Dynamic Pricing in the Ferry Industry

Lead Research Organisation: University of Southampton
Department Name: Sch of Mathematical Sciences


Choosing the "best" ticket prices is one of the key challenges in the ferry industry, especially for ferry operators providing a service to both individuals and freight. When setting the ticket price, the operators need to (1) forecast the demand for ferry services by various types of passengers and their vehicles; (2) decide how much space should be allocated to different vehicle types; and (3) estimate how easily vehicles can be packed into the available deck space.

Forecasting demand, finding the most profitable allocation of space to different customers, and pricing of tickets fall under the umbrella term of Revenue Management (RM), which was originally developed for airlines, but is applicable across a wide-range of industries. What is new in this first part of the project is the inclusion of packing. By incorporating optimal packing of vehicles on the ferry into RM, we will find pricing and allocation solutions that increase the efficiency of ferry services and ensure the pricing properly reflects the cost of packing a vehicle into the limited deck space.

Traditionally, RM has focused on maximising the revenue on each individual journey, but there is a need to look at the bigger picture and consider the effects of prices on the long-term profitability of the operator. Ferries are used by tourists who travel relatively infrequently and by regular customers, e.g. freight, commuters and regular coach services. By optimizing revenue in the longer term, e.g. over one year, as well as considering individual sailings, we will be able to take account of the total contribution of regular customers. For example, a freight company that operates year round or commuters who use the ferry regularly should not be priced out of the market during the peak summer season, but should be offered a price that reflects their long-term value to the company. Surprisingly little work has been carried out in this area, which is relevant to nearly all transport providers and is vital to avoid over-pricing tickets for regular customers at peak times.

Through working with P&O Ferries and Red Funnel, who operate ferries between mainland Britain and the Continent, and the Isle of Wight, respectively, we will use real data to inform the models. These real data are collected from various internal or external systems/sources (e.g. ticket booking systems, company's websites, frontline operating systems, marketing campaign records, market competitiveness reports, etc.). This project will first look at how to link these data together so that they could be used in building and testing our proposed quantitative models. The result of this project will therefore become a good example of utilising the potential of "Big Data".

After collecting and preparing the data, our models will be developed to estimate the ticket prices which maximise revenue for the ferry operator. Improving revenues will be achieved in two ways: (1) increasing the number of vehicles that can be packed onto the ferry thanks to more effective packing algorithms; (2) optimizing prices based on forecast demand for different sailings. Improving the mix of vehicles on the ferry and the way they are packed will increase the efficiency of ferry services, having a positive environmental impact.

The work has wide-ranging implications in a number of industry sectors, particularly in optimal pricing for freight, where packing needs to be taken into account when setting delivery charges. Developing methods for optimizing revenue in the long-term could improve the pricing in any industries in which there is a mix of regular and occasional traffic.

Planned Impact

The proposed project will bring beneficial impact to a wide range of stakeholders. We consider it essential that the research work feeds into and back from real-world applications and our collaborators will of course have the opportunity to bring ideas into the research, and frame the problems we are trying to tackle, as well as hearing our results first hand. Our partners, P&O Ferries and Red Funnel, will thus gain insight into how to employ new models to understand their customers so as improve their Revenue Management (RM) strategies. Members of RMAPI, the society for RM professionals within the UK, will also have opportunities to gain from the work and provide feedback on its direction through seminars and networking.

The generic tools that we develop as part of this project will be freely available for download from the project website, alongside YouTube videos explaining the key ideas of the methods and relevant articles written by the research team. Smaller-scale organisations will therefore have access to new technology and resources, without undergoing the risk associated with research and development.

The University of Southampton's close link with RMAPI is vital for the transformation of academic results into real-world applications, with obvious benefits for UK industry. Dr Currie is a regular presenter at the RMAPI conferences and this will help with dissemination of results.

Teaming up three researchers from different specialities to apply mathematical models within a Revenue Management project will obviously benefit the field of Operational Research, but due to the strong industry relevance of the research, we would expect a wider academic community in computer science and social science to gain from the deepening of expertise in this area. Through attending conferences, holding workshops and seminars, and liaising with industrial partners, the project team will develop and strengthen their research and leadership skills. In particular, they will be more capable to lead or participate in high-impact industry-oriented projects in the future. Having more effective interfaces between Higher Education Institutes and Business is one of the key elements in helping the UK to become an innovative economy.

Increasing the efficiency of ferry transportation will reduce fuel bills and hence reduce costs and greenhouse emissions. Increasing the revenue available to ferry operators will make the industry more sustainable within the UK. Being an island nation, reliant on shipping for most importing and exporting, as well as foreign travel, a sustainable shipping operation is vital for a healthy economy.

The project will enable value to be extracted from the ever-growing quantities of online and offline data. In recent years, there has been increasing investment in data acquisition, and how to utilize "Big Data" is a topical question for both government and business. This research will become a classic example of how to create knowledge efficiently and effectively from data to face emerging challenges. It may not be possible to measure this impact directly but both the academic community and society will draw inspiration from this project.

A further impact of this project is on people. We will develop and present a workshop to school children, demonstrating the importance of mathematics outside of the classroom. In addition, by providing training and experience for the PDRA working on the project, and by sharing our experiences with students on the MSc programmes in Operational Research and Management Sciences at the University of Southampton, we will be increasing expertise in the UK in this vital area of OR.

In summary, the project results will be useful for a wide range of audiences to achieve policy goals, social goals or, most likely, to achieve commercial goals.


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Bayliss C (2019) Dynamic pricing for vehicle ferries: Using packing and simulation to optimize revenues in European Journal of Operational Research

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Bayliss C (2021) Queue-constrained packing: A vehicle ferry case study in European Journal of Operational Research

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Martinez-Sykora A (2021) Optimizing pricing and packing of variable-sized cargo in IMA Journal of Management Mathematics

Description We have developed a practical method for determining a dynamic pricing policy for vehicle ferries. The policies take account of how well vehicles can be fitted onto a ferry given the traffic that has already been accepted when setting the price to charge, which is allowed to vary during the selling period.

The heuristic methods that we have developed perform well relative to optimal pricing and work with real problems.

We have also developed a simulator that can be used to estimate space used on the vehicle decks and suggest an optimal configuration for vehicles on the decks of a vehicle ferry. These vehicles vary in size from motorcycles to large articulated lorries and so the packing problem is non-trivial.
Exploitation Route Red Funnel have been using our models on a regular basis to help improve the efficiency of their packing and to highlight loads that are likely to be difficult to fit on the ferry. Prior to the covid-19 pandemic there was a chance of some follow on work with other vehicle ferry operators, using the results of this grant, but this seems unlikely to go ahead given the current slow down in demand.

The work has the potential to be used in other sectors such as bespoke manufacturing and delivery and logistics applications.
Sectors Aerospace, Defence and Marine,Digital/Communication/Information Technologies (including Software),Manufacturing, including Industrial Biotechology,Transport

Description As reported in other sections of the submission, we have continued a successful partnership with Red Funnel Ferries who operate vehicle ferries between the mainland and the Isle of Wight. The ferries form a vital link for inhabitants of the Isle of Wight and are used to transport nearly all freight on and off the island, as well as tourists during the summer months and commuters all year round. The wide range of vehicle sizes on the ferry and the different journey purposes results in a complex packing and pricing problem. Our research has led to a better understanding of optimal solutions for packing the ferries among Red Funnel staff. In particular, we have developed a loading simulator that has been implemented in two different products: 1. as a training tool for helping staff learn how to choose the placement of vehicles on the decks to optimize the utilisation; 2. as an alert tool that indicates at the start of each day which crossings are likely to be problematic and to suggest possible loading configurations. The alert tool is being used at Red Funnel currently . Meetings with Red Funnel have also helped them to think of other ways of improving their business processes. We have not been able to replicate this impact with P&O Ferries, as planned in the project proposal because, despite our efforts, they stopped engaging with the project.
First Year Of Impact 2018
Sector Aerospace, Defence and Marine,Transport
Impact Types Economic

Description Dynamic loading in Marine Transport (DYLMT) - internal grant from the Southampton Marine and Maritime Institute
Amount £8,248 (GBP)
Organisation University of Southampton 
Sector Academic/University
Country United Kingdom
Start 11/2018 
End 07/2020
Description Packing and Pricing with Red Funnel 
Organisation Red Funnel
Country United Kingdom 
Sector Private 
PI Contribution The team has contributed expertise in estimating customer lifetime value, optimal packing and optimal pricing. This has taken place through meetings with Red Funnel and regular e-mail communication. In February 2018, we shared software with Red Funnel that can be used to train personnel who work to load the ferries. In 2019 we extended the software to allow it to be used as an alert tool, which indicates when the ferry has the potential to be overloaded and suggests how packing could be carried out efficiently.
Collaborator Contribution Red Funnel has contributed their expertise in the practical aspects of the ferry industry. They have also contributed considerable time, showing the team the docks and the ferries. We have used Red Funnel data to test our methods and the Red Funnel analysts have spent time extracting the correct data for us and explaining its meaning.
Impact This collaboration helped with the research needed to write the article: A Simheuristic Approach to the Vehicle Ferry Revenue Management Problem (doi: 10.1109/wsc.2016.7822274) and the follow up journal publication (https://doi.org/10.1016/j.ejor.2018.08.004).
Start Year 2015
Title Vehicle Ferry Loading Simulation 
Description The software simulates the loading process for a vehicle ferry, accounting for different vehicle dimensions. As well as allowing the user to test out different packing configurations, it also incorporates an optimisation algorithm that can be used to find a (near) optimal solution. The the code is written in Java. 
Type Of Technology Software 
Year Produced 2018 
Impact The software is being trialled by one of our partners. 
Description Invited talk at a national forum for revenue management: Revenue Management and Pricing International 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Industry/Business
Results and Impact The PI, Dr Christine Currie and our main contact at Red Funnel Ferries gave a joint talk describing the work that we had done as part of the grant to an audience of revenue management practitioners and senior managers from across the UK.
Year(s) Of Engagement Activity 2018
Description Optimization Master Class 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach Regional
Primary Audience Schools
Results and Impact Christine Currie ran an Optimization Master Class for talented 15-16 year olds, as part of the Royal Society's series of master classes. The session lasted for half a day and attracted around 50 children. As part of the master class, the participants took part in a Revenue Management game, which gave them the opportunity to see where mathematics could be used in a practical setting. Worksheets developed for the class were also made available to any school teachers present on the day, to aid with dissemination.
Year(s) Of Engagement Activity 2016
Description Packing a Ferry Activity at Science and Engineering Day 2016 
Form Of Engagement Activity Participation in an open day or visit at my research institution
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Public/other audiences
Results and Impact We designed an outreach activity based on the research problem addressed in the grant, namely packing a ferry effectively and optimizing the revenue. Between 100 and 200 people carried out the activity. This led to further questions about the research and a wider discussion of the use of Mathematics, particularly Operational Research, in the real world. To support these questions, we produced a poster that participants could read after carrying out the practical activity.
Year(s) Of Engagement Activity 2016
Description Schools talk on real world maths 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Regional
Primary Audience Schools
Results and Impact The activity involved giving a talk to school girls about how mathematics is used in the real world, using models that we have developed on this project as one of my examples. We gave the talk twice, reaching around 100 school girls of secondary school age.
Year(s) Of Engagement Activity 2017
Description Talk on Pricing and Ferry Packing at Southampton Science Cafe 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Public/other audiences
Results and Impact Around 20 people attended this general interest talk, which led to some interesting debate and gave the participants a better understanding of how mathematics can be used to solve real-world problems.
Year(s) Of Engagement Activity 2019