题目：Berth allocation considering fuel consumption and vessel emissions
作者：Yuquan Du, Qiushuang Chen, Xiongwen Quan, Lei Long, Richard Y. K. Fung

摘要

We propose a more elaborate model on berth allocation considering fuel consumption than before, and overcome the nonlinear complexity by casting it as a mixed integer second order cone programming model. Furthermore, we conduct the vessel emission (in sailing periods) calculation with the widely-used emission factors. Besides, vessel emissions in mooring periods are also analyzed through a post-optimization phase on waiting time. Experimental results demonstrate that the new berth allocation strategy, reflected by the proposed model, is competent to significantly reduce fuel consumption and vessel emissions, while simultaneously retaining the service level of the terminal.

批注：在孟强老师2014的那篇关于集装箱班轮运输路径规划和调度的论文种列举了四种处理航速和燃油价格非线性关系的方法——（1）在局部用线性关系近似（2）用精确算法处理不了这种关系就用启发式算法做（3）把有不同航速的船当作不同类型的船即使他们实际上是同类船（4）使用分段线性近似。本文则创新地给出了第五种处理方法模型转换为SOCP。在创新方面，这是第一篇把污染物排放纳入BAP进行同步优化的文章。

背景部分

As autonomic enterprises, the port and the shipping lines have different business concerns. The port seeks to reduce the vessel emissions for mooring in the port, without lowering the customer service level, by reducing vessel waiting time as much as possible in the berth plan. The shipping lines are concerned about the fuel consumption in the sailing period, and the ensuing vessel emissions.The operation plans of the terminal are closely interrelated to the shipping schedules of the shipping lines. On one hand, the arrival times of vessels determined by the shipping schedule are key parameters of the berth plan; on the other hand, Notteboom (2006) demonstrates that port congestion is currently the main cause of shipping schedule unreliability.This close relationship between the berth plan and the shipping schedule calls for the cooperative efforts of the terminal and the shipping line. The terminal should take into account the operational efficiency of its customers, the shipping lines, instead of planning its operations in isolation.

批注：航运公司和港口作为独立运营的实体有着不同的商业考量，航运公司追求的是在遵循时刻表的同时在航行过程中燃油消耗尽可能少，并且尽可能减少污染物的排放；而港口关心的则是能否最大限度的减少船舶的等待时间（就是船舶到港后直到自己泊位可用的这段时间），同时尽可能减少船舶在停泊期间的污染物排放。但是航运公司的时刻表和码头的运营计划是密切关联的，航运公司的时刻表是港口做泊位分配的重要依据，而港口泊位分配的好坏又直接影响着航运公司能否履行自己制定的时刻表，所以港口和航运企业之间应该要有一种协作机制，而不是追求单方面的最优。

前序研究

泊位分配可以分为——（1）静态泊位分配和动态泊位分配，所谓静态泊位分配就是指在泊位分配规划期开始所有船舶都以及到港口等待着，而动态泊位分配则是船舶会在规划期不断到港口等待；（2）离散泊位空间的泊位分配和连续泊位空间的泊位分配，很好理解，前者就像画了线的停车区域而后者则是没有画线的停车区域。在早期的BAP研究里面，主要都是站在港口运营方进行优化的，去减少船舶离开时间的延误或者船舶等待时间之类的指标。Golias, M.M., Saharidis, G.K., Boile, M., Theofanis, S., Ierapetritou, M.G., 2009. The berth allocation problem: optimizing vessel arrival time的这篇文章应该是第一个考虑港口和码头之间协作的，通过将船舶的到达时间设置为变量而不是原先的常量参数进行研究。以及后面Lang and Veenstra (2010)、Alvarez et al. (2010)都把船舶到达时间作为了决策变量。但这三个研究和本文的最大区别是他们对燃油消耗量和污染排放要么考虑的不全面，要么采用的是近似方法。

模型部分

符号说明

集合和参数

  • ：在泊位计划中所考虑的船舶的集合。
  • ：集装箱码头的长度。
  • ：船舶的长度。
  • ：船舶在泊位上要停靠的时间。
  • ：从航运公司船期表获悉的船舶的到港时间。
  • ：从船期表获悉的船舶离开港口的时间。
  • ：一个充分大的正数。

决策变量和辅助变量

  • ：船舶停在码头时船头的位置。
  • ：船舶开始在码头停泊的时间。
  • ：船舶的泊位是否在船舶的左边。
  • ：船舶是否在船离开之后才在码头开始停泊的。

模型建立

批注：这个BAP的目标函数就是最小化船舶的离港延误；约束（2）表示船身不能跑到码头外了；约束（3）表示船舶开始在码头停泊的时间小于他到达码头的时间；约束（4）~（6）闲置船舶之间的位置关系和停靠时间关系。

批注：上面给那个模型是把船舶到港时间作为参数的，这里是把它作为决策变量，然后还同时优化了航行过程中的燃油消耗量。

Now we discuss the calculation method of vessel emissions. The absence of reporting methodologies and monitoring programs disable the precise calculation of vessel emissions like the calculation of car emissions. Generally, until now, vessel emissions are roughly calculated by the fuel consumption and the emission factors as

船舶排放（）燃油消耗量（）排放因子（）

Due to the absence of measurement equipments of emission factors installed in vessels, emission factors of vessel fuel are always chosen in a generic sense. In practice, the emission factors issued by the authorities like IPCC and IMO are widely used. For instance, COSCO adopts the emission factors in Table 1 in the calculation of vessel emissions (COSCO, 2009). In this study, we also adopt the emission factors in Table 1, except that we fix the emission factor of NOX as 87 g/kg-fuel, since the majority of sea-going vessels have 2-stroke main engines and 4-stroke auxiliary engines installed, and the fuel consumption of main engines is dominant.

未来研究方向

  • 没有考虑到岸桥的分配，这个好像Models on ship scheduling in transshipment hubs with considering bunker cost这篇文章已经做了。
  • 出口集装箱需要在堆场集中2到3天，所以未来可以考虑把货物堆载计划和BAP一块协同优化。
  • 本文研究的是单一集装箱码头，未来可以拓展到多码头甚至多港口。这个好像Models on ship scheduling in transshipment hubs with considering bunker cost这篇文章也做了。