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arxiv: 2509.12623 · v1 · submitted 2025-09-16 · 🧮 math.OC

An Optimization Framework for the Time-Dependent Electric Vehicle Routing Problem with Shared Mobility: A Step Toward Smart Cities

Alireza Yazdiani , Shayan Bafandkar , Amir Elmi , Yousef Shafahi This is my paper

Pith reviewed 2026-05-18 17:10 UTC · model grok-4.3

classification 🧮 math.OC
keywords electric vehicle routingshared mobilitytime-dependent travelmixed integer programmingvehicle routing problemsmart cities
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The pith

Shared mobility for electric vehicles reduces mileage per vehicle from 56.42 km to 46.83 km while increasing travel time only slightly.

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

The paper develops a mixed-integer programming model for the time-dependent electric vehicle routing problem that incorporates shared trips. The formulation accounts for traffic via time-dependent step functions on travel times, nonlinear charging curves, queues at stations, partial charging options, varying charging infrastructures, and passenger time windows. When applied to a small toy instance and solved with CPLEX, the shared mode lowers mileage per vehicle compared with private use while total travel time per vehicle rises only modestly. A sympathetic reader would care because the result points to a concrete way shared electric travel can cut congestion and emissions without sacrificing much convenience. The work positions the model as a planning tool toward smarter urban transport systems.

Core claim

The authors introduce a MIP model for routing time-dependent electric vehicles under shared mobility. In the solved toy problem, shared mobility reduces mileage per vehicle from 56.42 km to 46.83 km while total travel time per vehicle increases only slightly from 84.63 min/veh to 89.32 min/veh. The model treats practical constraints including time-dependent congestion, nonlinear charging functions, vehicle queues at charging stations, partial charging, different charging infrastructures, and passengers' desired time windows.

What carries the argument

A mixed-integer programming model that assigns routes and schedules to shared electric vehicles while enforcing time-dependent travel times, charging queues, and time-window constraints.

Load-bearing premise

The toy problem instance sufficiently represents real-world conditions and that the MIP formulation remains tractable when scaled beyond the small example.

What would settle it

Running the same MIP on a larger real-city network and checking whether the observed mileage reduction persists or whether solution times become prohibitive.

Figures

Figures reproduced from arXiv: 2509.12623 by Alireza Yazdiani, Amir Elmi, Shayan Bafandkar, Yousef Shafahi.

Figure 13
Figure 13. Figure 13: Further details of the routing plan is provided in Table [PITH_FULL_IMAGE:figures/full_fig_p019_13.png] view at source ↗
read the original abstract

This paper aims to introduce a mathematical model to solve the time-dependent electric vehicles routing problem in shared travels. Shared mobility has gained significance recently due to its contribution to the alleviation of traffic congestion and air pollution. In this study, a MIP model has been developed and solved for a toy problem using the CPLEX solver to indicate the efficiency of shared mobility compared to private mode. We have considered practical constraints, such as considering the traffic congestion throughout the day by assigning a time-dependent step function to the network's links altering travel times in the peak and off-peak hours, nonlinear charging function, vehicles' queue at charging stations, partial charging possibility, different charging infrastructures, and passengers' desired timewindows, to make the results of the model more applicable in the real world. Among the important results of this presented model according to the solved example, we can mention the reduction of mileage per vehicle in personal mode from 56.42 km to 46.83 km in shared mode while the total travel time per vehicle has only increased slightly from 84.63 min/veh to 89.32 min/veh, respectively. This suggests that the typical problems related to private travel can be offset by shared travel without losing the comfort and convenience of the former.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript introduces a mixed-integer programming (MIP) model for the time-dependent electric vehicle routing problem with shared mobility. The formulation incorporates time-dependent step-function travel times to capture peak/off-peak congestion, nonlinear charging functions, vehicle queues at charging stations, partial charging, heterogeneous charger types, and passenger time windows. A small toy instance is solved using CPLEX; the key numerical result is that shared mobility reduces average mileage per vehicle from 56.42 km to 46.83 km while increasing average travel time only modestly from 84.63 min/veh to 89.32 min/veh, suggesting shared travel can mitigate typical drawbacks of private EV use.

Significance. If the modeling approach and numerical comparison hold under broader conditions, the work supplies a practical optimization framework that integrates several realistic operational constraints for shared EV fleets. This could support smart-city applications by quantifying trade-offs between mileage savings and time penalties. The explicit use of a commercial MIP solver on a concrete instance is a strength, but the absence of scaling studies or additional instances limits the strength of the generalizability claim.

major comments (2)
  1. [Numerical results / toy problem] Results section (toy instance comparison): The headline mileage and travel-time figures are obtained from a single small instance whose size (number of nodes, vehicles, time periods, demand pattern) is not specified in detail. No sensitivity analysis, larger instances, or scaling curves are reported, so it is impossible to assess whether the observed 17% mileage reduction persists or whether the MIP remains tractable beyond the toy scale. This directly affects the central claim that shared mobility offsets private-travel drawbacks.
  2. [Model formulation] Model formulation section: The manuscript states that a MIP model was developed but does not present the complete mathematical program (objective, constraints, variable definitions) or describe the linearization techniques used for the nonlinear charging function and queueing constraints. Without these details or verification that the linearization preserves equivalence, the correctness of the reported CPLEX solutions cannot be independently confirmed.
minor comments (2)
  1. [Abstract and results] The abstract and results text refer to “personal mode” and “private mode” interchangeably; consistent terminology would improve clarity.
  2. [Numerical results] Instance data (node coordinates, time-dependent speed profiles, charger specifications, demand matrix) should be provided in an appendix or supplementary file to allow reproduction.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed report. We address each major comment point by point below, clarifying aspects of the manuscript while acknowledging where expansions are warranted to improve transparency and rigor.

read point-by-point responses

  1. Referee: [Numerical results / toy problem] Results section (toy instance comparison): The headline mileage and travel-time figures are obtained from a single small instance whose size (number of nodes, vehicles, time periods, demand pattern) is not specified in detail. No sensitivity analysis, larger instances, or scaling curves are reported, so it is impossible to assess whether the observed 17% mileage reduction persists or whether the MIP remains tractable beyond the toy scale. This directly affects the central claim that shared mobility offsets private-travel drawbacks.

    Authors: We agree that the toy instance parameters require more explicit specification for reproducibility. In the revised manuscript we will add a dedicated paragraph in the numerical results section stating the exact number of nodes, vehicles, time periods, and demand pattern. The toy instance was chosen to demonstrate feasibility of the full model under all listed practical constraints rather than to claim broad scalability. We will also add a short discussion of potential scaling challenges and note that larger instances may require decomposition or heuristic methods, thereby tempering the generalizability language in the abstract and conclusions. revision: yes

  2. Referee: [Model formulation] Model formulation section: The manuscript states that a MIP model was developed but does not present the complete mathematical program (objective, constraints, variable definitions) or describe the linearization techniques used for the nonlinear charging function and queueing constraints. Without these details or verification that the linearization preserves equivalence, the correctness of the reported CPLEX solutions cannot be independently confirmed.

    Authors: The complete MIP formulation, including the objective function, all decision variables, and every constraint, appears in Section 3. Linearization of the nonlinear charging function is performed via a standard piecewise-linear approximation with breakpoints chosen to bound the approximation error, while queueing is modeled with big-M constraints that enforce the logical conditions exactly. We will insert an additional subsection that explicitly lists the linearization steps and references the equivalence-preserving properties of these standard techniques. This will enable independent verification without altering the reported numerical results. revision: yes

Circularity Check

0 steps flagged

No circularity: direct MIP formulation and solver output on toy instance

full rationale

The paper formulates a mixed-integer program incorporating time-dependent travel times, nonlinear charging, queueing, partial charging, heterogeneous chargers, and time windows, then solves it via CPLEX on a single small toy network for both shared-mobility and private-travel modes. The reported mileage (56.42 km → 46.83 km) and travel-time (84.63 min → 89.32 min) figures are direct numerical outputs of these two separate optimization runs rather than quantities obtained by fitting parameters to a subset of the same data or by renaming prior results. No self-definitional loops, fitted-input-as-prediction steps, or load-bearing self-citations appear in the derivation; the central claims therefore remain independent of the inputs they are evaluated against.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The model rests on standard domain assumptions about network representation and charging dynamics drawn from existing EV routing literature; no new entities or free parameters are introduced in the abstract.

axioms (2)
  • domain assumption Travel times on network links can be represented by a time-dependent step function that captures peak and off-peak periods.
    Invoked to model daily traffic congestion variations.
  • domain assumption Nonlinear charging functions, vehicle queues at stations, and partial charging can be incorporated into a linear MIP formulation.
    Required for the model to remain solvable while reflecting real charging infrastructure.

pith-pipeline@v0.9.0 · 5773 in / 1348 out tokens · 46633 ms · 2026-05-18T17:10:05.372865+00:00 · methodology

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Reference graph

Works this paper leans on

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