考虑港口拥堵和碳减排的航线配船优化模型与策略

doi:10.16381/j.cnki.issn1003-207x.2024.0283

Abstract

Abstract:

In recent years， a discernible incongruence has emerged between the slowly improving service capacity of coastal ports and the escalating pace of maritime requisites. This asymmetry in growth has engendered a recurrent proliferation of port congestion， precipitously impacted the scheduling of maritime fleets and thereby culminated in the clustering of vessels within ports. The confluence of these ramifications has reverberated with profound repercussions upon both regional economies and environmental domains. In response to the entwined issues of port congestion and emissions reduction， a variation inequality model is proffered that optimizes ship routes and allocation strategies. Encompassing considerations of ship propulsion types， varying congestion degrees across distinct ports and alternative harbor options， this model crystallizes around the manifold facets of temporal costs， transport expenditures， and carbon emissions. An improved diagonalization algorithm is devised to solve this problem. Rooted in the context of China's coastal routes， the empirical investigation proffers some insights.As the standard diagonalization algorithm uses network allocation and scalar solutions to determine the iteration direction and step size， it saves 14.61% of the solution time on average to find the same optimal solutions for small-scale problems， compared to the projection algorithm. Furthermore， the improved diagonalization algorithm saves 28.36% of the time compared to the projection algorithm. More importantly， the improved diagonalization algorithm can find the optimal solution within 12，000 seconds for large-scale problems. Lastly， as port congestion intensifies，（1） Shipping enterprises grapple with escalating costs associated with waiting times and voyage schedule losses. （2） A predilection emerges within shipping entities to divert vessels towards alternative harbors. （3） Maritime enterprises gravitate towards more eco-friendly fuels when confronted with the convergence of lowered clean energy costs or elevated carbon taxation rates.

Key words: ocean transportation, route allocation, port congestion, carbon tax, variational inequality

CLC Number:

U121

Shaolong Hu,Xudong Wang,Chuanfeng Han, et al. Optimization Model and Strategies for Route and Fleet Allocation Considering Port Congestion and Carbon Emission Reduction[J]. Chinese Journal of Management Science, 2026, 34(4): 156-167.

Figures/Tables 9

符号	说明
集合
$S$	顶点（港口）集, $s ∈ S$
$A$	弧边（航段）集, $a ∈ A$
$I$	船舶种类集， $i ∈ I$
$W$	O/D（起点/终点）对集， $w ∈ W$
$P$	航线集， $p ∈ P$
$P w$	O/D对 $W$ 的路径集， $P w ⊂ P$
参数/变量
$p$	航线索引， $∀ p ∈ P$
$a$	航段索引， $∀ a ∈ A$
$d w$	O/D对 $w$ 间货物需求
$x a i$	航段 $a$ 上 $i$ 类船舶的数量
$X s$	目的港口为港口 $s$ 的所有航段上的船舶数量总和
$M s$	港口 $s$ 一天内可装卸服务船舶最大数量
$v a i$	航段 $a$ 上 $i$ 类船舶的船速
$v 1$	设计航速
$f p i$	航线 $p$ 上 $i$ 类船舶的数量
$t a i$	航段 $a$ 上 $i$ 类船舶的时间成本
$T a i$	航段 $a$ 上 $i$ 类船舶的航行时间
$T a i *$	航段 $a$ 上 $i$ 类船舶航行中因拥堵造成等待的时间
$T a s$	在航段上 $a$ 港口 $s$ 锚地的排队停留天数
$c a i$	航段 $a$ 上 $i$ 类船舶的运输成本
$c a F$	目的港口为 $s$ 的航段 $a$ 上集装箱船舶的港口服务成本
$c a s$	每天锚地使用费用
$C i$	$i$ 类船舶燃料的单位费用
$u a i$	航段 $a$ 上 $i$ 类船舶的广义成本
$h p i$	航线 $p$ 上 $i$ 类船舶的广义成本
$α a$	航段 $a$ 上最大船舶数量
$γ a$	航段 $a$ 上船舶最大等待时间
$β a$	模拟船舶在港口等待时间影响参数
$q a i$	$i$ 类船舶在航段 $a$ 上航行的燃料消耗量
$M F i$	$i$ 类船舶的主机日油耗
$A F i$	$i$ 类船舶的辅机日油耗
$Q i$	$i$ 类船舶可载集装箱箱量
$C Q a i$	航段 $a$ 上 $i$ 类船舶每单位TEU所征收拥堵附加费
$R i$	$i$ 类船舶燃料消耗直接碳排放系数
$A L C V i$	$i$ 类船舶燃料的平均低位发热量
$C C i$	$i$ 类船舶燃料的单位热值含碳量
$C O i$	$i$ 类船舶燃料的碳氧化率

航段	航段因终点港口拥堵停留天数/天
$(s 1 - s 4)$	1
$(s 1 - s 2)$	3
$(s 4 - s 3)$	1
$(s 2 - s 3)$	1

航段	拥堵停留天数/天	航段	拥堵停留天数/天
$(s 1 - s 2)$	2	$(s 4 - s 6)$	1
$(s 1 - s 3)$	5	$(s 4 - s 7)$	3
$(s 2 - s 4)$	2	$(s 5 - s 6)$	1
$(s 2 - s 5)$	4	$(s 5 - s 7)$	3
$(s 3 - s 4)$	2	$(s 6 - s 8)$	2
$(s 3 - s 5)$	4	$(s 7 - s 8)$	2

References 40

[1]	Gui D， Wang H， Yu M， et al. Risk assessment of port congestion risk during the COVID-19 pandemic［J］. Journal of Marine Science and Engineering， 2022， 10（2）： 150.
[2]	Xiao G， Wang T， Chen X， et al. Evaluation of ship pollutant emissions in the ports of los angeles and long beach［J］. Journal of Marine Science and Engineering， 2022， 10（9）： 1206.
[3]	Gidado U M. Consequences of port congestion on logistics and supply chain in African ports［J］. Developing Country Studies， 2015， 5： 160-167.
[4]	Steinbach S. Port congestion， container shortages， and U.S. foreign trade［J］. Economics Letters， 2022， 213： 110392.
[5]	Peng W， Bai X， Yang D， et al. A deep learning approach for port congestion estimation and prediction［J］. Maritime Policy & Management， 2023， 50（7）： 835-860.
[6]	Tai H H， Chang C C. Cost advantages of far east/Europe trunk route deployment with port selection in east Asia［J］. Journal of Marine Science and Technology， 2023， 31（1）： 6.
[7]	Chen J， Ye J， Zhuang C， et al. Liner shipping alliance management： Overview and future research directions［J］ Ocean & Coastal Management， 2022， 219： 106039.
[8]	Koza D F， Desaulniers G， Ropke S. Integrated liner shipping network design and scheduling［J］. Transportation Science， 2020， 54（2）： 512-533.
[9]	Huang L， Tan Y， Guan X. Hub-and-spoke network design for container shipping considering disruption and congestion in the post COVID-19 era［J］. Ocean & Coastal Management， 2022， 225： 106230.
[10]	Wang S， Meng Q. Robust schedule design for liner shipping services［J］. Transportation Research Part E： Logistics and Transportation Review， 2012， 48（6）： 1093-1106.
[11]	Meng L， Wang X， Jin J， et al. Optimization model for container liner ship scheduling considering disruption risks and carbon emission reduction［J］. Journal of Marine Science and Engineering， 2023， 11（7）： 1449.
[12]	黄肖玲，代霞梅，纪国良，等. 基于“前港后厂”模式的进口铁矿石采购物流成本优化［J］. 中国管理科学， 2021， 29（8）： 218-228.
	Huang X L， Dai X M， Ji G L， et al. Optimization on the procurement logistics system of importing iron ore based on the “port before factory” mode［J］. Chinese Journal of Management Science， 2021， 29（8）： 218-228.
[13]	Jin J G， Meng Q， Wang H. Feeder vessel routing and transshipment coordination at a congested hub port［J］. Transportation Research Part B： Methodological， 2021， 151： 1-21.
[14]	Abioye O F， Dulebenets M A， Kavoosi M， et al. Vessel schedule recovery in liner shipping： Modeling alternative recovery options［J］. IEEE Transactions on Intelligent Transportation Systems， 2021， 22（10）： 6420-6434.
[15]	Bütün C， Petrovic S， Muyldermans L. The capacitated directed cycle hub location and routing problem under congestion［J］. European Journal of Operational Research， 2021， 292（2）： 714-734.
[16]	Mohammadi M， Tavakkoli-Moghaddam R， Siadat A， et al. Design of a reliable logistics network with hub disruption under uncertainty［J］. Applied Mathematical Modelling， 2016， 40（9-10）： 5621-5642.
[17]	Tsao Y C， Linh V T. Seaport- dry port network design considering multimodal transport and carbon emissions［J］. Journal of Cleaner Production， 2018， 199： 481-492.
[18]	Snyder L V， Daskin M S. Reliability models for facility location： The expected failure cost case［J］. Transportation Science， 2005， 39（3）： 400-416.
[19]	Cui T， Ouyang Y， Shen Z M. Reliable facility location design under the risk of disruptions［J］. Operations Research， 2010， 58（4-Part-1）： 998-1011.
[20]	Rahimi Y， Ali Torabi S， Tavakkoli-Moghaddam R. A new robust-possibilistic reliable hub protection model with elastic demands and backup hubs under risk［J］. Engineering Applications of Artificial Intelligence， 2019， 86： 68-82.
[21]	An Y， Zhang Y， Zeng B. The reliable hub-and-spoke design problem： Models and algorithms［J］. Transportation Research Part B： Methodological， 2015， 77： 103-122.
[22]	周海英，李伯棠. 碳税与客户低碳偏好下港航企业减排决策分析［J］. 中国航海， 2022， 45（3）： 72-79.
	Zhou H Y， Li B T. The ways for port and shipping enterprises to make decision on emission-reduction in the context of carbon tax and client’s low carbon preference［J］. Navigation of China， 2022， 45（3）： 72-79.
[23]	夏凡，王欢，王之扬. “双碳”背景下我国碳排放权交易体系与碳税协调发展机制研究［J］. 西南金融， 2023（1）： 3-15.
	Xia F， Wang H， Wang Z Y. Research on the coordinated development mechanism of China’s carbon emission trading system and carbon tax in the background of “carbon peaking and carbon neutrality”［J］. Southwest Finance， 2023（1）： 3-15.
[24]	Wang S， Zhen L， Psaraftis H N， et al. Implications of the EU’s inclusion of maritime transport in the emissions trading system for shipping companies［J］. Engineering， 2021， 7（5）： 554-557.
[25]	镇璐，诸葛丹，汪小帆. 绿色港口与航运管理研究综述［J］.系统工程理论与实践，2020，40（8）：2037-2050.
	Zhen L， Zhuge D， Wang X F. Researches on green ports and shipping management： An overview［J］. Systems Engineering-Theory & Practice， 2020， 40（8）： 2037-2050.
[26]	Mallouppas G， Yfantis E A， Mallouppas G， et al. Decarbonization in shipping industry： A review of research， technology development， and innovation proposals［J］. Journal of Marine Science and Engineering， 2021， 9（4）： 415.
[27]	Reinhardt L B， Pisinger D， Sigurd M M， et al. Speed optimizations for liner networks with business constraints［J］. European Journal of Operational Research， 2020， 285（3）： 1127-1140.
[28]	Zhen L， Wu Y， Wang S， et al. Green technology adoption for fleet deployment in a shipping network［J］. Transportation Research Part B： Methodological， 2020， 139： 388-410.
[29]	Leurent F. Cost versus time equilibrium over a network［J］. European Journal of Operational Research， 1993， 71（2）： 205-221.
[30]	Abrahamsson T， Lundqvist L. Formulation and estimation of combined network equilibrium models with applications to Stockholm［J］. Transportation Science， 1999， 33（1）： 80-100.
[31]	Lions J L， Stampacchia G. Variational inequalities［J］. Communications on Pure and Applied Mathematics， 1967， 20（3）： 493-519.
[32]	Nagurney A， Dong J， Zhang D. A supply chain network equilibrium model［J］. Transportation Research Part E： Logistics and Transportation Review， 2002， 38（5）： 281-303.
[33]	Nagurney A， Besik D， Dong J. Tariffs and quotas in world trade： A unified variational inequality framework［J］. European Journal of Operational Research， 2019， 275（1）： 347-360.
[34]	Dafermos S， Nagurney A. A network formulation of market equilibrium problems and variational inequalities［J］.Operations Research Letters，1984，3（5）： 247-250.
[35]	Matsypura D， Nagurney A， Liu Z. Modeling of electric power supply chain networks with fuel suppliers via variational inequalities［J］. International Journal of Emerging Electric Power Systems， 2007， 8（1）： 5.
[36]	Wu Y， Wang S， Zhen L， et al. How to operate ship fleets under uncertainty［J］. Production and Operations Management， 2023， 32（10）： 3043-3061.
[37]	Corbett J J， Wang H， Winebrake J J. The effectiveness and costs of speed reductions on emissions from international shipping［J］. Transportation Research Part D： Transport and Environment， 2009， 14（8）： 593-598.
[38]	Sheffi Y. Urban Transportation Networks［M］. New Jersey， USA： Prentice Hall， 1985.
[39]	Mahmassani H S， Mouskos K C. Some numerical results on the diagonalization algorithm for network assignment with asymmetric interactions between cars and trucks［J］. Transportation Research Part B： Methodological， 1988， 22（4）： 275-290.
[40]	Meng L， Wang X， He J， et al. Ship allocation considering energy type and transportation preference： A variational inequality approach［J］. Advanced Engineering Informatics， 2024， 59： 102291.

数据集	港口数/航线数/航段数	投影算法（秒）	标准对角化算法（秒）	改进对角化算法（秒）
S1	4/2/2	16	15	14
S2	8/8/12	239	223	197
S3	37/65/75	1,417	1,030	864
S4	30/50/109	3,102	2,419	1,920
S5	47/79/56	3,652	3,299	2,541
S6	37/65/163	-	3,510	2,892
S7	30/50/129	-	5,193	4,252
S8	37/65/327	-	5,459	4,287
S9	47/79/100	-	-	9,737
S10	47/79/141	-	-	10,084

Optimization Model and Strategies for Route and Fleet Allocation Considering Port Congestion and Carbon Emission Reduction

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 9

References 40

Related Articles 15

Metrics

Comments

Recommended 0

[1]	Yeming Dai, Shuang Yu. Remanufacturing Closed-loop Supply Chain Decision Considering Retailer’s Dual Behavior Preference under Carbon Tax Regulation [J]. Chinese Journal of Management Science, 2025, 33(8): 308-320.
[2]	Lin Pan,Xiajing Xu,Rongting Zhou. Research on Dual Channel Dynamic Pricing of Community Fresh Food Supply Chain from the Perspective of Competition [J]. Chinese Journal of Management Science, 2024, 32(7): 300-310.
[3]	Haixiang Wu,Bing Xu. Multi-period International Supply Chain Network Equilibrium under Technology Diffusion and Trade Protectionism [J]. Chinese Journal of Management Science, 2024, 32(2): 324-334.
[4]	Xiu-li MENG,Yi-fan WU,Bo LIU. Multi-Period Crowdsourcing Logistics Service Quality Optimization Considering Delay Insurance [J]. Chinese Journal of Management Science, 2023, 31(12): 87-95.
[5]	XIA Xi-qiang, LI Biao. A Study on the Impact of Government Carbon Tax and Subsidy Policies on Outsourced Remanufacturing [J]. Chinese Journal of Management Science, 2022, 30(9): 105-115.
[6]	CAO Yu, YI Chao-qun, WAN Guang-yu. Inventory Decisions and Coordination Mechanism for Dual-Channel Supply Chain under Carbon Tax Policy [J]. Chinese Journal of Management Science, 2022, 30(1): 111-123.
[7]	WANG Jun, CHENG Xian-xue, JIANG Yu-shan, DONG Zhen-min. Behavior Selection of Supply Chain Members Considering Reference Carbon Emission under Carbon Tax Policy [J]. Chinese Journal of Management Science, 2021, 29(7): 128-138.
[8]	YANG Jian-hua, HAN Meng-ying. The Influence Research on the Joint Ordering Policy for Spare Parts Considering Carbon Tax [J]. Chinese Journal of Management Science, 2021, 29(7): 23-32.
[9]	DIAO Xin-wei, ZENG Zhen-xiang, SUN Cheng. Research on Coordination of Supply Chain with Two Products Based on Mix Carbon Policy [J]. Chinese Journal of Management Science, 2021, 29(2): 149-159.
[10]	GUO Jie. Online Tourism Supply Chain Network Equilibrium Model with the Transaction Risk Investment [J]. Chinese Journal of Management Science, 2020, 28(6): 137-145.
[11]	WANG Shan-shan, ZHANG Li-hao, FAN Ti-jun. Equilibrium Strategies of Carbon Reduction Technology Adoption in Competitive Supply Chains [J]. Chinese Journal of Management Science, 2020, 28(6): 73-82.
[12]	ZHOU Yan-ju, HU Feng-ying, ZHOU Zheng-long. Pricing Strategy and Social Welfare in Supply Chain with Competing Manufacturers Based on Carbon Tax Policy [J]. Chinese Journal of Management Science, 2019, 27(7): 94-105.
[13]	ZHOU Zhang-jin, FU Xiao-ling, LI Min. Research on Stations Distribution of Waste Collection Based on Carbon Emission [J]. Chinese Journal of Management Science, 2018, 26(4): 41-48.
[14]	CAO Bin-bin, XIAO Zhong-dong, ZHU Chun-yang. Research on Decision-making of Supply Chain with Dual Sale Mode Considering Government's Low-carbon Policies [J]. Chinese Journal of Management Science, 2018, 26(4): 30-40.
[15]	MI Chuan-min, LI Dan-dan, ZHANG Ting, QIAN Yuan-yuan, ZHOU Zhi-peng. Study on Financial Market Supernetwork Equilibrium Considering Social Network and Internet Finance [J]. Chinese Journal of Management Science, 2018, 26(12): 56-65.