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.