Pith. sign in

REVIEW 4 major objections 5 minor 45 references

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

T0 review · 4 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read This paper proves that fully subsidizing scheduled-line freight services, financed by a road tax, is an optimal and budget-efficient policy for reducing inner-city truck distance.

desk verdict A novel bi-level model for urban freight modal shift with a clean-looking full-subsidy theorem, but the proof of Proposition 4 has a tie-breaking gap and the numerics need cleanup; send to review with major revision expected. read the letter →

arxiv 2501.09467 v1 pith:VAXJ5XSL submitted 2025-01-16 math.OC

Krissada Tundulyasaree , Layla Martin , Rolf N. van Lieshout , Tom Van Woensel This is my paper · ORCID
classification math.OC MSC 90B0690C59
keywords modalshiftscheduledlineservicesroadtaxsubsidybi-leveloptimizationfreight-on-transitpickupanddeliveryproblemwithtimewindowsurbanfreighttransport
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper asks whether a public authority can use road taxes and subsidies for scheduled line services (buses, metros, trams, barges) to shift inner-city freight off the road, and what the best such policy looks like. Modeling the authority as a leader and a cost-minimizing freight forwarder as follower in a bi-level Stackelberg game, the paper proves that fully subsidizing the scheduled line is optimal and budget-efficient: if the required subsidy does not exceed the forwarder's scheduled-line cost under free service, the authority can always achieve the smallest possible truck distance by setting the scheduled line fare to zero and financing it with a road tax. This matters because it turns a complex pricing problem into a simple rule, and numerical experiments confirm large modal shifts and driving-distance reductions (up to about 12.5%). The cost is a higher operational burden on forwarders, which the authority can offset by allocating an additional budget.

What carries the argument

The key object is the bi-level model in equations (1) through (4). The upper level minimizes road distance $d$ subject to the budget-balance constraint $sf^*(s,t) - t d^*(s,t) = B$ (with unit road cost normalized to 1), and the lower level is the freight forwarder's Pickup and Delivery Problem with Time Windows and Scheduled Lines, whose cost is $(1+t)d + (1-s)f$. The load-bearing observation is that setting the subsidy to 1 (fully subsidizing the scheduled line) removes the $f$ term from the forwarder's objective, so the forwarder minimizes road distance alone; the resulting distance $d_{\text{full}}$ is a lower bound for every policy, and choosing the tax to balance the budget reaches this bound. This reduction of a two-dimensional policy search to a single tax calculation is what carries the proof of optimality.

What would settle it

Add a fixed cost per vehicle to the forwarder's objective in the paper's model and re-solve the bi-level problem on the smallest test instances; if the optimal subsidy drops below 1 or the distance savings fall, the full-subsidy optimality result no longer holds in that setting.

Watch

Extended reading notes

Core claim

The central claim is Proposition 4: let $f_{\text{full}}$ be the freight forwarder's scheduled-line flow cost under the policy $(s=1, t=0)$, and let $d_{\text{full}}$ be the corresponding road distance. If $B \le f_{\text{full}}$, there exists an optimal policy with full subsidy $s=1$; if $B > f_{\text{full}}$, no feasible policy exists. Concretely, the authority can make the scheduled line free and set the road tax to $t=(f_{\text{full}}-B)/d_{\text{full}}$, achieving the lower-bound distance $d_{\text{full}}$ while balancing the budget $sf - td = B$. Because with $s=1$ the forwarder's objective reduces to minimizing road distance alone, $d_{\text{full}}$ is the global minimum possible distance, so this policy is optimal among all feasible tax-subsidy pairs. The paper also proves (Proposition 5) that under the full-subsidy policy the forwarder's routing decision is independent of the budget, and every extra unit of budget reduces the forwarder's total cost by one unit.

Load-bearing premise

The proof assumes the freight forwarder's cost is exactly the distance-proportional road cost plus the flow-proportional scheduled-line cost, with no fixed or per-vehicle costs; the paper's authors state in the conclusion that vehicle fixed costs are omitted.

Editorial extensions

If this is right

  • A transport authority that can make scheduled lines free and levy a road tax will reach the smallest possible total road distance available under any tax-subsidy policy.
  • Under the full-subsidy policy, extra authority budget does not change routing choices; it is transferred one-for-one into lower freight-forwarder costs.
  • Numerical experiments on 100-request instances show driving-distance reductions of 4.3% to 12.5% and modal shifts that can exceed 40%, at higher forwarder operating cost.
  • Higher scheduled-line frequency and wider time windows increase the attainable modal shift, while the savings saturate once frequency exceeds a threshold.
  • In the Berlin case study, the policy yields up to 2.9% distance reduction with 23.2% of demand moved to the S-Bahn when line costs are set high.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The proof of optimality depends only on the additive distance/flow cost structure, so the full-subsidy rule should carry over to any lower-level model with two transport channels of that form, including settings with pickup/delivery constraints beyond the PDPTW-SL.
  • The paper's own caveat about omitted per-vehicle costs suggests a natural stress test: adding a fixed cost per vehicle may break the full-subsidy optimum, since the experiments show the optimal policy already increases the number of vehicles.
  • Because the numerical results come from an ALNS heuristic without a reported optimality gap, an exact lower-level solver on small instances would bound how much of the 12.5% saving is real versus an artifact of the search.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper studies a bilevel model in which a public authority chooses a road tax t and a subsidy s for scheduled-line freight services, subject to a budget-balance constraint, while a freight forwarder minimizes its total transportation cost in a pickup-and-delivery problem with scheduled lines. The main theoretical claim is that fully subsidizing the scheduled line is optimal and budget-efficient: under the optimal policy the minimum possible road distance is attained, and the required tax rate is (f_full - B)/d_full. The paper also reports numerical experiments on generated instances and a Berlin case study, claiming driving-distance reductions of up to 12.5% (and up to 15.0% in Table 1) and substantial modal shifts. The proofs are collected in Appendix A. The numerical solution uses a bisection search at the upper level and an Adaptive Large Neighbourhood Search at the lower level.

Significance. If the full-subsidy theorem is correct, it provides a strikingly simple policy prescription for urban freight: make scheduled-line services free and use a road tax to balance the budget. This is a falsifiable, actionable result rather than a purely structural observation, and the paper gives it a transparent proof framework. The experimental study is extensive, includes sensitivity analyses on scattering and service frequency, and applies the model to a realistic Berlin network. The paper does not supply code or data, but the instance generation and parameter choices are described in sufficient detail to be reproduced. The central theoretical proof, however, currently depends on an unstated tie-breaking assumption, and the numerical claims contain an internal inconsistency between the reported maximum reduction and the abstract; both must be resolved before the result is fully convincing.

major comments (4)
  1. [§3.3 and Appendix A, proof of Proposition 4] The proof of Proposition 4 silently assumes that the deterministic lower-level solution selected at (s=1,t=0) remains the selected solution at the constructed tax rate t=(f_full−B)/d_full. At s=1 the lower-level objective is (1+t)d, so every solution attaining d_full remains optimal for every t≥0, regardless of its scheduled-line cost f. Section 3.3 fixes the selection only for a single input (s,t); it does not state that the selection is invariant across tax rates. Consequently, the constructed policy can violate the budget constraint (2) if the follower switches to another min-distance solution with different f, and the infeasibility claim for B>f_full does not follow without an additional argument bounding f* by f_full. The proof needs an explicit tie-breaking rule, such as a t-invariant deterministic selection or an optimistic (cooperative) selection, together with a proof that the budget equality is met under that rule.
  2. [§6.2, Table 1, and abstract] The abstract, Result 1, and the conclusions state that the optimal policy reduces driving distance by up to 12.5%, but Table 1 reports reductions of −14.0% for Inter-Diff-W and −15.0% for Inter-Rand-W. Since these are reductions in driving distance, the stated maximum is inconsistent with the reported numerical results. The percentages in the abstract, Section 6.2, and Section 8 need to be reconciled with Table 1.
  3. [Appendix A, proof of Proposition 3] The displayed derivation in the proof of Proposition 3 contains a garbled expression ("= d∗2 + t′d⋆(s)+B f ⋆(s) d∗2 d∗(s) f ∗(s) − s′f ∗2 + f2 − d∗2 d∗(s) B") that makes the argument impossible to verify as printed. The step that replaces s by s′ also uses without explicit justification the sign of (d2*/d*(s)) f*(s) − f2*; the sign can be derived from Lemma 1 and d2*>d*(s), but it must be stated. This proof is load-bearing because Proposition 3 is used to establish the full-subsidy optimality in Proposition 4.
  4. [§5 and §6.2] The numerical policies, including the tax rates and distance savings in Table 1, are computed with the ALNS heuristic, and Section 5 explicitly notes that Algorithm 1 may produce a suboptimal solution. No optimality gap or comparison with an exact method is reported for the instances used in the headline claims. Since the central empirical contribution is the magnitude of the distance reduction, the paper should either report an optimality gap estimate or validate the heuristic solutions against a branch-and-price method on the smaller instances, and it should state clearly that the reported distance reductions are heuristic upper bounds.
minor comments (5)
  1. [Algorithm 1] The pseudocode of Algorithm 1 tests whether f((x0+x1)/2) = B and uses |f((x0+x1)/2)| > epsilon, but the stopping condition should compare |f((x0+x1)/2) − B| to epsilon. As printed, the algorithm's termination criterion is incorrect.
  2. [Appendix A, proof of Proposition 2] The proof contains the typo "(1 + t1) (d⋆1 − d⋆1)", which should read "(1 + t1) (d⋆2 − d⋆1)", and the final displayed implication is a verbal shortcut: the correct conclusion is that (1+t1)>(1+t2), contradicting t1<t2. This is readily fixable but should be corrected.
  3. [§8] The limitation about omitting the initial cost of using more vehicles is acknowledged in Section 8; please make this limitation explicit in the abstract or introduction as well, since the numerical results show an increase in the number of vehicles under the optimal policy.
  4. [Abstract and §7] The phrase "an increase of multiple orders of magnitude" to describe the modal shift from 4.0% to 23.2% in the Berlin case study is inaccurate; 23.2/4.0 is less than one order of magnitude. Please reword.
  5. [§7] The decimal separator in "2,4 €" is inconsistent with the decimal notation used elsewhere in the paper; please harmonize.

Circularity Check

0 steps flagged · score 1.0 of 10

No material circularity: central theorems are derived from the stated model, not fitted to data; the main internal gap is an unproven tie-breaking assumption, which is a correctness issue rather than a circular reduction.

full rationale

The derivation chain is self-contained with respect to the paper's claims. Propositions 1-5 are proved algebraically from the stated bi-level model (Eqs. 1-4), not from fitted data. Proposition 4 constructs the full-subsidy policy from f_full and d_full defined at (s=1,t=0); the proof's unstated assumption that the follower's deterministic selection among min-distance solutions is invariant to t is a mathematical gap (Section 3.3's determinism assumption applies per input (s,t), not across tax rates), but it is a correctness concern, not a circular definition or a fitted quantity masquerading as a prediction. Numerical experiments use chosen parameters and an internal base scenario with no intervention; the claimed 12.5% reduction is an internal simulation result, not an out-of-sample prediction. Self-citations to Ghilas et al. (2016a, 2016b) for the ALNS solver and the PDPTW-SL model are background algorithmic/modeling references; they share an author but are not used to justify the optimality theorem, so they are not load-bearing. Section 8 explicitly acknowledges the omitted per-vehicle fixed cost, which limits external validity but does not make the derivation circular. No step in the paper reduces a claimed result to its own input by construction.

Assumptions & free parameters 2 free parameters · 8 assumptions · 0 invented entities

The model is built on standard OR assumptions: a cost-minimizing follower, a single leader objective, fixed transit supply, and no demand response. The most consequential omissions are the absence of fixed vehicle costs (explicitly acknowledged in Section 8) and the reliance on a heuristic for the lower level. No new physical or economic entities are introduced.

free parameters (2)
  • per-unit road distance cost phi = phi = 1 in theoretical proofs; phi = 0.25 in synthetic experiments
    Chosen as an input, not fitted; scales the tax level and the forwarder's cost in Eq. (4).
  • per-unit scheduled-line cost coefficient = 0.1 per unit distance in synthetic experiments; 2 and 4 euros in the Berlin case study
    Chosen input parameter; the modal shift and distance savings depend on this value, as shown in Table 3.
assumptions (8)
  • domain assumption Freight forwarder minimizes total cost (1+t)phi d + (1-s)f (Eq. 4).
    Behavioral model of the lower-level Stackelberg follower; all theoretical results build on this objective.
  • domain assumption Demand is exogenous and constant regardless of tax or subsidy.
    Section 3.1 states freight demands remain constant; the forwarder is a price-taker. This rules out demand-side responses.
  • domain assumption Scheduled line network, capacity, and timetable are fixed inputs.
    Section 3.1 treats strategic and tactical decisions as given; the operational PDPTW-SL is the only response.
  • domain assumption Budget constraint is exactly balanced: s f* - t phi d* = B (Eq. 2).
    Defines revenue recycling; if the authority could run a surplus or deficit, the full-subsidy result would change.
  • domain assumption Authority's objective is solely to minimize total road distance (Eq. 1).
    No weight on freight forwarder costs, emissions, or equity; Proposition 4's optimality is relative to this single objective.
  • domain assumption Freight forwarder cost excludes fixed and per-vehicle costs.
    Lower-level objective has only distance and line-flow terms; Section 8 acknowledges this omission ('omits the initial cost of using more vehicles').
  • ad hoc to paper Deterministic tie-breaking among multiple lower-level optima.
    Section 3.3 assumes a deterministic selection to make d*(s,t) and f*(s,t) well-defined; not independently justified.
  • ad hoc to paper Lower-level solutions used in experiments are near-optimal (ALNS).
    Section 5 uses ALNS instead of exact optimization; the reported policy values are only as good as the heuristic, with no optimality gap reported.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Optimal taxes and subsidies to incentivize modal shift for inner-city freight transport." pith.science (2026). https://pith.science/paper/VAXJ5XSL

@misc{pith2026250109467,
  author       = {Pith},
  title        = {Pith review of: Optimal taxes and subsidies to incentivize modal shift for inner-city freight transport},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VAXJ5XSL}},
  note         = {Machine review of arXiv:2501.09467}
}
read the original 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.

Figures

Figures reproduced from arXiv: 2501.09467 by the authors.

Figure 1
Figure 1. Different order location geographies 6. Numerical Experiments This section presents the findings from a series of numerical experiments with the bi-level model. We describe the experimental design and then dis￾cuss the benefits and consequences of optimal policies for transportation au￾thorities and freight forwarders. Moreover, we conduct a sensitivity analysis to assess the impact of the scatteredness of order and… view at source ↗
Figure 2
Figure 2. Impact of order scatteredness on the performances of base and optimal policies [PITH_FULL_IMAGE:figures/full_fig_p019_2.png] view at source ↗
Figure 3
Figure 3. Impact of train frequency per hour on the performances of base and optimal [PITH_FULL_IMAGE:figures/full_fig_p020_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Trade-off between transportation authority and freight forwarder for policies [PITH_FULL_IMAGE:figures/full_fig_p022_4.png]
Figure 5
Figure 5. Figure 5: a Berlin case study driving distance, although not as low as the driven distance in the base scenario. The optimal policy provides a 1.1% distance saving with a higher modal shift. Conversely, when the scheduled line cost is high, the freight forwarder uses it less oft…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

45 extracted references · 40 canonical work pages

  1. [1]

    write newline

    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in ":" * " " * FUNCTION f...

  2. [2]

    , author Bernauer, T

    author Beiser-McGrath, L.F. , author Bernauer, T. , year 2019 . title Could revenue recycling make effective carbon taxation politically feasible? journal Science advances volume 5 , pages eaax3323

    work page 2019

  3. [3]

    , author Labb \'e , M

    author Brotcorne, L. , author Labb \'e , M. , author Marcotte, P. , author Savard, G. , year 2008 . title Joint design and pricing on a network . journal Operations research volume 56 , pages 1104--1115

    work page 2008

  4. [4]

    , author Khodaparasti, S

    author Bruni, M.E. , author Khodaparasti, S. , author Perboli, G. , year 2024 . title A bi-level approach for last-mile delivery with multiple satellites . journal Transportation Research Part C: Emerging Technologies volume 160 , pages 104495

    work page 2024

  5. [5]

    , author Carvalho, M

    author Carattini, S. , author Carvalho, M. , author Fankhauser, S. , year 2018 . title Overcoming public resistance to carbon taxes . journal Wiley Interdisciplinary Reviews: Climate Change volume 9 , pages e531

    work page 2018

  6. [6]

    , author Iori, M

    author Caselli, G. , author Iori, M. , author Ljubi \'c , I. , year 2024 . title Bilevel optimization with sustainability perspective: a survey on applications . journal arXiv preprint arXiv:2406.07184

    arXiv 2024

  7. [7]

    , author Jiang, Y

    author Cheng, R. , author Jiang, Y. , author Nielsen, O.A. , year 2023 . title Integrated people-and-goods transportation systems: from a literature review to a general framework for future research . journal Transport Reviews , pages 1--24

    work page 2023

  8. [8]

    , author Cottrill, C

    author Cleophas, C. , author Cottrill, C. , author Ehmke, J.F. , author Tierney, K. , year 2019 . title Collaborative urban transportation: Recent advances in theory and practice . journal European Journal of Operational Research volume 273 , pages 801--816

    work page 2019

Show all 45 references
  1. [9]

    , author Ghiani, G

    author De Maio, A. , author Ghiani, G. , author Lagan \`a , D. , author Manni, E. , year 2024 . title Sustainable last-mile distribution with autonomous delivery robots and public transportation . journal Transportation Research Part C: Emerging Technologies volume 163 , pages 104615

    2024

  2. [10]

    , year 2024

    author Dempe, S. , year 2024 . title Bilevel programming: Implicit function approach , in: booktitle Encyclopedia of optimization . publisher Springer , pp. pages 1--8

    2024

  3. [11]

    , author Rentschler, J

    author Elbert, R. , author Rentschler, J. , year 2022 . title Freight on urban public transportation: A systematic literature review . journal Research in Transportation Business & Management volume 45 , pages 100679

    2022

  4. [12]

    title Special report 08/2023: Intermodal freight transport: EU still far from getting freight off the road

    author European Court of Auditors , year 2023 . title Special report 08/2023: Intermodal freight transport: EU still far from getting freight off the road . publisher Publications Office of the European Union

    2023

  5. [13]

    , author Crainic, T.G

    author Fontaine, P. , author Crainic, T.G. , author Jabali, O. , author Rei, W. , year 2021 . title Scheduled service network design with resource management for two-tier multimodal city logistics . journal European Journal of Operational Research volume 294 , pages 558--570

    2021

  6. [14]

    , author Cordeau, J.F

    author Ghilas, V. , author Cordeau, J.F. , author Demir, E. , author Woensel, T.V. , year 2018 . title Branch-and-price for the pickup and delivery problem with time windows and scheduled lines . journal Transportation Science volume 52 , pages 1191--1210

    2018

  7. [15]

    , author Demir, E

    author Ghilas, V. , author Demir, E. , author Van Woensel, T. , year 2016 a. title An adaptive large neighborhood search heuristic for the pickup and delivery problem with time windows and scheduled lines . journal Computers & Operations Research volume 72 , pages 12--30

    2016

  8. [16]

    , author Demir, E

    author Ghilas, V. , author Demir, E. , author Van Woensel, T. , year 2016 b. title The pickup and delivery problem with time windows and scheduled lines . journal INFOR: Information Systems and Operational Research volume 54 , pages 147--167

    2016

  9. [17]

    , author Demir, E

    author Ghilas, V. , author Demir, E. , author Van Woensel, T. , year 2016 c. title A scenario-based planning for the pickup and delivery problem with time windows, scheduled lines and stochastic demands . journal Transportation Research Part B: Methodological volume 91 , pages 34--51

    2016

  10. [18]

    , author Ceder, A.A

    author He, D. , author Ceder, A.A. , author Zhang, W. , author Guan, W. , author Qi, G. , year 2023 . title Optimization of a rural bus service integrated with e-commerce deliveries guided by a new sustainable policy in china . journal Transportation Research Part E: Logistics...

    2023

  11. [19]

    , author Guan, W

    author He, D. , author Guan, W. , year 2023 . title Promoting service quality with incentive contracts in rural bus integrated passenger-freight service . journal Transportation Research Part A: Policy and Practice volume 175 , pages 103781

    2023

  12. [20]

    , author Cleophas, C

    author H \"o rsting, L. , author Cleophas, C. , year 2023 . title Scheduling shared passenger and freight transport on a fixed infrastructure . journal European Journal of Operational Research volume 306 , pages 1158--1169

    2023

  13. [21]

    , author Gu, W

    author Hu, Q. , author Gu, W. , author Wang, S. , year 2022 . title Optimal subsidy scheme design for promoting intermodal freight transport . journal Transportation Research Part E: Logistics and Transportation Review volume 157 , pages 102561

    2022

  14. [22]

    , author Martinsson, J

    author Jagers, S.C. , author Martinsson, J. , author Matti, S. , year 2019 . title The impact of compensatory measures on public support for carbon taxation: An experimental study in sweden . journal Climate policy volume 19 , pages 147--160

    2019

  15. [23]

    , year 2021

    author Jiang, C. , year 2021 . title Aviation tax and railway subsidy: An integrated policy . journal Transportation Research Part B: Methodological volume 146 , pages 1--13

    2021

  16. [24]

    , author Marcotte, P

    author Labb \'e , M. , author Marcotte, P. , author Savard, G. , year 1998 . title A bilevel model of taxation and its application to optimal highway pricing . journal Management Science volume 44 , pages 1608--1622

    1998

  17. [25]

    , author Violin, A

    author Labb \'e , M. , author Violin, A. , year 2016 . title Bilevel programming and price setting problems . journal Annals of operations research volume 240 , pages 141--169

    2016

  18. [26]

    , author Fan, Y

    author Liu, J. , author Fan, Y. , author Chen, Z. , author Zheng, Y. , year 2018 . title Pessimistic bilevel optimization: a survey . journal International Journal of Computational Intelligence Systems volume 11 , pages 725--736

    2018

  19. [27]

    , author Zhang, F

    author Ma, M. , author Zhang, F. , author Liu, W. , author Dixit, V. , year 2022 . title A game theoretical analysis of metro-integrated city logistics systems . journal Transportation Research Part B: Methodological volume 156 , pages 14--27

    2022

  20. [28]

    , author Zhang, F

    author Ma, M. , author Zhang, F. , author Liu, W. , author Dixit, V. , year 2023 . title On urban co-modality: Non-cooperative and cooperative games among freight forwarder, carrier and transit operator . journal Transportation Research Part C: Emerging Technologies volume 153...

    2023

  21. [29]

    , author Trentini, A

    author Masson, R. , author Trentini, A. , author Lehu \'e d \'e , F. , author Malh \'e n \'e , N. , author P \'e ton, O. , author Tlahig, H. , year 2017 . title Optimization of a city logistics transportation system with mixed passengers and goods . journal EURO Journal on Tra...

    2017

  22. [30]

    , author Yao, Y

    author Mo, P. , author Yao, Y. , author D’Ariano, A. , author Liu, Z. , year 2023 . title The vehicle routing problem with underground logistics: Formulation and algorithm . journal Transportation Research Part E: Logistics and Transportation Review volume 179 , pages 103286

    2023

  23. [31]

    , author Thompson, R

    author Mohri, S.S. , author Thompson, R. , year 2022 . title Designing sustainable intermodal freight transportation networks using a controlled rail tariff discounting policy--the iranian case . journal Transportation Research Part A: Policy and Practice volume 157 , pages 59--77

    2022

  24. [32]

    , author Puchinger, J

    author Mourad, A. , author Puchinger, J. , author Van Woensel, T. , year 2021 . title Integrating autonomous delivery service into a passenger transportation system . journal International Journal of Production Research volume 59 , pages 2116--2139

    2021

  25. [33]

    , author Patrick, J

    author Ozturk, O. , author Patrick, J. , year 2018 . title An optimization model for freight transport using urban rail transit . journal European Journal of Operational Research volume 267 , pages 1110--1121

    2018

  26. [34]

    , author Xu, J

    author Qiu, R. , author Xu, J. , author Ke, R. , author Zeng, Z. , author Wang, Y. , year 2020 a. title Carbon pricing initiatives-based bi-level pollution routing problem . journal European Journal of Operational Research volume 286 , pages 203--217

    2020

  27. [35]

    , author Xu, J

    author Qiu, R. , author Xu, J. , author Xie, H. , author Zeng, Z. , author Lv, C. , year 2020 b. title Carbon tax incentive policy towards air passenger transport carbon emissions reduction . journal Transportation Research Part D: Transport and Environment volume 85 , pages 102441

    2020

  28. [36]

    , author Behrendt, H

    author Santos, G. , author Behrendt, H. , author Maconi, L. , author Shirvani, T. , author Teytelboym, A. , year 2010 . title Part i: Externalities and economic policies in road transport . journal Research in transportation economics volume 28 , pages 2--45

    2010

  29. [37]

    , author Buriol, L.S

    author Sartori, C.S. , author Buriol, L.S. , year 2020 . title A study on the pickup and delivery problem with time windows: Matheuristics and new instances . journal Computers and Operations Research volume 124 , pages 105065

    2020

  30. [38]

    , author Van Woensel, T

    author Savelsbergh, M. , author Van Woensel, T. , year 2016 . title 50th anniversary invited article—city logistics: Challenges and opportunities . journal Transportation science volume 50 , pages 579--590

    2016

  31. [39]

    , author Tilk, C

    author Schmidt, J. , author Tilk, C. , author Irnich, S. , year 2024 . title Using public transport in a 2-echelon last-mile delivery network . journal European Journal of Operational Research volume 317 , pages 827--840

    2024

  32. [40]

    , year 2024

    author Snyder, K. , year 2024 . title 35 e-commerce statistics of 2024 . https://www.forbes.com/uk/advisor/business/ecommerce-statistics. note accessed: 2024-09-20

    2024

  33. [41]

    , author Marques, A

    author Soares, R. , author Marques, A. , author Amorim, P. , author Parragh, S.N. , year 2024 . title Synchronisation in vehicle routing: Classification schema, modelling framework and literature review . journal European Journal of Operational Research volume 313 , pages 817--840

    2024

  34. [42]

    , author Gonzalez-Aregall, M

    author Takman, J. , author Gonzalez-Aregall, M. , year 2023 . title Public policy instruments to promote freight modal shift in europe: evidence from evaluations . journal Transport Reviews , pages 1--22

    2023

  35. [43]

    , author Wiesemann, W

    author Tsoukalas, A. , author Wiesemann, W. , author Rustem, B. , et al., year 2009 . title Global optimisation of pessimistic bi-level problems . journal Lectures on global optimization volume 55 , pages 215--243

    2009

  36. [44]

    , author Zhu, X

    author Wang, S. , author Zhu, X. , author Shang, P. , author Liu, W. , author Lin, X. , author Tavasszy, L. , year 2024 . title Two-echelon pickup and delivery problem using public transport in city logistics . journal Journal of Advanced Transportation volume 2024 , pages 1203246

    2024

  37. [45]

    , author Zhang, Z.A

    author Yin, C. , author Zhang, Z.A. , author Fu, X. , author Ge, Y.E. , year 2024 . title A low-carbon transportation network: Collaborative effects of a rail freight subsidy and carbon trading mechanism . journal Transportation Research Part A: Policy and Practice volume 184 ...

    2024

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.