Mathematical modeling for optimizing the sustainability of car sharing
Lead Research Organisation:
King's College London
Department Name: Engineering
Abstract
Private mobility has a high carbon footprint due to the manufacturing, use, parking, and disposal of vehicles. Private cars spend 96% of their time idle and were responsible for 60.7% of total CO2 emissions from road transport. To reduce CO2 emissions, this research proposes the development of the mathematical tools needed to deliver a financially sustainable, car sharing service that nudges private car owners toward adopting shared car usage.
This research will design new mathematical models that will allow optimal dynamic pricing of journeys over time and space; thus, will support shared mobility and net-zero goals. These models will combine queuing theory, stochastic dynamic programming, and simulation optimization. They will enable a more competitive pricing of journeys, a higher availability of shared cars, lower council subsidies, and reduced private car usage. They will constitute an exploratory phase of the larger scale aim of designing better demand models that support the financial sustainability of mobility as a service and investigate how these services may operate in (non-) urban contexts. They will be the prelude to the ambitious goal of designing a digital twin for car sharing systems. The increased awareness of climate change and the significant increase in fuel and living costs offer an opportunity to shift the behaviour of private car owners towards shared mobility, making this research timely and relevant.
This research will determine key metrics, and a better rich understanding of the state of shared cars across the UK. Through the engagement with stakeholders, it will define the constraints, and differences imposed by rural and urban contexts. This will enhance the feasibility and implementation of proposed solutions, inspire and guide car sharing usage.
It will design new mathematical models and numerical solution techniques for pricing using queuing theory and continuous time Markov chains, combined with optimization. An ambitious aim of this proposal is to experiment with frameworks for stochastic dynamic programming and their application to simple examples.
A key part of the project will be simulating car share services under different scenarios; allowing us to assess the steady state versus transient behaviour of the optimal solutions of queuing models; and conduct what-if experiments to inform policy and investment scenarios, with the ultimate aim of reaching real-time simulation of services and building a digital twin framework.
Finally, it will design a framework for real-time simulation and optimization of car sharing scenarios using a multi-fidelity optimization approach: a low-fidelity Markov chain model to identify a set of good solutions and a high-fidelity simulation model to refine the results. The model will find optimal pricing car-location strategies that maximize profits over a fixed time horizon.
Combining these optimization techniques addresses the practical challenge and advances an exciting new interdisciplinary research area for shared cars. The algorithmic approach also has the potential to be adapted to electric and autonomous vehicles in the future.
In summary, this project aims to lay the foundation for making car sharing more financially attractive to service providers by developing innovative mathematical models and simulation optimization methods that will allow its financial sustainability. This will offer direct societal benefits to the public and local authorities. If appropriately priced, it will reduce private car usage and local authorities' subsidies of the service. Thus, it will advance mathematical sciences and optimization techniques while it contributes to EPSRC's 4 economic growth and social prosperity outcomes and aligns with EPSRC's Digital Economy theme.
This research will design new mathematical models that will allow optimal dynamic pricing of journeys over time and space; thus, will support shared mobility and net-zero goals. These models will combine queuing theory, stochastic dynamic programming, and simulation optimization. They will enable a more competitive pricing of journeys, a higher availability of shared cars, lower council subsidies, and reduced private car usage. They will constitute an exploratory phase of the larger scale aim of designing better demand models that support the financial sustainability of mobility as a service and investigate how these services may operate in (non-) urban contexts. They will be the prelude to the ambitious goal of designing a digital twin for car sharing systems. The increased awareness of climate change and the significant increase in fuel and living costs offer an opportunity to shift the behaviour of private car owners towards shared mobility, making this research timely and relevant.
This research will determine key metrics, and a better rich understanding of the state of shared cars across the UK. Through the engagement with stakeholders, it will define the constraints, and differences imposed by rural and urban contexts. This will enhance the feasibility and implementation of proposed solutions, inspire and guide car sharing usage.
It will design new mathematical models and numerical solution techniques for pricing using queuing theory and continuous time Markov chains, combined with optimization. An ambitious aim of this proposal is to experiment with frameworks for stochastic dynamic programming and their application to simple examples.
A key part of the project will be simulating car share services under different scenarios; allowing us to assess the steady state versus transient behaviour of the optimal solutions of queuing models; and conduct what-if experiments to inform policy and investment scenarios, with the ultimate aim of reaching real-time simulation of services and building a digital twin framework.
Finally, it will design a framework for real-time simulation and optimization of car sharing scenarios using a multi-fidelity optimization approach: a low-fidelity Markov chain model to identify a set of good solutions and a high-fidelity simulation model to refine the results. The model will find optimal pricing car-location strategies that maximize profits over a fixed time horizon.
Combining these optimization techniques addresses the practical challenge and advances an exciting new interdisciplinary research area for shared cars. The algorithmic approach also has the potential to be adapted to electric and autonomous vehicles in the future.
In summary, this project aims to lay the foundation for making car sharing more financially attractive to service providers by developing innovative mathematical models and simulation optimization methods that will allow its financial sustainability. This will offer direct societal benefits to the public and local authorities. If appropriately priced, it will reduce private car usage and local authorities' subsidies of the service. Thus, it will advance mathematical sciences and optimization techniques while it contributes to EPSRC's 4 economic growth and social prosperity outcomes and aligns with EPSRC's Digital Economy theme.
Publications
Hou N
(2025)
Qualitative insights into travel behavior change from using private cars to shared cars
in International Journal of Sustainable Transportation
| Description | The most significant technical achievement from the award is the design of fast, tractable algorithms for optimising the prices charged in car sharing schemes where customers return cars to the base at the end of the hire, so-called round trip hires. These are complemented by a simulation model that allows more complexities to be included and simulation optimisation algorithms that can be used to find optimal prices for round-trip hires. We have also built good links with businesses, charities and local government working in the area through two in-person workshops held during the grant. The insights from these meetings have fed into the technical work. |
| Exploitation Route | We are writing up results on the technical work for publication in peer-reviewed journals and are investigating opportunities for future funding to take this work forward. |
| Sectors | Transport |
| Description | We engaged the different stakeholders in car sharing within the UK at two workshops. This gave local councils the opportunity to listen to the challenges and barriers to entry faced by commercial companies operating car sharing. It also helped us to scope the real problems within car sharing. For example, much of the current research in this area concentrates on one-way hires in which cars are picked up and dropped off at different locations, whereas in the UK almost all car sharing companies operate a back-to-base model. The full extent of the impact from this workshop is still being developed. The project has led to new MSc and PhD studentships at King's College London, University of Southampton and Lancaster University on the topic of car sharing. |
| First Year Of Impact | 2024 |
| Sector | Transport |
| Impact Types | Policy & public services |
| Description | What areas are good for car sharing? |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Policymakers/politicians |
| Results and Impact | The workshop had two purposes: (i) to develop a white paper describing the state of current research and practice in car sharing with a focus on how characteristics of a location impact on the effectiveness of car sharing; (ii) to inform potential funding bids and build partnerships. Through engagement with a breadth of stakeholders, the workshop will explore current practice, gain knowledge from previous and current car share services, and identify research priorities. Objectives • To gain an understanding of where car sharing works well. • To better understand the infrastructure requirements of car sharing schemes. • To learn from the experiences of existing services. • To scope a larger project and investigate interesting new research directions. Workshop notes are available: Currie, C. S., M'Hallah, R., and Oliveira, B. B. (2025). Notes from a workshop on what areas are good for car share schemes. doi.org/10.5258/SOTON/D3413. |
| Year(s) Of Engagement Activity | 2025 |
| Description | Workshop on Future Directions in Modelling Car Share Schemes |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | National |
| Primary Audience | Policymakers/politicians |
| Results and Impact | The workshop was designed to inform the scope and specification of the project, exploring current best practice, capturing learning from previous and current car share services, identifying research priorities, and establishing key measures of success. Objectives To engage with car sharing stakeholders: local councils, shared car providers (e.g., Zipcar), CoMoUK, and users. To finalise the problem framework, determine key metrics, and better understand the state of shared cars across the UK. To build from the experiences of stakeholders, understand their constraints, and appreciate the differences imposed by rural and urban contexts. To support the specification of the service so that its pricing is implementable in practice. Workshop notes available: Currie, C. S. and M'Hallah, R. (2024). Notes from a workshop on future directions in modelling car share schemes. doi.org/10.5258/SOTON/D3414. |
| Year(s) Of Engagement Activity | 2024 |