# American Institute of Mathematical Sciences

## Modeling and solution for inbound container storage assignment problem in dual cycling mode

 Logistics Engineering College, Shanghai Maritime University, Shanghai 201306, China

* Corresponding author: Weijian Mi

Received  March 2019 Revised  May 2019 Published  December 2019

As an indispensable decision problem in both artificial and automated container terminals, storage assignment has been the research focus for many years. In this research, storage assignment in quay crane dual cycling mode is discussed since dual cycling is a widely used handling method to improve handling efficiency. Tractor dual cycling is also considered to optimize horizontal transportation efficiency. A mixed integer programming model is proposed to formulate this problem, and a CF algorithm is proposed for solution. Validity and effectiveness of proposed algorithm is verified by numerical experiments.

Citation: Ning Zhao, Mengjue Xia, Weijian Mi. Modeling and solution for inbound container storage assignment problem in dual cycling mode. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2020208
##### References:
 [1] M. Bazzazi, N. Safaei and N. Javadian, A genetic algorithm to solve the storage space allocation problem in a container terminal, Computers & Industrial Engineering, 56 (2009), 44-52.  doi: 10.1016/j.cie.2008.03.012.  Google Scholar [2] L. Chen and Z. Lu, The storage location assignment problem for outbound containers in a maritime terminal, International Journal of Production Economics, 135 (2012), 73-80.  doi: 10.1016/j.ijpe.2010.09.019.  Google Scholar [3] C.-Y. Chung and J.-Y. Shin, Efficient yard operation for the dual cycling in container terminal, Journal of Navigation and Port Research, 35 (2011), 71-76.  doi: 10.5394/KINPR.2011.35.1.71.  Google Scholar [4] J.-F. Cordeau, M. Gaudioso, G. Laporte and L. Moccia, The service allocation problem at the gioia tauro maritime terminal, European Journal of Operational Research, 176 (2007), 1167-1184.  doi: 10.1016/j.ejor.2005.09.004.  Google Scholar [5] Z. Fu, Y. Li, A. Lim and B. 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Weijian, Storage allocation in automated container terminals: The upper level, Polish Maritime Research, 23 (2016), 160-174.  doi: 10.1515/pomr-2016-0061.  Google Scholar [14] C. Mi, Y. Shen, W. Mi and Y. Huang, Ship identification algorithm based on 3d point cloud for automated ship loaders, Journal of Coastal Research, 73 (2015), 28-34.  doi: 10.2112/SI73-006.1.  Google Scholar [15] C. Mi, J. Wang, W. Mi, Y. Huang, Z. Zhang, Y. Yang, J. Jiang and P. Octavian, Research on regional clustering and two-stage svm method for container truck recognition, Discrete & Continuous Dynamical Systems-Series S, 12 (2009), 1117-1133.   Google Scholar [16] C. Mi, Z.-W. Zhang, Y.-F. Huang and Y. Shen, A fast automated vision system for container corner casting recognition, Journal of Marine Science and Technology. Google Scholar [17] K. G. Murty, Yard crane pools and optimum layouts for storage yards of container terminals. Google Scholar [18] K. G. Murty, J. Liu, Y.-w. Wan and R. Linn, A decision support system for operations in a container terminal, Decision Support Systems, 39 (2005), 309-332.  doi: 10.1016/j.dss.2003.11.002.  Google Scholar [19] K. G. Murty, Y.-w. Wan, J. Liu, M. M. Tseng, E. Leung, K.-K. Lai and H. W. Chiu, Hongkong international terminals gains elastic capacity using a data-intensive decision-support system, Interfaces, 35 (2005), 61-75.  doi: 10.1287/inte.1040.0120.  Google Scholar [20] V. D. Nguyen and K.-H. Kim, Minimizing empty trips of yard trucks in container terminals by dual cycle operations, Industrial Engineering and Management Systems, 9 (2010), 28-40.  doi: 10.7232/iems.2010.9.1.028.  Google Scholar [21] E. Nishimura, A. Imai, G. K. Janssens and S. Papadimitriou, Container storage and transshipment marine terminals, Transportation Research Part E: Logistics and Transportation Review, 45 (2009), 771-786.  doi: 10.1016/j.tre.2009.03.003.  Google Scholar [22] T. Park, R. Choe, Y. H. Kim and K. R. Ryu, Dynamic adjustment of container stacking policy in an automated container terminal, International Journal of Production Economics, 133 (2011), 385-392.  doi: 10.1016/j.ijpe.2010.03.024.  Google Scholar [23] Y. J. Woo and K. H. Kim, Estimating the space requirement for outbound container inventories in port container terminals, International Journal of Production Economics, 133 (2011), 293-301.  doi: 10.1016/j.ijpe.2010.04.032.  Google Scholar [24] M. Yu and X. Qi, Storage space allocation models for inbound containers in an automatic container terminal, European Journal of Operational Research, 226 (2013), 32-45.  doi: 10.1016/j.ejor.2012.10.045.  Google Scholar [25] H. Zhang and K. H. Kim, Maximizing the number of dual-cycle operations of quay cranes in container terminals, Computers & Industrial Engineering, 56 (2009), 979-992.  doi: 10.1016/j.cie.2008.09.008.  Google Scholar [26] N. Zhao, M. Xia, C. Mi, Z. Bian and J. Jin, Simulation-based optimization for storage allocation problem of outbound containers in automated container terminals, Mathematical Problems in Engineering, 2015 (2015), Article ID 548762, 14 pages. doi: 10.1155/2015/548762.  Google Scholar

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##### References:
 [1] M. Bazzazi, N. Safaei and N. Javadian, A genetic algorithm to solve the storage space allocation problem in a container terminal, Computers & Industrial Engineering, 56 (2009), 44-52.  doi: 10.1016/j.cie.2008.03.012.  Google Scholar [2] L. Chen and Z. Lu, The storage location assignment problem for outbound containers in a maritime terminal, International Journal of Production Economics, 135 (2012), 73-80.  doi: 10.1016/j.ijpe.2010.09.019.  Google Scholar [3] C.-Y. Chung and J.-Y. Shin, Efficient yard operation for the dual cycling in container terminal, Journal of Navigation and Port Research, 35 (2011), 71-76.  doi: 10.5394/KINPR.2011.35.1.71.  Google Scholar [4] J.-F. Cordeau, M. Gaudioso, G. Laporte and L. Moccia, The service allocation problem at the gioia tauro maritime terminal, European Journal of Operational Research, 176 (2007), 1167-1184.  doi: 10.1016/j.ejor.2005.09.004.  Google Scholar [5] Z. Fu, Y. Li, A. Lim and B. Rodrigues, Port space allocation with a time dimension, Journal of the Operational Research Society, 58 (2007), 797-807.  doi: 10.1057/palgrave.jors.2602192.  Google Scholar [6] E. Guldogan, Simulation-based analysis for hierarchical storage assignment policies in a container terminal, Simulation, 87 (2011), 523-537.  doi: 10.1177/0037549710369812.  Google Scholar [7] Y. Han, L. H. Lee, E. P. Chew and K. C. Tan, A yard storage strategy for minimizing traffic congestion in a marine container transshipment hub, OR spectrum, 30 (2008), 697-720.  doi: 10.1007/s00291-008-0127-6.  Google Scholar [8] J. S. Huang and Z. Z. Ren, Research on sa-based addressing model of slot in container terminal, in Applied Mechanics and Materials, Trans Tech Publ, 97 (2011), 985–989. doi: 10.4028/www.scientific.net/AMM.97-98.985.  Google Scholar [9] Y.-H. Jeong, K.-H. Kim, Y.-J. Woo and B.-H. Seo, A simulation study on a workload-based operation planning method in container terminals, Industrial Engineering and Management Systems, 11 (2012), 103-113.  doi: 10.7232/iems.2012.11.1.103.  Google Scholar [10] X. Jiang, L. H. Lee, E. P. Chew, Y. Han and K. C. Tan, A container yard storage strategy for improving land utilization and operation efficiency in a transshipment hub port, European Journal of Operational Research, 221 (2012), 64-73.  doi: 10.1016/j.ejor.2012.03.011.  Google Scholar [11] N. Laik and E. Hadjiconstantnou, Container assignment and yard crane deployment in a container terminal: A case study, Maritime Economics & Logistics, 10 (2008), 90-107.  doi: 10.1057/palgrave.mel.9100193.  Google Scholar [12] L. H. Lee, E. P. Chew, K. C. Tan and Y. Han, An optimization model for storage yard management in transshipment hubs, in Container Terminals and Cargo Systems, Springer, 2007,107–129. doi: 10.1007/978-3-540-49550-5_6.  Google Scholar [13] X. Mengjue, Z. Ning and M. Weijian, Storage allocation in automated container terminals: The upper level, Polish Maritime Research, 23 (2016), 160-174.  doi: 10.1515/pomr-2016-0061.  Google Scholar [14] C. Mi, Y. Shen, W. Mi and Y. Huang, Ship identification algorithm based on 3d point cloud for automated ship loaders, Journal of Coastal Research, 73 (2015), 28-34.  doi: 10.2112/SI73-006.1.  Google Scholar [15] C. Mi, J. Wang, W. Mi, Y. Huang, Z. Zhang, Y. Yang, J. Jiang and P. Octavian, Research on regional clustering and two-stage svm method for container truck recognition, Discrete & Continuous Dynamical Systems-Series S, 12 (2009), 1117-1133.   Google Scholar [16] C. Mi, Z.-W. Zhang, Y.-F. Huang and Y. Shen, A fast automated vision system for container corner casting recognition, Journal of Marine Science and Technology. Google Scholar [17] K. G. Murty, Yard crane pools and optimum layouts for storage yards of container terminals. Google Scholar [18] K. G. Murty, J. Liu, Y.-w. Wan and R. Linn, A decision support system for operations in a container terminal, Decision Support Systems, 39 (2005), 309-332.  doi: 10.1016/j.dss.2003.11.002.  Google Scholar [19] K. G. Murty, Y.-w. Wan, J. Liu, M. M. Tseng, E. Leung, K.-K. Lai and H. W. Chiu, Hongkong international terminals gains elastic capacity using a data-intensive decision-support system, Interfaces, 35 (2005), 61-75.  doi: 10.1287/inte.1040.0120.  Google Scholar [20] V. D. Nguyen and K.-H. Kim, Minimizing empty trips of yard trucks in container terminals by dual cycle operations, Industrial Engineering and Management Systems, 9 (2010), 28-40.  doi: 10.7232/iems.2010.9.1.028.  Google Scholar [21] E. Nishimura, A. Imai, G. K. Janssens and S. Papadimitriou, Container storage and transshipment marine terminals, Transportation Research Part E: Logistics and Transportation Review, 45 (2009), 771-786.  doi: 10.1016/j.tre.2009.03.003.  Google Scholar [22] T. Park, R. Choe, Y. H. Kim and K. R. Ryu, Dynamic adjustment of container stacking policy in an automated container terminal, International Journal of Production Economics, 133 (2011), 385-392.  doi: 10.1016/j.ijpe.2010.03.024.  Google Scholar [23] Y. J. Woo and K. H. Kim, Estimating the space requirement for outbound container inventories in port container terminals, International Journal of Production Economics, 133 (2011), 293-301.  doi: 10.1016/j.ijpe.2010.04.032.  Google Scholar [24] M. Yu and X. Qi, Storage space allocation models for inbound containers in an automatic container terminal, European Journal of Operational Research, 226 (2013), 32-45.  doi: 10.1016/j.ejor.2012.10.045.  Google Scholar [25] H. Zhang and K. H. Kim, Maximizing the number of dual-cycle operations of quay cranes in container terminals, Computers & Industrial Engineering, 56 (2009), 979-992.  doi: 10.1016/j.cie.2008.09.008.  Google Scholar [26] N. Zhao, M. Xia, C. Mi, Z. Bian and J. Jin, Simulation-based optimization for storage allocation problem of outbound containers in automated container terminals, Mathematical Problems in Engineering, 2015 (2015), Article ID 548762, 14 pages. doi: 10.1155/2015/548762.  Google Scholar
Quay crane dual cycling process
Dual-cycle Handling of tractors
Sequential yard crane handling
Correlation between number of variables and peak mem. cost
Correlation between number of containers and peak mem. cost
Correlation between number of variables and solving time
Correlation between number of containers and solving time
Inbound container information
 Container NO. Size Type Specialty Status Owner POD CCLU7598392 20 FR IF APL CNSHA CCLU4837684 20 GP HZ IF NYK CNSHA CCLU9077976 40 GP IF NYK CNSHA CCLU8798962 40 GP IF CSC CNSHA CCLU5745463 40 GP IF APL CNSHA CCLU7586903 45 GP IF CSC CNSHA
 Container NO. Size Type Specialty Status Owner POD CCLU7598392 20 FR IF APL CNSHA CCLU4837684 20 GP HZ IF NYK CNSHA CCLU9077976 40 GP IF NYK CNSHA CCLU8798962 40 GP IF CSC CNSHA CCLU5745463 40 GP IF APL CNSHA CCLU7586903 45 GP IF CSC CNSHA
Storage Plan
 Block Bay Size Type Specialty Status Owner POD Capacity A1 02 40 GP IF 2 A1 06 40 GP IF 4 A2 02 40 GP IF 3 A2 06 40 GP IF 6 A3 02 45 GP IF 2 A3 06 40 GP HZ IF 6 B1 01 20 FR IF 2 B1 03 20 FR IF 2 B1 05 20 FR IF 5 B2 01 20 GP IF 5 B2 03 20 GP IF 5 B2 05 20 GP IF 6 B3 01 20 GP HZ IF 8
 Block Bay Size Type Specialty Status Owner POD Capacity A1 02 40 GP IF 2 A1 06 40 GP IF 4 A2 02 40 GP IF 3 A2 06 40 GP IF 6 A3 02 45 GP IF 2 A3 06 40 GP HZ IF 6 B1 01 20 FR IF 2 B1 03 20 FR IF 2 B1 05 20 FR IF 5 B2 01 20 GP IF 5 B2 03 20 GP IF 5 B2 05 20 GP IF 6 B3 01 20 GP HZ IF 8
YC Coverage
 YC Number of Tasks Status Block Coverage L01 3 Operational A1 L02 4 In Malfunction A2 L03 5 Operational A3 L04 3 Operational B1 L05 2 Operational B2 L06 3 Operational B3
 YC Number of Tasks Status Block Coverage L01 3 Operational A1 L02 4 In Malfunction A2 L03 5 Operational A3 L04 3 Operational B1 L05 2 Operational B2 L06 3 Operational B3
Tractor information
 Container NO. Tractor Tractor Pool Blocks of Load Tasks of Tractor CCLU9077976 T01 2 CPLU8798962 T02 0 B2 CCLU5745463 T03 1 A3 CCLU4837684 T04 1 A3 CCLU7598392 T04 1 A3 CCLU7586903 T05 1 A3
 Container NO. Tractor Tractor Pool Blocks of Load Tasks of Tractor CCLU9077976 T01 2 CPLU8798962 T02 0 B2 CCLU5745463 T03 1 A3 CCLU4837684 T04 1 A3 CCLU7598392 T04 1 A3 CCLU7586903 T05 1 A3
Case Solution
 CCLU 9077976 CPLU 8798962 CCLU 5745463 CCLU 7598392 CCLU 4837684 CCLU 7586903 A1 02 $\sqrt{}$ $\sqrt{}$ A3 02 $\sqrt{}$ A3 06 $\sqrt{}$ B1 01 $\sqrt{}$ B3 01 $\sqrt{}$
 CCLU 9077976 CPLU 8798962 CCLU 5745463 CCLU 7598392 CCLU 4837684 CCLU 7586903 A1 02 $\sqrt{}$ $\sqrt{}$ A3 02 $\sqrt{}$ A3 06 $\sqrt{}$ B1 01 $\sqrt{}$ B3 01 $\sqrt{}$
Cases for Efficiency Analysis
 Case Containers Yard Bays Variables Solving Time(s) Peak Mem.(Mb) Case 1 6 6 36 0.02 1.9 Case 2 6 8 48 0.04 2.2 Case 3 6 9 54 0.05 2.5 Case 4 7 8 56 0.06 2.8 Case 5 8 9 72 0.08 3.1 Case 6 8 10 80 0.09 3.4 Case 7 10 11 110 0.11 4.8 Case 8 15 16 240 0.2 10.1 Case 9 20 21 420 0.4 18.0 Case 10 25 30 750 1.2 33.5
 Case Containers Yard Bays Variables Solving Time(s) Peak Mem.(Mb) Case 1 6 6 36 0.02 1.9 Case 2 6 8 48 0.04 2.2 Case 3 6 9 54 0.05 2.5 Case 4 7 8 56 0.06 2.8 Case 5 8 9 72 0.08 3.1 Case 6 8 10 80 0.09 3.4 Case 7 10 11 110 0.11 4.8 Case 8 15 16 240 0.2 10.1 Case 9 20 21 420 0.4 18.0 Case 10 25 30 750 1.2 33.5
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