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Frontiers of Computer Science

ISSN 2095-2228

ISSN 2095-2236(Online)

CN 10-1014/TP

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Front Comput Sci Chin    0, Vol. Issue () : 486-495    https://doi.org/10.1007/s11704-011-1013-y
RESEARCH ARTICLE
A recursive model for static empty container allocation
Zijian GUO1, Wenyuan WANG1, Guolei TANG1(), Jun HUANG2
1. Faculty of Infrastructure Engineering, Dalian University of Technology, Dalian 116023, China; 2. Transport Planning and Research Institute, Ministry of Communications, Beijing 100028, China
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Abstract

Backlogged empty containers have gradually turned into a serious burden to shipping networks. Empty container allocation has become an urgent settlement issue for the container shipping industry on a global scale. Therefore, this paper proposes an improved immune algorithm based recursive model for optimizing static empty container allocation which integrates with the global maritime container shipping network. This model minimizes the operating and capital costs during container shipping considering 0-1 mixed-integer programming. So an immune algorithm procedure based on a special two-dimensional chromosome encoding is proposed. Finally, computational experiments are performed to optimize a 10-port static empty container shipping system. The results indicate that the proposed recursive model for static empty container allocation is effective in making an optimal strategy for empty container allocation.
Keywords immune algorithm      shipping network      empty container allocation     
Corresponding Author(s): TANG Guolei,Email:tangguolei@gmail.com   
Issue Date: 05 December 2011
 Cite this article:   
Zijian GUO,Wenyuan WANG,Guolei TANG, et al. A recursive model for static empty container allocation[J]. Front Comput Sci Chin, 0, (): 486-495.
 URL:  
https://academic.hep.com.cn/fcs/EN/10.1007/s11704-011-1013-y
https://academic.hep.com.cn/fcs/EN/Y0/V/I/486
Fig.1  Hub-and-spoke network for container transportation
NotationsDefinitions
NThe number of ports in shipping network
i & jThe sequence number of each port
kThe sequence number of the port of origin
tThe sequence number of the destination port
MThe number of ship types, indexed by m
XktOrigin-Destination (O-D) distribution matrices of loaded container in twenty-foot equivalent unit (TEU)
EkThe excess containers at port k (TEU)
StThe demanded containers at port t (TEU)
QmContainer capacity for a ship of type m (TEU)
DijShipping distance between port i and j (nautical miles)
vmAverage service speed for a ship of type m (knots)
CijmShipping cost for a ship of type m from port i to j
CSijmShip-related costs for a ship of type m from port i to j
CPijmPort-related costs for a ship of type m from port i to j
CmCDTime charter cost for a ship of type m
ei (ej)Handling time (loading or unloading) per container at port i (j)
fi (fj)Standby time for departure and arrival at port i (j)
RFuelFuel consumption (g/hp/h)
CFuelFuel cost (US$/metric ton)
RLubLubricant consumption (g/hp/h)
CLubLubricant cost (US$/metric ton)
HPmAverage engine horsepower for a ship of type m
A & BThe constant, AQm + B means port entry cost for a ship of type m (US$)
Ci (Cj)Handling cost per container at port i (j)
Xij′Annual cargo volume of loaded container from port i to j involving transshipped amount (TEU)
Wij′Annual cargo volume of empty container from port i to j involving transshipped amount (TEU)
xijAverage cargo volume of loaded container including transshipped one to a specified ship
wijAverage cargo volume of empty container including transshipped one to a specified ship
qijService frequency of containership from port i to j (vessel/month)
WktO-D (Origin-Destination) distribution matrix of empty container
PktijThe decision variable, showing the relationship of container transshipment process
Tab.1  Notation table
No.AntibodyDepart.Trans. 1Trans. 2Arrival
1X141504
2X161236
3X25.2005
……………
UX6N610N
Tab.2  Sample of the two-dimensional chromosome encoding
PatternDepart.Trans. 1Trans. 2Arrival
Aki0t
Bk0it
Ckit
Tab.3  Redundant antibody examples for
Fig.2  Method to eliminate redundant scheme
Fig.3  OD_e: empty container OD; OD_l: loaded container OD; 2-d: two-dimensional
Flow chart of recursive model for shipping network optimization
SchemeCombination of different ship types
1{1 000, 2 500, 5 000, 7 500, 10 000}
2{500, 1 000, 1 500, 2 500, 3 500}
Tab.4  Combination of different ship types
Fig.4  OD distributions of empty containers of optimum solution for the given carrier (1 000 TEU’s)
Ship tonnage/TEU50010001500250035005000750010000
Charter rates/US$·day-1752511350158002145025700324504300051700
Average speed/Knots151719212324.625.125
Average engine horsepower/kW804616092201152682040231550006200070000
Loading unloading efficiency/TEU·hour-123477195140180270320
Tab.5  Parameters of different containerships
Fig.5  Trend of total cost when = {400, 500, 600, 700}
Fig.6  Trend line of the total cost when = {0.03, 0.05}
Fig.7  Trend of total cost when = {100, 200, 300, 400}
Fig.8  Comparison of the optimized effects
CapacityQDTJDLHKSPSALAVCRDHB
QD-2 5002 5002 5002 50010 0003 50005 0005 000
TJ2 500-2 5002 50010 00010 0002 5005 00007 500
DL2 5002 500-2 5002 50010 0003 5005 0005 0000
HK02 5002 500-2 5005 0003 50010 0007 5007 500
SP7 5002 5007 5002 500-1 0003 50010 00010 00010 000
SA2 5002 500010 0002 500-5 0007 5005 0002 500
LA5 0005 0002 50010 0007 5002 500-2 500075 00
VC01 0001 0007 50007 5002 500-2 5000
RD1 00001 0005 0007 5005 0007 5007 500-2 500
HB2 5002 50001 0007 5005 00010 00010 0002 500-
Tab.6  Allocation of different sized containerships for optimum solution (TEU)
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