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Backcasting the Optimal Decisions in Transport Systems: An Example with Electric Vehicle Purchase Incentives

Vinith Lakshmanan, Xavier Guichet, Antonio Sciarretta

TL;DR

The paper develops a backcasting framework for transport policy using optimal control to design policy roadmaps that minimize public expenditure while meeting a target $CO_2$ emission level. It introduces a reduced-order fleet model with a logit-based adoption mechanism and an auxiliary full-order model with age-structured stocks, solving the resulting OCP via analytical Lambert W solutions in the simplified case and numerical trust-region methods in the full model. A Metropolitan France case study demonstrates that an optimally decaying EV purchase incentive can meet the $CO_2$ target with substantial budget savings relative to a constant-incentive benchmark, and reveals a Pareto-like trade-off between emissions and incentives. The work provides a principled, dynamically optimized alternative to scenario-based policy design and suggests pathways for more detailed, regionally disaggregated and mode-diverse extensions with policy-relevant implications for decarbonizing road transport.

Abstract

This study represents a first attempt to build a backcasting methodology to identify the optimal policy roadmaps in transport systems. In this methodology, desired objectives are set by decision makers at a given time horizon, and then the optimal combinations of policies to achieve these objectives are computed as a function of time (i.e., ``backcasted''). This approach is illustrated on the transportation sector by considering a specific subsystem with a single policy decision. The subsystem describes the evolution of the passenger car fleet within a given region and its impact on greenhouse gas emissions. The optimized policy is a monetary incentive for the purchase of electric vehicles while minimizing the total budget of the state and achieving a desired CO$_2$ target. A case study applied to Metropolitan France is presented to illustrate the approach. Additionally, alternative policy scenarios are also analyzed to provide further insights.

Backcasting the Optimal Decisions in Transport Systems: An Example with Electric Vehicle Purchase Incentives

TL;DR

The paper develops a backcasting framework for transport policy using optimal control to design policy roadmaps that minimize public expenditure while meeting a target emission level. It introduces a reduced-order fleet model with a logit-based adoption mechanism and an auxiliary full-order model with age-structured stocks, solving the resulting OCP via analytical Lambert W solutions in the simplified case and numerical trust-region methods in the full model. A Metropolitan France case study demonstrates that an optimally decaying EV purchase incentive can meet the target with substantial budget savings relative to a constant-incentive benchmark, and reveals a Pareto-like trade-off between emissions and incentives. The work provides a principled, dynamically optimized alternative to scenario-based policy design and suggests pathways for more detailed, regionally disaggregated and mode-diverse extensions with policy-relevant implications for decarbonizing road transport.

Abstract

This study represents a first attempt to build a backcasting methodology to identify the optimal policy roadmaps in transport systems. In this methodology, desired objectives are set by decision makers at a given time horizon, and then the optimal combinations of policies to achieve these objectives are computed as a function of time (i.e., ``backcasted''). This approach is illustrated on the transportation sector by considering a specific subsystem with a single policy decision. The subsystem describes the evolution of the passenger car fleet within a given region and its impact on greenhouse gas emissions. The optimized policy is a monetary incentive for the purchase of electric vehicles while minimizing the total budget of the state and achieving a desired CO target. A case study applied to Metropolitan France is presented to illustrate the approach. Additionally, alternative policy scenarios are also analyzed to provide further insights.

Paper Structure

This paper contains 10 sections, 39 equations, 6 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. Assumptions
  4. Modeling and backcasting: Reduced-order model
  5. Modeling and backcasting: Full-order model
  6. Results and discussion
  7. Case study: Data
  8. Reference Scenarios
  9. Backcasting results
  10. Conclusions

Figures (6)

  • Figure 1: Model Inputs and Parameters
  • Figure 2: Determinants used in the logit model.
  • Figure 3: Reference Scenarios with the full model: CO$_2$ emissions (top) and EV stock (bottom) as a function of time.
  • Figure 4: Incentive (top), Yearly Emission (bottom left), and Cumulative Emission (bottom right) Profile
  • Figure 5: Vehicle Sales (top) and Vehicle Stock (bottom)
  • ...and 1 more figures