Abstract
The container retrieval problem (CRP) is a very important issue for container terminals. The CRP seeks to find an optimal sequence of operations for the crane to retrieve all the containers from the bay according to a predefined order. An optimal sequence of operations is obtained by either reducing the number of container relocations or reducing any kind of working cost performed by the crane, i.e., energy, time, etc. Although the former is the main objective function discussed in the literature, minimizing the number of relocations does not ensure the solution with the minimal working cost, as evidenced in this paper. Therefore, in this study, a crane’s trajectory is defined to better measure the crane’s working cost, and the optimization goal is to minimize the crane’s working time considering the crane’s trajectory. Moreover, it proposes exact methods and a reactive GRASP algorithm for the CRP. The experimental results show that the proposed algorithm is able to provide better solutions for both the number of container relocations and the crane’s working time, when compared to heuristic approaches in the recent literature.













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Azari, E.: Notes on “A mathematical formulation and complexity considerations for the blocks relocation problem”. Sci. Iran. 22(6), 2722–2728 (2015)
Carlo, H.J., Vis, I.F., Roodbergen, K.J.: Storage yard operations in container terminals: literature overview, trends, and research directions. Eur. J. Oper. Res. 235(2), 412–430 (2014). https://doi.org/10.1016/j.ejor.2013.10.054
Carraro, L.A., De Castro L.N.: A clonal selection algorithm for the container stacking problem. In: Proceedings of the 2011 3rd World Congress on Nature and Biologically Inspired Computing, pp 569–574. IEEE (2011). https://doi.org/10.1109/NaBIC.2011.6089651
Caserta, M., Voß, S., Sniedovich, M.: Applying the corridor method to a blocks relocation problem. OR Spectr. 33(4), 915–929 (2011). https://doi.org/10.1007/s00291-009-0176-5
Caserta, M., Schwarze, S., Voß, S.: A mathematical formulation and complexity considerations for the blocks relocation problem. Eur. J. Oper. Res. 219(1), 96–104 (2012). https://doi.org/10.1016/j.ejor.2011.12.039
Casey, B., Kozan, E.: Optimising container storage processes at multimodal terminals. J. Oper. Res. Soc. 63(8), 1126–1142 (2012). https://doi.org/10.1016/S0895-7177(00)00092-3
Deng, Y., Bard, J.F.: A reactive grasp with path relinking for capacitated clustering. J. Heuristics 17(2), 119–152 (2011). https://doi.org/10.1007/s10732-010-9129-z
de Melo da Silva M, Erdoğan, G., Battarra, M., Strusevich V.: The block retrieval problem. Eur. J. Oper. Res. 265(3), 931–950 (2018). https://doi.org/10.1016/j.ejor.2017.08.048
Expósito-Izquierdo, C., Melián-Batista, B., Moreno-Vega, J.M.: Pre-marshalling problem: heuristic solution method and instances generator. Expert Syst. Appl. 39(9), 8337–8349 (2012). https://doi.org/10.1016/j.eswa.2012.01.187
Expósito-Izquierdo, C., Melián-Batista, B., Moreno-Vega, J.M.: A domain-specific knowledge-based heuristic for the blocks relocation problem. Adv. Eng. Inform. 28(4), 327–343 (2014). https://doi.org/10.1016/j.aei.2014.03.003
Expósito-Izquierdo, C., Melián-Batista, B., Moreno-Vega, J.M.: An exact approach for the blocks relocation problem. Expert Syst. Appl. 42(17–18), 6408–6422 (2015). https://doi.org/10.1016/j.eswa.2015.04.021
Firmino, A.S., Silva, R.M.A., Times, V.C.: An exact approach for the container retrieval problem to reduce crane’s trajectory. In: 2016 IEEE 19th International Conference on Intelligent Transportation Systems (ITSC), pp 933–938 (2016a). https://doi.org/10.1109/itsc.2016.7795667
Firmino, A.S., Times, V.C., Silva, R.M.A., Mateus, G.R.: Reactive grasp with path relinking for selecting olap views. In: XLVIII SBPO (2016) (2016b). www.sbpo2016.iltc.br/pdf/156026.pdf
Forster, F., Bortfeldt, A.: A tree search heuristic for the container retrieval problem. In: Klatte D, Lüthi HJ, Schmedders K (eds) Operations Research Proceedings 2011 SE - 41, Operations Research Proceedings, pp. 257–262. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-29210-1_41
Galle, V., Barnhart, C., Jaillet, P.: A new binary formulation of the restricted container relocation problem based on a binary encoding of configurations. Eur. J. Oper. Res. 267, 467–477 (2018). https://doi.org/10.1016/j.ejor.2017.11.053
Hakan Akyüz, M., Lee, C.Y.: A mathematical formulation and efficient heuristics for the dynamic container relocation problem. Nav. Res. Logist. 61(2), 101–118 (2014). https://doi.org/10.1002/nav.21569
Hussein, M., Petering, M.E.H.: Genetic algorithm-based simulation optimization of stacking algorithms for yard cranes to reduce fuel consumption at seaport container transshipment terminals. In: 2012 IEEE Congress on Evolutionary Computation (CEC), pp. 1–8. IEEE (2012). https://doi.org/10.1109/CEC.2012.6256471
Jin, B., Zhu, W., Lim, A.: Solving the container relocation problem by an improved greedy look-ahead heuristic. Eur. J. Oper. Res. 240(3), 837–847 (2015). https://doi.org/10.1016/j.ejor.2014.07.038
Jovanovic, R., Voß, S.: A chain heuristic for the blocks relocation problem. Comput. Ind. Eng. 75, 79–86 (2014). https://doi.org/10.1016/j.cie.2014.06.010
Kim, K.H., Hong, G.P.: A heuristic rule for relocating blocks. Comput. Oper. Res. 33(4), 940–954 (2006). https://doi.org/10.1016/j.cor.2004.08.005
Kim, Y., Kim, T., Lee, H.: Heuristic algorithm for retrieving containers. Comput. Ind. Eng. (2016). https://doi.org/10.1016/j.cie.2016.08.022
Ku, D., Arthanari, T.S.: On the abstraction method for the container relocation problem. Comput. Oper. Res. 68, 110–122 (2016). https://doi.org/10.1016/j.cor.2015.11.006
Lee, Y., Lee, Y.J.: A heuristic for retrieving containers from a yard. Comput. Oper. Res. 37(6), 1139–1147 (2010). https://doi.org/10.1016/j.cor.2009.10.005
Li, J., Yu, H.X.: Optimizing retrieval sequencing in container yards. In: Proceedings—2010 International Conference on Optoelectronics and Image Processing, IEEE, vol. 2, pp. 90–92 (2010). https://doi.org/10.1109/ICOIP.2010.236
Lin, D.Y., Lee, Y.J., Lee, Y.: The container retrieval problem with respect to relocation. Transp. Res. C Emerg. Technol. 52, 132–143 (2015). https://doi.org/10.1016/j.trc.2015.01.024
Murty, K.G., Liu, J., Yw, Wan, Linn, R.: A decision support system for operations in a container terminal. Decis. Support Syst. 39(3), 309–332 (2005). https://doi.org/10.1016/j.dss.2003.11.002
Olsen, M., Gross, A.: Average case analysis of blocks relocation heuristics. In: González-Ramírez, R.G., Schulte, F., Voß, S., Ceroni Díaz, J.A. (eds.) Computational Logistics. ICCL 2014, pp. 81–92. Springer International Publishing (2014). https://doi.org/10.1007/978-3-319-11421-7_6
Petering, M.E., Hussein, M.I.: A new mixed integer program and extended look-ahead heuristic algorithm for the block relocation problem. Eur. J. Oper. Res. 231(1), 120–130 (2013). https://doi.org/10.1016/j.ejor.2013.05.037
Resende, M., Ribeiro, C.: Optimization by GRASP: Greedy Randomized Adaptive Search Procedures. Springer, New York (2016). https://doi.org/10.1007/978-1-4939-6530-4
Sheskin, D.J.: Handbook of Parametric and Nonparametric Statistical Procedures, 4th edn. Chapman & Hall/CRC, Boca Raton (2007)
Tanaka, S., Takii, K.: A faster branch-and-bound algorithm for the block relocation problem. Autom. Sci. Eng. 13(1), 181–190 (2016). https://doi.org/10.1109/TASE.2015.2434417
Ting, C.J., Wu, K.C.: Optimizing container relocation operations at container yards with beam search. Transp. Res. E Logist. Transp. Rev. 103, 17–31 (2017). https://doi.org/10.1016/j.tre.2017.04.010
Tricoire, F., Scagnetti, J., Beham, A.: New insights on the block relocation problem. Comput. Oper. Res. 89, 127–139 (2018). https://doi.org/10.1016/J.COR.2017.08.010
Ünlüyurt, T., Aydin, C.: Improved rehandling strategies for the container retrieval process. J. Adv. Transp. 46(4), 378–393 (2012). https://doi.org/10.1002/atr.1193
Wan, Y., Liu, J., Tsai, P.C.: The assignment of storage locations to containers for a container stack. Nav. Res. Logist. 56(8), 699–713 (2009). https://doi.org/10.1002/nav.20373
World Bank: Container port traffic (teu: 20 foot equivalent units) (2018). http://data.worldbank.org/indicator/IS.SHP.GOOD.TU?end=2018&start=2000. Accessed 04 June 2018
Wu, K.C., Ting, C.J.: A beam search algorithm for minimizing reshuffle operations at container yards. In: International Conference on Logistics and Maritime Systems, pp. 15–17 (2010)
Wu, K.C., Ting, C.J.: Heuristic approaches for minimizing reshuffle operations at container yard. In: Kachitvichyanukul, V., Luong, H.T., Pitakaso, R. (eds.) Asia Pacific Industrial Engineering and Management Systems Conference, pp. 1407–1415 (2012)
Zehendner, E., Caserta, M., Feillet, D., Schwarze, S., Voß, S.: An improved mathematical formulation for the blocks relocation problem. Eur. J. Oper. Res. 245(2), 415–422 (2015). https://doi.org/10.1016/j.ejor.2015.03.032
Zhang, C.: Resource planning in container storage yard. Ph.D. thesis, Hong Kong University of Science and Technology (2000)
Zhang, H., Guo, S., Zhu, W., Lim, A., Cheang, B.: An investigation of ida* algorithms for the container relocation problem. In: García-Pedrajas, N., Herrera, F., Fyfe, C., Benítez, J.M., Ali, M. (eds.) Trends in Applied Intelligent Systems SE - 4, Lecture Notes in Computer Science, vol. 6096, pp. 31–40. Springer, Berlin (2010). https://doi.org/10.1007/978-3-642-13022-9_4
Zhu, W., Qin, H., Lim, A., Zhang, H.: Iterative deepening a* algorithms for the container relocation problem. Autom. Sci. Eng. 9(4), 710–722 (2012). https://doi.org/10.1109/TASE.2012.2198642
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da Silva Firmino, A., de Abreu Silva, R.M. & Times, V.C. A reactive GRASP metaheuristic for the container retrieval problem to reduce crane’s working time. J Heuristics 25, 141–173 (2019). https://doi.org/10.1007/s10732-018-9390-0
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DOI: https://doi.org/10.1007/s10732-018-9390-0