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Optimal taxes and subsidies to incentivize modal shift for inner-city freight transport

Krissada Tundulyasaree, Layla Martin, Rolf N. van Lieshout, Tom Van Woensel

TL;DR

The paper tackles inner-city freight modal shift by a bilevel model in which a transportation authority sets distance-based road taxes $t$ and per-unit subsidies $s$, financed through revenue recycling from budget $B$, and freight forwarders respond with a PDPTW-SL routing to minimize costs. The upper level uses a bi-section approach to optimize $(s,t)$ while the lower level solves the PDPTW-SL routing, with the forwarder’s decisions feeding back into the budget constraint $B = s f^*(s,t) - t \phi d^*(s,t)$. Theoretical results show that fully subsidizing the scheduled line is optimal under feasibility, and numerical experiments (including a Berlin case) demonstrate driven-distance reductions up to $12.5\%$ and substantial modal shifts as scheduled-line frequency increases, albeit with higher system costs borne by the forwarder unless offset by budget. The findings underscore the practical potential of revenue-recycling-based subsidies to achieve intermodal freight goals, and highlight trade-offs related to order distribution, service frequency, and policy budgets, pointing to avenues for refining exact solution methods and extending to multiple forwarders.

Abstract

With increasing freight demands for inner-city transport, shifting freight from road to scheduled line services such as buses, metros, trams, and barges is a sustainable solution. Public authorities typically impose economic policies, including road taxes and subsidies for scheduled line services, to achieve this modal shift. This study models such a policy using a bi-level approach: at the upper level, authorities set road taxes and scheduled line subsidies, while at the lower level, freight forwarders arrange transportation via road or a combination of road and scheduled lines. We prove that fully subsidizing the scheduled line is an optimal and budget-efficient policy. Due to its computational complexity, we solve the problem heuristically using a bi-section algorithm for the upper level and an Adaptive Large Neighbourhood Search for the lower level. Our results show that optimally setting subsidy and tax can reduce the driving distance by up to 12.5\% and substantially increase modal shift, albeit at a higher operational cost due to increased taxes. Furthermore, increased scheduled line frequency and decreased geographical scatteredness of freight orders increase modal shift. For the partial subsidy policy, we found that an additional budget provides a better trade-off between minimizing distance and transportation costs than solely increasing the subsidy level. In a Berlin, Germany, case study, we find that we can achieve up to 2.9\% reduction in driven distance due to 23.2\% scheduled line usage, which amounts to an increase of multiple orders of magnitude, despite only using a few stations for transshipment.

Optimal taxes and subsidies to incentivize modal shift for inner-city freight transport

TL;DR

The paper tackles inner-city freight modal shift by a bilevel model in which a transportation authority sets distance-based road taxes and per-unit subsidies , financed through revenue recycling from budget , and freight forwarders respond with a PDPTW-SL routing to minimize costs. The upper level uses a bi-section approach to optimize while the lower level solves the PDPTW-SL routing, with the forwarder’s decisions feeding back into the budget constraint . Theoretical results show that fully subsidizing the scheduled line is optimal under feasibility, and numerical experiments (including a Berlin case) demonstrate driven-distance reductions up to and substantial modal shifts as scheduled-line frequency increases, albeit with higher system costs borne by the forwarder unless offset by budget. The findings underscore the practical potential of revenue-recycling-based subsidies to achieve intermodal freight goals, and highlight trade-offs related to order distribution, service frequency, and policy budgets, pointing to avenues for refining exact solution methods and extending to multiple forwarders.

Abstract

With increasing freight demands for inner-city transport, shifting freight from road to scheduled line services such as buses, metros, trams, and barges is a sustainable solution. Public authorities typically impose economic policies, including road taxes and subsidies for scheduled line services, to achieve this modal shift. This study models such a policy using a bi-level approach: at the upper level, authorities set road taxes and scheduled line subsidies, while at the lower level, freight forwarders arrange transportation via road or a combination of road and scheduled lines. We prove that fully subsidizing the scheduled line is an optimal and budget-efficient policy. Due to its computational complexity, we solve the problem heuristically using a bi-section algorithm for the upper level and an Adaptive Large Neighbourhood Search for the lower level. Our results show that optimally setting subsidy and tax can reduce the driving distance by up to 12.5\% and substantially increase modal shift, albeit at a higher operational cost due to increased taxes. Furthermore, increased scheduled line frequency and decreased geographical scatteredness of freight orders increase modal shift. For the partial subsidy policy, we found that an additional budget provides a better trade-off between minimizing distance and transportation costs than solely increasing the subsidy level. In a Berlin, Germany, case study, we find that we can achieve up to 2.9\% reduction in driven distance due to 23.2\% scheduled line usage, which amounts to an increase of multiple orders of magnitude, despite only using a few stations for transshipment.
Paper Structure (18 sections, 11 theorems, 15 equations, 5 figures, 3 tables, 1 algorithm)

This paper contains 18 sections, 11 theorems, 15 equations, 5 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Literature Review
  3. Modal Shift Regulations
  4. Last-mile delivery using Scheduled Lines
  5. Problem Description and Formulation
  6. Problem Narrative
  7. Freight Forwarder Decision Model
  8. Bilevel Road Tax and Train Subsidy Model
  9. Properties of the optimal policy
  10. Solution algorithm
  11. Numerical Experiments
  12. Experimental Design
  13. Optimal Policies for the Transportation Authority and the Freight Forwarder
  14. Order Scatteredness and Scheduled Line Services Frequency
  15. A trade-off between minimizing distances and minimizing total cost of transportation under different policies
  16. ...and 3 more sections

Key Result

Proposition 1

For a given budget $B$, the freight forwarder's total cost decreases if and only if the driven distance is increasing, i.e., for two feasible solutions $\langle s_1,t_1,d_1^\star,f_1^\star\rangle$, $\langle s_2, t_2,d_2^\star,f_2^\star\rangle$,

Figures (5)

  • Figure 1: Different order location geographies
  • Figure 2: Impact of order scatteredness on the performances of base and optimal policies
  • Figure 3: Impact of train frequency per hour on the performances of base and optimal policies
  • Figure 4: Trade-off between transportation authority and freight forwarder for policies with partial subsidy and optimal policy with different budgets.
  • Figure 5: a Berlin case study

Theorems & Definitions (18)

  • Proposition 1
  • Proposition 2
  • Example 1
  • Proposition 3
  • Proposition 4
  • Proposition 5
  • Lemma 1
  • proof
  • Proposition 1
  • proof
  • ...and 8 more