面向梯级船闸通航拥堵的船舶过坝协同策略研究

doi:10.16381/j.cnki.issn1003-207x.2024.1091

Abstract

Abstract:

Aiming at the vessel navigation congestion problem caused by the bottleneck effect of stepped locks， congestion charging and differential dam-over subsidy mechanism are introduced to enhance the shipping efficiency. Firstly， based on the dynamics of ships crossing the locks in a cycle， and the difference of the ideal time interval between two locks in a row， a double bottleneck model without charging is established， and the total cost of the system is derived under different scenarios； and then， through the establishment of the optimal charging equilibrium model， the congestion charge is taken as the subsidy for dam overturning， and the two-line linkage mechanism of ‘crossing the locks and overturning the dams’ is put forward. Then， by establishing the optimal toll equilibrium model and taking the congestion fee as the dam-over subsidy， a two-lane linkage mechanism of ‘gate crossing + dam-over’ is proposed to realise the synergy of navigable vessels crossing dams. It is shown that： toll management can effectively reduce the social cost of ship navigation and alleviate the congestion problem in front of the dam， and the dam-over subsidy can effectively promote the transfer of the dam-over mode； navigation managers can regulate the capacity of the downstream bottleneck when the upstream and downstream ships are not balanced to avoid the backlog of ships between the locks of the ladder level， so as to make effective use of the capacity of the dam-over； at the same time， by giving the larger tonnage ships a higher priority for the lock-over system， the function of the dam-over system can be brought into full play， and the total number of ships crossing the dams can be increased. At the same time， giving higher priority to larger tonnage ships can give full play to the function of the over-dam system and increase the total number of ships crossing the dam.

Key words: waterway transportation, ship management, series bottleneck, congestion pricing, subsidy for dam overturning

CLC Number:

U641.7

Pan Gao,Zeao Xu,Xueying Zhang, et al. Research on Cooperative Strategy of Ship Crossing Dam for Traffic Congestion of Cascade Lock[J]. Chinese Journal of Management Science, 2026, 34(5): 153-165.

Figures/Tables 14

参数符号	说明	参数符号	说明
$N$	每天通过船闸的船舶数：艘	$T *$	船舶平均过坝时间
$s 1$	瓶颈I的船闸通过能力：艘/时	$ω t$	船舶载重量：
$s 2$	瓶颈II的船闸通过能力：艘/时	$w 1, w 2$	瓶颈I的船闸运行时间
$t q$	第一艘船舶到锚时间	$w 3, w 4$	瓶颈II的船闸运行时间
$t q'$	最后一艘船舶到锚时间	$C 0$	船舶油耗成本
$L s$	船舶航行距离	$L g$	货物翻坝距离
$t 1'$	通过瓶颈I的最佳时间	$A$	调整低船速油耗常数项
$t 2'$	通过瓶颈II的最佳时间	$B$	船舶通航耗油量模型速度项
$α$	出行时间价值：元/时	$v 1$	船舶平均航速
$γ$	计划延误成本：元/时	$Δ t$	船舶通过瓶颈I和瓶颈II的时间差
$β$	计划提前成本：元/时	$ε$	锚地等待成本
$r$	船舶出发速率	$χ$	平均装卸效率（吨/h）
$μ$	平均装卸费率（元/吨）	$η$	翻坝运输单位费率（元/吨 $∙$ 千米）
中介变量
$T i w (t)$	$t$ 时刻坝前排队时间，i=1,2	$D i (t)$	$t$ 时刻坝前排队长度，i=1,2
$T i (t)$	$t$ 时刻出行者通过瓶颈 $i$ 的行驶时间	$r (t)$	船舶出发速率：艘/时
$t 1 *$	船舶通过瓶颈I的偏好时间	$t 2 *$	船舶通过瓶颈II的偏好时间
$C (x), C (n)$	船舶过闸时个体时间成本
决策变量
$τ (t)$	最优动态收费	$R i$	补贴总额：元

时段	出发时间	时间成本
1	$[t q, t 1')$	$ε (w 1 - t) + α T 1 w (t) + β [t 1 * - w 1 - T 1 w (t)] + α T 2 w (t) + β (t 2 * - t - T 2 (t))$
2	$[t 1', t 2')$	$ε (w 1 - t) + α T 1 w (t) + γ [w 1 + T 1 w (t) - t 1 ] + α T 2 w (t) + β [t 2 - t - T 2 (t)]$
3	$[t 2', w 1]$	$ε (w 1 - t) + α T 1 w (t) + γ [w 1 + T 1 w (t) - t 1 ] + α T 2 w (t) + γ [t + T 2 (t) - t 2 ]$

时段	出发时间	时间成本
1	$[t q, t 1')$	$ε (w 1 - t) + α T 1 w (t) + β [t 1 * - w 1 - T 1 w (t)] + α T 2 w (t) + β [t 2 * - t - T 2 (t)]$
2	$[t 1', w 1]$	$ε (w 1 - t) + α T 1 w (t) + γ [w 1 + T 1 w (t) - t 1 ] + α T 2 w (t) + β [t 2 - t - T 2 (t)]$

参数	单位	参数	单位
$ε$	450元/小时	$L s$	90.2和79.2
$α$	450元/小时	$L g$	90和77.4
$β$	200元/小时	$v 1$	8km/小时
$λ$	833元/小时	$v 2$	45km/小时
$[w 1, w 2]$	$[5,24]$	$k$	0.191
$[w 3, w 4]$	$[5,24]$	$η$	0.3（元/吨 $∙$ 千米）
$s 1$	4	$μ$	平均装卸费率:5（元/吨）
$s 2$	$[2,4]$	$P$	7.45元/升
$t 1 *$	11	$A$	0
$Δ t$ 取值	14、32	$B$	19.8
$χ$	1000吨/小时	$ω t$	3000吨、4000吨、5000吨
$T *$	1.5小时

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Research on Cooperative Strategy of Ship Crossing Dam for Traffic Congestion of Cascade Lock

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