research, 22(1), 15–24.
De Castilho, B., & Daganzo, C. F. (1993). Handling strategies for import containers at marine terminals. Transportation Research Part B: Methodological, 27(2), 151–166.
Dekker, R., Voogd, P., & van Asperen, E. (2006). Advanced methods for container stacking. OR Spectrum, 28(4), 563–586.
Dorndorf, U., & Schneider, F. (2010). Scheduling automated triple cross-over stacking cranes in a container yard. OR Spectrum, 32(3), 617–632.
Duinkerken, M. B., Evers, J. J. M., & Ottjes, J. A. (2001). A simulation model for integrating quay transport and stacking policies on automated container terminals. In Proceedings of the 15th european simulation multiconference, Prague (pp. 909–916).
Froyland, G., Koch, T., Megow, N., Duane, E., & Wren, H. (2008). Optimizing the landside operation of a container terminal. OR Spectrum, 30(1), 53–75.
Garey, M. R., & Johnson, D. S. (1979). Computers and intractability – a guide to the theory of NP-completeness. San Francisco, CA: Freeman.
Goldberg, D. E. (1989). Genetic algorithms in search, optimization and machine learning. Boston, MA: Addison-Wesley Longman.
Goldberg, D. E., & Deb, K. (1991). A comparative analysis of selection schemes used in genetic algorithms. In G. J. E. Rawlins (Ed.), Foundations of genetic algorithms (pp. 69–93). Waltham, MA: Morgan Kaufmann.
Grötschel, M., Krumke, S. O., Rambau, J., Winter, T., & Zimmermann, U. (2001). Combinatorial online optimization in real time. In M. Grötschel, S. O. Krumke, & J. Rambau (Eds.), Online optimization of large scale systems (pp. 679–704). Berlin: Springer.
Han, Y., Lee, L., Chew, E., & Tan, K. (2008). A yard storage strategy for minimizing traffic congestion in a marine container transshipment hub. OR Spectrum, 30(4), 697–720.
Hering, E., Martin, R., & Stohrer, M. (2009). Taschenbuch der Mathematik und Physik (5th ed.). Berlin: Springer.
Hirashima, Y. (2008). A Q-learning system for container transfer scheduling based on shipping order at container terminals. International Journal of Innovative Computing, Information and Control, 4(3), 547–558.
Hirashima, Y. (2009). A Q-learning system for container marshalling with group-based learning model at container yard terminals. In Proceedings of the international multi-conference of engineers and computer scientist (pp. 18–20).
Hirashima, Y., Takeda, K., Harada, S., Deng, M., & Inoue, A. (2006). A Q-learning for group-based plan of container transfer scheduling. JSME International Journal Series C, 49(2), 473–479.
Holland, J. H. (1992). Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence. Cambridge, MA: MIT.
Jung, S. H., & Kim, K. H. (2006). Load scheduling for multiple quay cranes in port container terminals. Journal of Intelligent Manufacturing, 17(4), 479–492.
Kang, J., Oh, M.-S., Ahn, E. Y., Ryu, K. R., & Kim, K. H. (2006). Planning for intra-block remarshalling in a container terminal. In M. Ali & R. Dapoigny (Eds.), Advances in applied artificial intelligence, Volume 4031 of Lecture notes in computer science (pp. 1211–1220). Berlin: Springer.
Kang, J., Ryu, K. R., & Kim, K. H. (2006a). Deriving stacking strategies for export containers with uncertain weight information. Journal of Intelligent Manufacturing, 17(4), 399–410.
Kang, J., Ryu, K. R., & Kim, K. H. (2006b). Determination of storage locations for incoming containers of uncertain weight. In M. Ali & R. Dapoigny (Eds.), Advances in applied artificial intelligence, Vol. 4031 of Lecture notes in computer science (pp. 1159–1168). Berlin: Springer.
Kemme, N. (2011b). RMG crane scheduling and stacking: overview and implications on terminal planning. In J. W. Böse, R. Sharda, & S. Voß (Eds.), Handbook of terminal planning, Vol. 49 of Operations research/computer science interfaces series (pp. 271–301). Berlin: Springer.
Kemme, N. (2011c). RMGC simulation model – documentation of a simulation model for automated rail-mounted-gantry-crane systems at seaport container terminals. Institute for Operations Research, University of Hamburg. www.uni-hamburg.de/OR/RMGC-Simulation, Accessed 09 September 2011.
Kim, K. H. (1997). Evaluating the number of rehandles in container yards. Computer and Industrial Engineering, 32(4), 701–711.
Kim, K. H., & Bae, J. W. (1998). Re-marshalling export containers in port container terminals. Computer and Industrial Engineering, 35(3/4), 655–658.
Kim, K. H., & Hong, G.-P. (2006). A heuristic rule for relocating blocks. Computers and Operations Research, 33(4), 940–954.
Kim, K. H., & Kim, H. B. (1999a). Segregating space allocation models for container inventories in port container terminals. International Journal of Production Economics, 59(1–3), 415–423.
Kim, K. H., & Kim, K. Y. (1999b). An optimal routing algorithm for a transfer crane in port container terminals. Transportation Science, 33(1), 17–33.
Kim, K. H., Park, Y. M., & Ryu, K. R. (2000). Deriving decision rules to locate export containers in container yards. European Journal of Operational Research, 124(1), 89–100.
Kim, K. H., Wang, S. J., Park, Y.-M., Yang, C.-H., & Bae, J. W. (2002). A simulation study on operation rules for automated container yards. In Proceedings of the 7th annual international conference on industrial engineering, Busan (pp. 250–253).
Kim, K. H., Kang, J. S., & Ryu, K. R. (2004). A beam search algorithm for the load sequencing of outbound containers in port container terminals. In H.-O. Günther & K. H. Kim (Eds.), Container terminals and automated transport systems (pp. 183–206). Berlin: Springer.
Kim, K. Y., & Kim, K. H. (1997). A routing algorithm for a single transfer crane to load export containers onto a containership. Computer and Industrial Engineering, 33(3/4), 673–676.
Kim, K. Y., & Kim, K. H. (2003). Heuristic algorithms for routing yard-side equipment for minimizing loading times in container terminals. Naval Research Logistics, 50(5), 498–514.
Kozan, E., & Preston, P. (1999). Genetic algorithms to schedule container transfers at multi-modal terminals. International Transactions in Operational Research, 6(3), 311–329.
Lee, D.-H., Meng, Q., & Cao, Z. (2006). Scheduling of multiple-yard crane system with container loading sequence consideration. In TRB 85th annual meeting compendium of papers CD-ROM (pp. 1–16).
Lee, D.-H., Cao, Z., & Meng, Q. (2007). Scheduling of two-transtainer systems for loading outbound containers in port container terminals with simulated annealing algorithm. International Journal of Production Economics, 107(1), 115–124.
Lee, L. H., Chew, E. P. Tan, K. C., & Han, Y. (2006). An optimization model for storage yard management in transshipment hubs. OR Spectrum, 28(4), 539–561.
Lee, Y., & Hsu, N.-Y. (2007). An optimization model for the container pre-marshalling problem. Computers and Operations Research, 34(11), 3295–3313.
Li, W., Wu, Y., Petering, M. E. H., Goh, M., & de Souza, R. (2009). Discrete time model and algorithms for container yard crane scheduling. European Journal of Operational Research, 198(1), 165–172.
Linn, R. J., & Zhang, C.-Q. (2003). A heuristic for dynamic yard crane deployment in a container terminal. IIE Transactions, 35(2), 161–174.
Meersmans, P. J. M. (2002). Optimization of container handling systems. Ph.D. Thesis, Tinbergen Institute, Rotterdam.
Mühlenbein, H. (1997). Genetic algorithms. In E. H. L. Aarts & J. K. Lenstra (Eds.), Local search in combinatorial optimization (pp. 137–171). Princeton, NJ: Princeton University Press.
Mühlenbein, H., & Schlierkamp-Voosen, D. (1995). Analysis of selection, mutation and recombination in genetic algorithms. In W. Banzhaf & F. Eeckman (Eds.), Evolution and biocomputation, Vol. 899 of Lecture notes in computer science (pp. 142–168). Berlin: Springer.
Murty, K. G., Liu, J., Wan, Y.-W., & Linn, R. (2005). a decision support system for operations in a container terminal. Decision Support Systems, 39(3), 309–332.
Narasimhan, A., & Palekar, U. S. (2002). Analysis and algorithms for the transtainer routing problem in container port operations. Transportation Science, 36(1), 63–78.
Ng, W. C. (2005). Crane scheduling in container yards with inter-crane interference. European Journal of Operational Research, 164(1), 64–78.
Ng, W. C., & Mak, K. L. (2005a). An effective heuristic for scheduling a yard crane to handle jobs with different ready times. Engineering Optimization, 37(8), 867–877.
Ng, W. C., & Mak, K. L. (2005b). Yard crane scheduling in port container terminals. Applied Mathematical Modelling, 29(3), 263–276.
Park, B., Choi, H., Kwon, H., & Kang, M. (2006). Simulation analysis on effective operation of handling equipments in automated container terminal. In A. Sattar & B.-H. Kang (Eds.), AI 2006: Advances in artificial intelligence, Vol. 4304 of Lecture notes in computer science (pp. 1231–1238). Berlin: Springer.
Park, T., Choe, R., Ok, S., & Ryu, K. R. (2010). Real-time scheduling for twin RMGs in an automated container yard. OR Spectrum, 32(3), 593–615.
Park, T., Choe, R., Kim, Y. H., & Ryu, K. R. (2011). Dynamic adjustment of container stacking policy in an automated container terminal. International Journal of Production Economics, 133(1), 385–392.
Petering, M. E. H., Wu, Y., Li, W., Goh, M., & de Souza, R. (2009). Development and simulation analysis of real-time yard crane control systems for seaport container transshipment terminals. OR Spectrum, 31(4), 801–835.
Saanen, Y. A. (2004). An approach for designing robotized maritime container terminals. Ph.D. Thesis, Technical University of Delft, Rotterdam.
Saanen, Y. A., & Dekker, R. (2006a). Intelligent stacking as way out of congested yards? Part1. Port Technology International, 31 (pp. 87–92).
Saanen, Y. A., & Dekker, R. (2006b). Intelligent stacking as way out of congested yards? Part2. Port Technology International, 32 (pp. 80–86).
Saanen, Y. A., van Meel, J., & Verbraeck, A. (2003). The design and assessement of next generation automated container terminals. In A. Verbraeck & V. Hlupic (Eds.), Proceedings 15th European simulation symposium, Delft (pp. 1–8).
Sniedovich, M., & Voß, S. (2006). The corridor method: a dynamic programming inspired metaheuristic. Control and Cybernetics, 35(2), 551–578.
Speer, U., John, G., & Fischer, K. (2011). Scheduling yard cranes considering crane interference. In J. Böse, H. Hu, C. Jahn, X. Shi, R. Stahlbock, & S. Voß (Eds.), Computational logistics, Vol. 6971 of Lecture notes in computer science (pp. 321–340). Berlin: Springer.
Stahlbock, R., & Voß, S. (2010). Efficiency considerations for sequencing and scheduling of double-rail-mounted gantry cranes at maritime container terminals. International Journal of Shipping and Transport Logistics, 2(1), 95–123.
Steenken, D., Voß, S., & Stahlbock, R. (2004). Container terminal operation and operations research - a classification and literature review. OR Spectrum, 26(1), 3–49.
Taleb-Ibrahimi, M., de Castilho, B., & Daganzo, C. F. (1993). Storage space vs handling work in container terminals. Transportation Research Part B: Methodological, 27(1), 13–32.
Urlings, T., Ruiz, R., & Serifoglu, F. S. (2010). Genetic algorithms with different representation schemes for complex hybrid flexible flow line problems. International Journal Metaheuristics, 1(1), 30–54.
Valkengoed, M. P. J. v. (2004). How passing cranes influence stack operations in a container terminal: a simulation study. Diploma Thesis, University of Amsterdam.
Vis, I. F. A., & Carlo, H. J. (2010). Sequencing two cooperating automated stacking cranes in a container terminal. Transportation Science, 44(2), 169–182.
Vis, I. F. A., & Roodbergen, K. J. (2009). Scheduling of container storage and retrieval. Operations Research, 57(2), 456–467.
Voß, S. (2001). Meta-heuristics: The state of the art. In A. Nareyek (Ed.), Local search for planning and scheduling, Vol. 2148 of Lecture notes in computer science (pp. 1–23). Berlin: Springer.
Zhang, C., Wan, Y.-W., Liu, J., & Linn, R. J. (2002). Dynamic crane deployment in container storage yards. Transportation Research Part B: Methodological, 36(6), 537–555.
Zhang, C., Chen, W., Shi, L., & Zheng, L. (2010). A note on deriving decision rules to locate export containers in container yards. European Journal of Operational Research, 205(2), 483–485.
Zyngiridis, I. (2005). Optimizing Container Movements Using one and two Automated Stacking Cranes. Master Thesis, Naval Postgraduate School Monterry, Monterey, CA.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Kemme, N. (2013). Operational RMGC-Planning Problems. In: Design and Operation of Automated Container Storage Systems. Contributions to Management Science. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-2885-6_5
Download citation
DOI: https://doi.org/10.1007/978-3-7908-2885-6_5
Published:
Publisher Name: Physica, Heidelberg
Print ISBN: 978-3-7908-2884-9
Online ISBN: 978-3-7908-2885-6
eBook Packages: Business and EconomicsBusiness and Management (R0)