# 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:

show all references

##### References:
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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