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August & September  2019, 12(4&5): 1101-1115. doi: 10.3934/dcdss.2019076

## An AIMMS-based decision-making model for optimizing the intelligent stowage of export containers in a single bay

 1 Scientific Research Academy, Shanghai Maritime University, China 2 Jiujiang Port Co. Ltd of Shanghai International Port Group, Jiangxi Province, China 3 Container Supply Chain Tech. Engineering Research Center, Shanghai Maritime University, China

* Corresponding author: Weijian Mi

Received  June 2017 Revised  November 2017 Published  November 2018

Stowage operations in container terminals are an important part of a port's operational system, as the quality of stowage operations will directly affect the efficiency of port loading and discharge operations, and the scheduling of container shipping liners. The intelligent stowage of containers in container ships was studied in this work. A multi-objective integer programming model was constructed with the minimization of container rehandling, yard crane movements, and the sum of weight differences between stacked container pairs as its objective functions, to address the need for intelligent optimization of single bay export container stowage on a ship's deck. This model also satisfies the stability requirements of preliminary stowage plans drawn by shipping companies, and the operational requirements of container terminals. Linear computational methods were then constructed to transform non-linear constraints into linear ones for better AIMMS solution. Through numerous case analyses and systematic tests, it was shown that our system is able to rapidly solve for stowage planning optimization problems with complex preliminary stowage data, thus proving the applicability and effectiveness of this model. In particular, the application of this model will simultaneously address the safety of ship voyages, the transportation quality of shipping containers and other forms of cargo, and the cost efficiency of ship operations. In addition, this model will also contribute to the optimization of loading and discharge processes in container terminals. Therefore, our model has immense practical value for improving port productivity, as it will contribute to the organization of port operations in a rational, orderly and effective manner.

Citation: Jian Jin, Weijian Mi. An AIMMS-based decision-making model for optimizing the intelligent stowage of export containers in a single bay. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1101-1115. doi: 10.3934/dcdss.2019076
##### References:
 [1] U. d. G. V. V.. G.. I. Ambrosino Daniela (Dipto. di Econ. e Metodi Quantit., A. Sciomachen and E. Tanfani, Stowing a containership: The master bay plan problem, Transportation Research Part A: Policy and Practice, 28 (2004), 81-99. Google Scholar [2] M. Avriel and M. Penn, Exact and approximate solutions of the container ship stowage problem, Computers & Industrial Engineering, 25 (1993), 271-274.   Google Scholar [3] M. Avriel, M. Penn, N. Shpirer and S. Witteboon, Stowage planning for container ships to reduce the number of shifts, Annals of Operations Research, 55-71. Google Scholar [4] M. Bonamy, B. Lévêque and A. Pinlou, Planar graphs with $≥ 7$ and no triangle adjacent to a c-4 are minimally edge and total choosable, Computer Science, 17 (2016), 131-145.   Google Scholar [5] R. C. Botter and M. A. Brinati, Stowage container planning: A model for getting an poptimal solution, 1992, 217-229. Google Scholar [6] J. Y. Cai, V. T. Khodyreva, E. A. and A. N. Khuziakhmetov, Higher education curricula designing on the basis of the regional labour market demands, Eurasia Journal of Mathematics Science & Technology Education, 13 (2017), 2805-2819.   Google Scholar [7] 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.   Google Scholar [8] Y. Chen, Z. Liu, B. Liu and X. Fu, Research on a fast human-detection algorithm for unmanned surveillance area in bulk ports, 2014, 1-17. Google Scholar [9] E. Elsborg, T. T. Hildebrandt and D. Sangiorgi, A constraint programming model for fast optimal stowage of container vessel bays, Trustworthy Global Computing, 220 (2012), 251-261.  doi: 10.1016/j.ejor.2012.01.028.  Google Scholar [10] H. S. Hwang and G. S. Cho, A hybrid geneticalgorithm with a new packing strategy for the three-dimensional bin packing problem, Applied Mathematics and Computation, 219 (2012), 1287-1299.  doi: 10.1016/j.amc.2012.07.036.  Google Scholar [11] A. Imai, E. Nishimura, S. Papadimitriou and M. Liu, Multi-objective simultaneous stowage and load planning for a container ship with container rehandle in yard stacks, European Journal of Operational Research, 171 (2006), 373-389.   Google Scholar [12] L. Junqueira, R. Morabito and D. S. Yamashita, Three-dimensional container loading models with cargo stability and load bearing constraints, Computers and Operations Research, 39 (2012), 74-85.  doi: 10.1016/j.cor.2010.07.017.  Google Scholar [13] K. H. Kim, J. S. Kang and K. R. Ryu, A beam search algorithm for the load sequencing of outbound containers in port container terminals, Or Spectrum, 26 (2004), 93-116.   Google Scholar [14] Y. Lee and N. Y. Hsu, A heuristic for retrieving containers from a yard, Computers & Operations Research, 37 (2010), 1139-1147.   Google Scholar [15] 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.   Google Scholar [16] C. Mi, Z. Zhang, Y. Huang and Y. Shen, A fast automated vision system for container corner casting recognition, Journal of Marine Science & Technology, 24 (2016), 54-60.   Google Scholar [17] J. Ren, Y. Tian and T. Sawaragi, A tree search method for the container loading problem with shipment priority, European Journal of Operational Research, 526-535. Google Scholar [18] M. A. Salido, M. Rodriguez-Molins and F. Barber, A decision support system for managing combinatorial problems in container terminals, Knowledge-Based Systems, 29 (2012), 63-74.   Google Scholar [19] A. Sciomachen, M. Acciaro and M. Liu, Department of economics and quantitative methods (diem), university of genova, via vivaldi 5, 16126 genova, italy; a 3d-bpp approach for optimising stowage plans and terminal productivity, European Journal of Operational Research, 183 (2007), 1433-1446.   Google Scholar [20] M. Shaabani and L. Pourmemar, On the definition of a probabilistic normed group, Journal of Interdisciplinary Mathematics, 20 (2007), 383-395.   Google Scholar [21] L. B. Si and H. Y. Qiao, Evaluation of technological innovation efficiency in equipment manufacturing industry based on input orientation-panel data analysis based on data envelopment model, Journal of Discrete Mathematical Sciences & Cryptography, 20 (2017), 1381-1386.   Google Scholar [22] I. D. Wilson and P. A. Roach, Principles of combinatorial optimization applied to container-ship stowage planning, Journal of Heuristics, 5 (1999), 403-418.   Google Scholar [23] I. D. Wilson and P. A. Roach, Department of mathematics, university of glamorgan, pontypridd, mid glamorgan cf37 1dl, united kingdom; container stowage pre-planning: Using search to generate solutions, Knowledge-Based Systems, 14 (2001), 137-145.   Google Scholar [24] T. Winter, Online and real-time dispatching problems. Ph.D. Thesis, Technical University of Braunschweig, Germany, 1999. Google Scholar [25] S. Q. Wu, Models for evaluating the technological innovation capability of small and micro enterprises with hesitant fuzzy information, Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology, 32 (2016), 249-256.   Google Scholar

show all references

##### References:
 [1] U. d. G. V. V.. G.. I. Ambrosino Daniela (Dipto. di Econ. e Metodi Quantit., A. Sciomachen and E. Tanfani, Stowing a containership: The master bay plan problem, Transportation Research Part A: Policy and Practice, 28 (2004), 81-99. Google Scholar [2] M. Avriel and M. Penn, Exact and approximate solutions of the container ship stowage problem, Computers & Industrial Engineering, 25 (1993), 271-274.   Google Scholar [3] M. Avriel, M. Penn, N. Shpirer and S. Witteboon, Stowage planning for container ships to reduce the number of shifts, Annals of Operations Research, 55-71. Google Scholar [4] M. Bonamy, B. Lévêque and A. Pinlou, Planar graphs with $≥ 7$ and no triangle adjacent to a c-4 are minimally edge and total choosable, Computer Science, 17 (2016), 131-145.   Google Scholar [5] R. C. Botter and M. A. Brinati, Stowage container planning: A model for getting an poptimal solution, 1992, 217-229. Google Scholar [6] J. Y. Cai, V. T. Khodyreva, E. A. and A. N. Khuziakhmetov, Higher education curricula designing on the basis of the regional labour market demands, Eurasia Journal of Mathematics Science & Technology Education, 13 (2017), 2805-2819.   Google Scholar [7] 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.   Google Scholar [8] Y. Chen, Z. Liu, B. Liu and X. Fu, Research on a fast human-detection algorithm for unmanned surveillance area in bulk ports, 2014, 1-17. Google Scholar [9] E. Elsborg, T. T. Hildebrandt and D. Sangiorgi, A constraint programming model for fast optimal stowage of container vessel bays, Trustworthy Global Computing, 220 (2012), 251-261.  doi: 10.1016/j.ejor.2012.01.028.  Google Scholar [10] H. S. Hwang and G. S. Cho, A hybrid geneticalgorithm with a new packing strategy for the three-dimensional bin packing problem, Applied Mathematics and Computation, 219 (2012), 1287-1299.  doi: 10.1016/j.amc.2012.07.036.  Google Scholar [11] A. Imai, E. Nishimura, S. Papadimitriou and M. Liu, Multi-objective simultaneous stowage and load planning for a container ship with container rehandle in yard stacks, European Journal of Operational Research, 171 (2006), 373-389.   Google Scholar [12] L. Junqueira, R. Morabito and D. S. Yamashita, Three-dimensional container loading models with cargo stability and load bearing constraints, Computers and Operations Research, 39 (2012), 74-85.  doi: 10.1016/j.cor.2010.07.017.  Google Scholar [13] K. H. Kim, J. S. Kang and K. R. Ryu, A beam search algorithm for the load sequencing of outbound containers in port container terminals, Or Spectrum, 26 (2004), 93-116.   Google Scholar [14] Y. Lee and N. Y. Hsu, A heuristic for retrieving containers from a yard, Computers & Operations Research, 37 (2010), 1139-1147.   Google Scholar [15] 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.   Google Scholar [16] C. Mi, Z. Zhang, Y. Huang and Y. Shen, A fast automated vision system for container corner casting recognition, Journal of Marine Science & Technology, 24 (2016), 54-60.   Google Scholar [17] J. Ren, Y. Tian and T. Sawaragi, A tree search method for the container loading problem with shipment priority, European Journal of Operational Research, 526-535. Google Scholar [18] M. A. Salido, M. Rodriguez-Molins and F. Barber, A decision support system for managing combinatorial problems in container terminals, Knowledge-Based Systems, 29 (2012), 63-74.   Google Scholar [19] A. Sciomachen, M. Acciaro and M. Liu, Department of economics and quantitative methods (diem), university of genova, via vivaldi 5, 16126 genova, italy; a 3d-bpp approach for optimising stowage plans and terminal productivity, European Journal of Operational Research, 183 (2007), 1433-1446.   Google Scholar [20] M. Shaabani and L. Pourmemar, On the definition of a probabilistic normed group, Journal of Interdisciplinary Mathematics, 20 (2007), 383-395.   Google Scholar [21] L. B. Si and H. Y. Qiao, Evaluation of technological innovation efficiency in equipment manufacturing industry based on input orientation-panel data analysis based on data envelopment model, Journal of Discrete Mathematical Sciences & Cryptography, 20 (2017), 1381-1386.   Google Scholar [22] I. D. Wilson and P. A. Roach, Principles of combinatorial optimization applied to container-ship stowage planning, Journal of Heuristics, 5 (1999), 403-418.   Google Scholar [23] I. D. Wilson and P. A. Roach, Department of mathematics, university of glamorgan, pontypridd, mid glamorgan cf37 1dl, united kingdom; container stowage pre-planning: Using search to generate solutions, Knowledge-Based Systems, 14 (2001), 137-145.   Google Scholar [24] T. Winter, Online and real-time dispatching problems. Ph.D. Thesis, Technical University of Braunschweig, Germany, 1999. Google Scholar [25] S. Q. Wu, Models for evaluating the technological innovation capability of small and micro enterprises with hesitant fuzzy information, Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology, 32 (2016), 249-256.   Google Scholar
A schematic diagram of the decision making processes in stowage planning
The permissible stacking limit of each stack
The permissible weight limits of each slot
The constraint in the tolerable difference in weight between stacked container pairs
The "bottom-to-top" constraint
A schematic of container rehandling in yard stacks
The effects of stowage plans on the number of yard crane movements
Line chart for comparing computational efficiency
Computational efficiency tests
 Test Number Containers to be Stowed Num. of Ship Slots Num. of Sequences Num. of Variable Nodes Solution Time(s) Memory Usage(M) 1 5 5 5 125 0.1 0.9 2 10 10 10 1000 0.2 1 3 15 15 15 3375 0.3 1.1 4 20 20 20 8000 0.5 1.1 5 25 25 25 15625 0.6 1.2 6 30 30 30 27000 0.9 1.4 7 35 35 35 42875 1.2 1.7 8 40 40 40 64000 1.4 2 9 45 45 45 91125 1.9 2.4 10 50 50 50 125000 2.5 2.8
 Test Number Containers to be Stowed Num. of Ship Slots Num. of Sequences Num. of Variable Nodes Solution Time(s) Memory Usage(M) 1 5 5 5 125 0.1 0.9 2 10 10 10 1000 0.2 1 3 15 15 15 3375 0.3 1.1 4 20 20 20 8000 0.5 1.1 5 25 25 25 15625 0.6 1.2 6 30 30 30 27000 0.9 1.4 7 35 35 35 42875 1.2 1.7 8 40 40 40 64000 1.4 2 9 45 45 45 91125 1.9 2.4 10 50 50 50 125000 2.5 2.8
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