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Vol.:(0123456789)

Flexible Services and Manufacturing Journal (2023) 35:29–69

https://doi.org/10.1007/s10696-022-09462-x

1 3

Robust berth scheduling using machine learning forvessel

arrival time prediction

LorenzKolley

· NicolasRückert

· MarvinKastner

· CarlosJahn

·

KathrinFischer

Accepted: 1 August 2022 / Published online: 1 September 2022

Abstract

In this work, the potentials of data-driven optimization for the well-known berth

allocation problem are studied. The aim of robust berth scheduling is to derive con-

ﬂict-free vessel assignments at the quay of a terminal, taking into account uncer-

tainty regarding the actual vessel arrival times which may result from external

inﬂuences as, e.g., cross wind and sea current. In order to achieve robustness, four

diﬀerent Machine Learning methods-from linear regression to an artiﬁcial neural

network-are employed for vessel arrival time prediction in this work. The diﬀerent

Machine Learning methods are analysed and evaluated with respect to their forecast

quality. The calculation and use of so-called dynamic time buﬀers (DTBs), which

are derived from the diﬀerent AIS-based forecasts and whose length depends on the

estimated forecast reliability, in the berth scheduling model enhance the robustness

of the resulting schedules considerably, as is shown in an extensive numerical study.

Furthermore, the results show that also rather simple Machine Learning approaches

are able to reach high forecast accuracy. The optimization model does not only lead

to more robust solutions, but also to less actual waiting times for the vessels and

hence to an enhanced service quality, as can be shown by studying the resulting

schedules for real vessel data. Moreover, it turns out that the accuracy of the result-

ing berthing schedules, measured as the deviation of planned and actually realisable

schedules, exceeds the accuracy of all forecasts which underlines the usefulness of

the DTB approach.

Keywords Berth allocation problem· Machine learning· Uncertainty· (Arrival

time) prediction· Robust optimization

* Lorenz Kolley

Lorenz.kolley@tuhh.de

Institute forOperations Research andInformation Systems, Hamburg University ofTechnology,

Am Schwarzenberg-Campus 4, 21073Hamburg, Germany

Institute ofMaritime Logistics, Hamburg University ofTechnology, Am

Schwarzenberg-Campus 4, 21073Hamburg, Germany

L.Kolley et al.

1 3

1 Introduction

A highly relevant issue in the planning of (maritime) supply chains and logistics

is the uncertainty of deep sea vessel arrivals at ports, as its consequences aﬀect

all further stages of the supply chain (Dobrkovic etal. 2016). However, the port

terminals are aﬀected most: Berth allocations have to be planned in advance, i.e.,

while a vessel has not yet arrived and hence either a berth can still be occupied

when a vessel arrives early (and the vessel cannot moor as planned) or a berth

remains empty when a vessel is delayed. Both eﬀects have negative economic

consequences, for the terminal as well as for the vessel owners and, as mentioned

above, also for the subsequent supply chain. Therefore, approaches for reducing

uncertainty in this ﬁeld are of huge importance.

As data and digitalization oﬀer new opportunities for uncertainty reduction

and mitigation, new approaches for terminal planning and management should

be developed from a “data-driven perspective,“ as Heilig etal. (2020) point out,

in order to enrich the traditional “optimization perspective”. However, currently

these authors still identify “a lack of data-driven approaches in the context of

container terminals.“ Moreover, they point out that data from external sources—

as, e.g., Automated Information System (AIS) data-are “under-analysed”, i.e.,

that often they are not yet fully exploited; instead, the focus is often still on

operational optimization, without suﬃcient consideration of patterns in existing

data. According to Yang etal. (2019), Data Mining-for extraction of the relevant

information-and vessel behaviour analysis-in order to ﬁnd patterns of maritime

traﬃc-are of high importance for future research in the ﬁeld, as, e.g., causality

analysis builds up on it. They point out that there is only little work in Operations

Research (OR) yet which makes use of AIS data and that berth allocation might

be one ﬁeld which could strongly beneﬁt from their exploitation in the future.

Therefore, this work is aimed at ﬁlling this gap with respect to a speciﬁc prob-

lem by developing and presenting a new machine-learning-based approach for

forecasting vessel arrival times. The results are then used in a berth allocation

approach, in order to improve the “traditional” berth allocation problem (BAP)

optimization procedure by an appropriate use of existing data. The forecasting

approach makes use of AIS data which are broadcast by vessels and, among other

information, provide the current position of a vessel on a regular basis. Following

Dobrkovic etal. (2016), data from 48h before the actual vessel arrivals are used

for forecasting, as this is the time frame within which vessel arrivals are usually

announced to the respective seaport container terminal.

Through the use of real AIS data from the past on which the forecasts are

based, but for which the actual vessel arrival times are already known as well,

the approach taken in this work allows an evaluation of the forecast quality of

the diﬀerent forecasting methods. In the forecasting, methods from the ﬁeld of

machine learning (ML) are used, namely linear regression (LR), k-nearest neigh-

bour (kNN), decision tree regressor (DTR) and artiﬁcial neural networks (ANN).

A berthing schedule is called (feasibility-)robust, when it remains stable at

least for smaller deviations from the originally assumed vessel arrival times, i.e.,

1 3

Robust berth scheduling using machine learning forvessel…

when the schedule stays feasible (Scholl 2001). To derive a robust berth allo-

cation based on the forecasts, the concepts of conﬂicts (Liu etal. 2017) and of

dynamic time buﬀers (DTBs) are used (Kolley et al. 2021) and further reﬁned.

More speciﬁcally, Liu etal. (2017) deﬁne and measure robustness as a function

of the service level that is achieved, where the service level in turn is deﬁned as

the number (or percentage) of vessels which-in the planned berth allocation-are

not in conﬂict with other vessels. In this work, this customer-oriented concept is

extended by the integration of time buﬀers which help to better prevent conﬂicts

even if actual vessel arrival times deviate from scheduled berthing times. Hence,

a robust schedule is deﬁned as a schedule with as little conﬂicts as possible which

remains valid under changing arrival times.

The purpose of the approach taken in this work is to reduce uncertainty and thus,

increase robustness by means of using diﬀerent forecasts-resulting from diﬀerent ML

methods as mentioned above-jointly in the berth scheduling. The forecasts are inter-

preted as possible future arrival times which are equally likely, hence uncertainty is

transformed into risk. The DTBs are then constructed based on the resulting “forecast

distributions”. The more the forecasts diﬀer, i.e., the more spread there is in the dis-

tribution, the higher is the uncertainty with respect to the respective arrival time and

hence, a larger buﬀer is needed for mitigating this uncertainty. On the contrary, with

very similar forecasts, uncertainty can be assumed to be low (which is why all methods

lead to similar results), there is little spread and hence, only a small buﬀer is necessary.

The aim of the BAP approach then is to avoid conﬂicts, i.e., overlaps, not only for the

planned berths, but also with respect to the time buﬀers, in order to enhance the sched-

ule’s robustness.

For this purpose, the BAP model using DTBs from Kolley etal. (2021) is further

modiﬁed and improved in this work. It is then applied to the forecast data. As the

respective model builds up on the model of Liu etal. (2017), on their scenario-based

approach and their robustness deﬁnition, the berth allocations which are derived using

the model presented below are compared to the results from Liu etal.’s model in order

to study the impact of the DTBs and the other changes made. The diﬀerences of the

models are discussed in detail in Sect.4.3.

The approach chosen in this work-the combination of AIS data exploration for fore-

casting, the subsequent use of an optimization approach which is based on the respec-

tive forecasts and the judgement of the quality of the results based on actual vessel

arrivals-is, to the authors’ knowledge, unique, even if some publications use AIS data

for forecasting. The contributions of this work hence are manifold:

a) It is discussed and shown how AIS data can be used for arrival time forecasting

and how the data sets can be cleaned and prepared beforehand. As Heilig etal.

(2020) point out, such “methodological insights regarding data preparation (e.g.,

data cleansing, feature selection) […] and model evaluation, are not discussed in

great detail in literature”; hence, this ﬁlls an important gap.

b) The diﬀerent ML methods which are applied in this work are studied with respect

to their forecast quality in order to judge which of them might be most appropriate

for vessel arrival time prediction.

L.Kolley et al.

1 3

c) It is shown how the forecast data can be used to derive more robust berth alloca-

tions by applying the concept of DTBs.

d) Moreover, the BAP model from Kolley etal. (2021) is further reﬁned such that

the solutions are of more practical use and relevance. This is shown by comparing

and benchmarking the resulting solutions with the model of Liu etal. (2017). The

latter model is used as a benchmark as its robustness concept, which concentrates

on the service level achieved in terms of vessels that can be served without con-

ﬂict, is the concept which, with further reﬁnements, is also used in this work.

e) The use of real data moreover allows for studying the true service level, i.e., the

resulting service level considering the real – not only the predicted – arrival times

of the vessels. Hence, the evaluation of the BAP models has high practical (and

not only theoretical) relevance.

In summary, the aim of this study is therefore to develop and examine a new

procedure that generates robust berthing plans by predicting vessel arrival times by

combining ML and OR methods. However, it has to be noted that increased robust-

ness can lead to losses in eﬃciency, as these two objectives are in conﬂict: More

robustness can be achieved by reserving more time for each vessel, but then the

quay’s capacity might not be fully exploited and there will be idle times, impeding

eﬃciency.

The remainder of this paper is structured as follows: Literature on trajectory fore

casting with ML in maritime logistics as well as on the BAP is reviewed in Sect.2.

Data pre-processing and the results of the ML algorithms are discussed in Sect.3. In

Sect.4, the mathematical model for the robust continuous berth allocation problem

with dynamic time buﬀers (ro-DTB-BAPc) is presented. The results of the numeri-

cal experiments are given and evaluated in Sect.5. Finally, the paper is concluded

by a critical discussion of the results, a summary and an outlook in Sect.6.

2 Literature review

2.1 AIS Data andmachine learning inmaritime logistics

AIS was developed in the 1990´s in order to improve maritime safety. Vessels

regularly broadcast information via AIS, which can be split into the categories of

static (e.g., vessel identity and size), dynamic (vessel’s position, speed etc.) and

voyage-related information (destination port and ETA), see Yang etal. (2019).

Yang etal. (2019) give an overview on maritime problems in which AIS data

are relevant and they review diﬀerent AIS data applications. In their review, Yang

etal. state that AIS data were ﬁrst mostly used in trajectory extraction and cluster-

ing for studies on navigation safety and the avoidance of vessel collisions, which

they call “basic applications”, but over time also “extended” and “advanced”

applications in other areas of maritime research were developed. In their litera-

ture review, the authors ﬁnd a strongly increasing number of publications on such

AIS data applications in particular in the more recent past, i.e., since 2015.

1 3

Robust berth scheduling using machine learning forvessel…

More involved (extended) problem ﬁelds in which AIS data were successfully

used are vessel behaviour analysis, e.g., with respect to ﬁshing or to investigate

navigation patterns or travel times and environmental evaluations, e.g., the analy-

sis of emissions and, subsequently, the optimization of sailing speed in order to

reduce such emissions.

AIS data are also used to analyse, in particular, activities at and near ports. For

example, Wu etal. (2020) discuss quality issues of AIS data and in particular the

problems these data can present with respect to identifying ports, i.e., how a “port

event” and the fact if a vessel is actually at a port can be identiﬁed from AIS data.

Feng etal. (2020) also use AIS data to derive trajectories in ports, while Chen

etal. (2020) exploit AIS data to identify the services and analyse the characteris-

tics of tugboat activities in ports. Franzkeit etal. (2020) investigate vessel waiting

times at ports based on AIS data.

ML recently has been applied in Maritime Logistics in very diﬀerent ways and

to diﬀerent planning problems. A structured review of the literature in this ﬁeld is

given by Dornemann et al. (2020); these authors also present an in-depth discus-

sion of the combination of OR and ML methods. Moreover, Filom etal. (2022) pre-

sent an extensive review of ML applications in ports. Therefore, just a few selected

recent examples on work relating to berthing and the BAP are given below:

Li and He (2020, 2021) predict liner berthing times using deep learning. While

Li and He (2020) present a more basic discussion of their approach, the data pre-

processing and some preliminary results, their procedure is reﬁned in the 2021 paper

where it is shown that feature extraction has a huge impact on prediction results. The

use of Deep Learning and an ANN for automatic berthing systems are suggested by

Lee etal. (2020), who combine AIS data with actual ML. The authors use nine dif-

ferent supervised ML methods for “predicting the risk range of an unsafe berthing

velocity when a ship approaches a port”, i.e., they study a very speciﬁc problem.

De Leon et al. (2017) employ ML for algorithm selection, i.e., for a meta-

learning problem, to solve the Bulk Carrier BAP. By their approach, the best

algorithm for the problem setting at hand can be determined, after the meta-algo-

rithm has been trained on diﬀerent problem settings and the relevant features hav-

ing an inﬂuence on algorithm performance have been found. In contrast, Chei-

manoﬀ etal. (2021) use ML for parameter tuning of the hyper-parameters that are

used in meta-heuristics for the Bulk Carrier BAP.

With respect to the topic of this work, it should be mentioned that De Leon etal.

(2017) as well as Cheimanoﬀ etal. (2021) and many other authors in the ﬁeld use

randomly generated vessel arrival times in their computational studies, i.e., no real

data are used and no arrival time prediction is employed, even in the most recent

publications. Consequently, no comparison with actual vessel arrival times can be

made, as it is the case in this work.

2.2 Trajectory forecasting

Many studies in the ﬁeld of maritime logistics estimate the time needed for given

routes under the assumption that the vessels sail at a known and given speed (Grida

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