A Joint Optimization of Vessel Scheduling and Refueling Strategy for Container Liner Shipping with Cooperative Agreements

doi:10.16183/j.cnki.jsjtu.2021.105

Abstract

Abstract:

This paper studies the joint optimization problem of vessel scheduling and refueling strategy for container liner shipping with cooperative agreements signed by the container terminal operators and the shipping company with multiple vessel arrival time windows, multiple start and end times, and multiple handling rates. A non-linear mixed integer programming model for vessel scheduling and refueling strategy problem of liner shipping is established considering fuel price difference and discount factors at different refueling ports, which aims to minimize the total cost of liner shipping service. A set of discretization and linearization technique is applied to the original model in accordance with the vessel navigation controlling practice. Taking the AEX1 route served by China COSCO Shipping Corporation Limited as an example, a large number of simulation verifications are conducted. The results of numerical examples show that the joint optimization of vessel scheduling and refueling strategy helps shipping companies to flexibly adjust vessel sailing speed. It can significantly reduce the total cost of liner shipping service. The sensitivity analysis indicates that the total cost of liner shipping service and the vessel refueling volume in a voyage will reduce with the expansion of time window of vessel arrival at port in the cooperative agreement. No matter how the fuel price changes, the joint optimization of vessel scheduling and refueling strategy can effectively reduce the total cost of liner shipping service.

Key words: liner shipping, cooperative agreement, vessel scheduling, refueling strategy, joint optimization

CLC Number:

U692.3

LI Dechang, YANG Hualong, DUAN Jingru. A Joint Optimization of Vessel Scheduling and Refueling Strategy for Container Liner Shipping with Cooperative Agreements[J]. Journal of Shanghai Jiao Tong University, 2022, 56(7): 953-964.

Figures/Tables 11

Fig.1

Fig.2

Tab.1

Relevant parameters

参数	取值
$F D v D 3$	0.013
α	3
C^oc/(美元·周^-1)	300000
W/t	5000
I₀/t	2000
C^F/(美元·次^-1)	1000
$C p i c$ /(美元·TEU^-1·h^-1)	0.5
λ_p₁, λ_p₂/%	95, 90
W_p₁, W_p₂/t	2000, 3000
v^min, v^max/kn	15, 25
m^max/艘	10

Tab.1

Tab.2

Port fuel prices and distances

港口	D_p/n mile	$C p f 0$ /(美元·t^-1)
青岛	408	429
上海	136	425
宁波	727	438
盐田	1 445	-
新加坡	204	395
巴生	8 012	398
费利克斯托	118	-
鹿特丹	302	372
汉堡	335	288
泽布吕赫	70	-
鹿特丹	8 088	372
巴生	1 649	398
盐田	1 105	-

Tab.2

Tab.3

Tab.4

Tab.5

Tab.6

Fig.3

Tab.7

Fig.4

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港口	最早到港时间/h	平均到港时间/h	最迟到港时间/h	最早离港时间/h	平均离港时间/h	最迟离港时间/h	最小加油量/t	平均加油量/t	最大加油量/t
青岛	0	0	0	4	32	80	-	-	-
上海	21	49	98	26	65	109	-	-	-
宁波	31	71	114	41	83	124	-	-	-
盐田	71	113	154	78	124	165	-	-	-
新加坡	137	185	230	142	195	240	-	-	-
巴生	151	204	248	166	214	256	500.00	2058.27	3000.00
费利克斯托	492	549	618	497	571	655	-	-	-
鹿特丹	502	576	660	518	586	674	-	-	-
汉堡	531	598	686	541	611	693	3432.00	4389.05	4500.00
泽布吕赫	556	625	707	565	637	714	-	-	-
鹿特丹	568	640	717	579	651	725	-	-	-
巴生	907	989	1 050	929	1 006	1 060	500.00	589.64	807.58
盐田	995	1 075	1 127	1 124	1 115	1 132	-	-	-
青岛	1 176	1 176	1 176	1 180	1 208	1 256	-	-	-

模型	取值	总加油量/t	营运成本× 10^-6/美元	装卸成本× 10^-6/美元	惩罚成本× 10^-3/美元	燃油成本× 10^-6/美元	库存成本× 10^-6/美元	总成本× 10^-7/美元
[M2]	最小值	5 824	2.100	3.474	0	1.777	3.982	1.2215
	平均值	7 037	2.100	4.689	89	2.265	4.709	1.3852
	最大值	7 647	2.100	6.011	1 399	2.560	5.382	1.5877
[M3]	最小值	6 044	2.100	3.306	0	1.856	4.026	1.2427
	平均值	6 774	2.100	4.896	302	2.169	4.807	1.4274
	最大值	7 624	2.100	6.346	4 426	2.478	5.365	1.8792
[M4]	最小值	5 841	2.100	3.515	0	2.281	3.966	1.2921
	平均值	7 065	2.100	4.682	95	2.759	4.704	1.4340
	最大值	7 651	2.100	6.011	1 528	2.988	5.418	1.6694

时间窗长度/h	各加油港加油量/t			合计/t
时间窗长度/h	巴生(去程)	汉堡	巴生(回程)	合计/t
U[24, 29]	2114.49	4373.21	584.58	7072.28
U[29, 34]	2102.04	4381.56	592.90	7076.50
U[34, 39]	2087.93	4383.51	590.06	7061.50
U[39, 44]	2080.80	4381.93	585.97	7048.70
U[44, 49]	2072.53	4379.49	590.29	7042.31
U[49, 54]	2058.27	4389.05	589.64	7036.96
U[54, 59]	2052.40	4379.20	589.83	7021.43
U[59, 64]	2044.22	4378.04	587.91	7010.17
U[64, 69]	2039.85	4370.51	585.93	6996.29
U[69, 74]	2019.83	4380.21	577.92	6977.96
U[74, 79]	2015.72	4376.71	583.13	6975.56

变化率/%	各加油港加油量/t					合计/t
变化率/%	新加坡	巴生	汉堡	鹿特丹	巴生	合计/t
-30	-	2313.64	4488.31	-	784.69	7586.64
-20	-	2220.44	4468.06	-	683.69	7372.19
-10	-	2099.90	4402.63	-	624.98	7127.51
0	-	2058.27	4389.05	-	589.64	7036.96
+10	-	2025.15	4365.62	-	556.03	6946.80
+20	-	1880.76	4334.44	-	517.25	6732.45
+30	1750.46	-	4274.87	-	500.00	6525.33
+40	1630.14	-	4188.93	-	500.00	6319.07
+50	1489.49	-	4139.83	-	500.00	6129.32
+60	1257.12	-	4191.41	500.00	-	5948.53