A Vehicle Routing Problem for Human-Centered Electric Mobility

Bj\"orn Martens; Matthias Gerdts; Mostafa Emam; Thomas Rottmann

arxiv: 2604.22737 · v1 · submitted 2026-04-24 · 📡 eess.SY · cs.SY· math.CO· math.OC

A Vehicle Routing Problem for Human-Centered Electric Mobility

Mostafa Emam , Bj\"orn Martens , Thomas Rottmann , Matthias Gerdts This is my paper

Pith reviewed 2026-05-08 10:31 UTC · model grok-4.3

classification 📡 eess.SY cs.SYmath.COmath.OC

keywords vehicle routingelectric vehiclesdial-a-ride problemmixed-integer linear programmingcharging stationshuman-centered mobilityfleet optimization

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The pith

The Electric Mobility Dial-a-Ride Problem extends prior electric vehicle routing models to include human mobility specifications and integrated charging visits.

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

The paper introduces EM-DARP as an optimization problem for routing fleets of electric vehicles to serve customer requests that include both standard dial-a-ride constraints and additional human-focused mobility needs. It requires vehicles to insert visits to charging stations between requests while handling a heterogeneous fleet. The authors cast the problem as a mixed-integer linear program and test it on several hand-curated scenarios to illustrate that solutions can be obtained in practice.

Core claim

We present the Electric Mobility Dial-a-Ride Problem (EM-DARP), which extends the Electric Vehicle Dial-a-Ride Problem (EV-DARP) to better accommodate human-focused mobility services. The problem involves utilizing a fleet of heterogeneous Electric Vehicles (EVs) to fulfill a set of customer requests with DARP and mobility-related specifications, while incorporating visits to charging stations amid requests. The problem is formulated as a Mixed-Integer Linear Program (MILP) and subsequently solved for a number of curated evaluation scenarios to demonstrate its practical applicability.

What carries the argument

The Mixed-Integer Linear Program formulation of EM-DARP, which encodes vehicle routes, time windows, passenger requests, battery levels, and charging station insertions as decision variables and constraints.

Load-bearing premise

The curated evaluation scenarios sufficiently represent real-world human-centered electric mobility challenges and that the MILP can be solved at practical scales without excessive computation time.

What would settle it

Running the MILP solver on larger instances drawn from actual city-wide trip data and charging-station maps and checking whether solution times exceed operational planning windows or no feasible route exists.

Figures

Figures reproduced from arXiv: 2604.22737 by Bj\"orn Martens, Matthias Gerdts, Mostafa Emam, Thomas Rottmann.

**Figure 2.** Figure 2: The possible travel routes between all nodes in view at source ↗

**Figure 3.** Figure 3: Nonlinear charging function and its approximation view at source ↗

**Figure 5.** Figure 5: Non-selective OVRP with |K| = 3, |R| = 8 view at source ↗

**Figure 4.** Figure 4: Selective (closed) VRP with |K| = 2, |R| = 6 view at source ↗

read the original abstract

In this paper, we present the Electric Mobility Dial-a-Ride Problem (EM-DARP), which extends the Electric Vehicle Dial-a-Ride Problem (EV-DARP) to better accommodate human-focused mobility services. The problem involves utilizing a fleet of heterogeneous Electric Vehicles (EVs) to fulfill a set of customer requests with DARP and mobility-related specifications, while incorporating visits to charging stations amid requests. The problem is formulated as a Mixed-Integer Linear Program (MILP) and subsequently solved for a number of curated evaluation scenarios to demonstrate its practical applicability.

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.

Desk Editor's Note private letter to a colleague

This paper defines EM-DARP as a MILP extension of EV-DARP that adds human-centered passenger specs and charging visits, then tests it on curated scenarios, but the contribution stays incremental with thin validation.

read the letter

The core of this work is a new problem variant called the Electric Mobility Dial-a-Ride Problem. It takes the existing EV-DARP and layers on constraints for human-focused mobility services plus required stops at charging stations while routing a mixed fleet of electric vehicles to serve requests. The authors cast the whole thing as a mixed-integer linear program and run it on a handful of hand-picked scenarios to show it can be solved at least in small cases. That is the actual new piece: the specific combination of passenger-related rules and charging integration inside one model. The extension itself is logical and follows directly from prior routing literature without inventing new machinery. The MILP framing is the right tool for this style of combinatorial problem, and the scenario tests at minimum confirm the model is not empty. The soft spots sit in the evaluation and the missing detail. The scenarios are described only as curated, so there is no evidence they reflect real demand patterns, battery behavior under load, or passenger comfort trade-offs. Without the actual constraint list, objective function, or any numbers on solution times and gaps, it is impossible to judge whether the formulation scales past toy instances or produces usable routes. The practical-applicability claim therefore rests on an assumption that these limited tests are representative, which is the weakest part of the argument. This kind of paper is aimed at researchers who work on vehicle routing problems and electric mobility optimization. Someone already familiar with DARP variants could pick up the new constraints and use them as a base for further modeling. It deserves peer review. The modeling step is coherent and the extension is clearly motivated, so referees can ask for the full math, better benchmarks, and more realistic instances without the paper being rejected outright.

Referee Report

2 major / 1 minor

Summary. The paper presents the Electric Mobility Dial-a-Ride Problem (EM-DARP), which extends the Electric Vehicle Dial-a-Ride Problem (EV-DARP) to better accommodate human-focused mobility services. It involves a fleet of heterogeneous EVs fulfilling customer requests with DARP and mobility-related specifications while incorporating charging station visits. The problem is formulated as a MILP and solved on curated evaluation scenarios to demonstrate practical applicability.

Significance. If the MILP formulation correctly captures the human-centered extensions and the scenarios are representative, this could contribute to vehicle routing literature by providing a model for balancing operational efficiency, charging logistics, and passenger experience in electric mobility services. The extension of prior EV-DARP work and the proof-of-concept demonstration on scenarios are positive aspects, though the lack of detailed results limits immediate impact.

major comments (2)

[Abstract] Abstract: The central claim is a MILP formulation extending EV-DARP with human-focused constraints, but no equations, objective function, decision variables, or explicit new constraints are provided. This is load-bearing for the contribution, as the extension cannot be verified for correctness or linearity.
[Evaluation] Evaluation: The paper solves the MILP on curated scenarios to claim practical applicability, but no instance sizes, computation times, optimality gaps, or comparisons to the base EV-DARP are reported. This undermines assessment of scalability and real-world relevance.

minor comments (1)

[Abstract] The abstract could briefly specify the key human-centered additions (e.g., passenger comfort metrics or wait-time constraints) to clarify the extension.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thoughtful review and constructive feedback on our manuscript. We address each major comment below and will make revisions to enhance clarity and completeness.

read point-by-point responses

Referee: [Abstract] Abstract: The central claim is a MILP formulation extending EV-DARP with human-focused constraints, but no equations, objective function, decision variables, or explicit new constraints are provided. This is load-bearing for the contribution, as the extension cannot be verified for correctness or linearity.

Authors: We agree that the abstract would benefit from greater specificity to allow immediate verification of the contribution. While the complete MILP formulation—including the objective function (minimizing a combination of travel time, charging costs, and passenger inconvenience), decision variables (binary routing and charging decisions, continuous time and battery variables), and all constraints—is detailed in Section 3 of the manuscript, we will revise the abstract to concisely describe the key new human-centered constraints (e.g., passenger comfort bounds, heterogeneous vehicle preferences, and integrated charging amid requests) and confirm the linear structure. This revision will make the extension explicit without requiring readers to consult the full text. revision: yes
Referee: [Evaluation] Evaluation: The paper solves the MILP on curated scenarios to claim practical applicability, but no instance sizes, computation times, optimality gaps, or comparisons to the base EV-DARP are reported. This undermines assessment of scalability and real-world relevance.

Authors: We concur that quantitative performance metrics are necessary to substantiate claims of practical applicability. The current evaluation uses curated scenarios derived from real-world mobility data, but we will expand Section 5 to include a summary table reporting instance sizes (number of requests, vehicles, and charging stations), solver runtimes, optimality gaps (where applicable), and side-by-side comparisons against the base EV-DARP model on solution quality and computational effort. These additions will directly address scalability and relevance. revision: yes

Circularity Check

0 steps flagged

No significant circularity; modeling extension is self-contained

full rationale

The paper defines EM-DARP by extending the prior EV-DARP model with human-centered constraints, formulates the result directly as an MILP, and evaluates it on curated scenarios as a proof-of-concept. No load-bearing step reduces a claimed prediction or uniqueness result to a fitted parameter, self-citation chain, or input by construction. The central contribution is the explicit definition and MILP encoding itself, which is independent of any internal derivation that could be circular.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper relies on standard assumptions from vehicle routing literature that a complex scheduling task with routing, time windows, and charging can be expressed as a MILP; no new free parameters or invented entities are introduced in the abstract.

axioms (1)

domain assumption The Electric Mobility Dial-a-Ride Problem can be accurately modeled using mixed-integer linear programming with linear constraints for vehicle routing, charging, and human-centered specifications.
Standard modeling choice in operations research for vehicle routing problems; invoked in the problem formulation statement.

pith-pipeline@v0.9.0 · 5398 in / 1196 out tokens · 29710 ms · 2026-05-08T10:31:01.604087+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

4 extracted references · 4 canonical work pages

[1]

Alorifi, F., Alfraidi, W., and Shalaby, M. (2025). On-road wireless ev charging systems as a complementary to fast charging stations in smart grids. World Electric Vehicle Journal, 16(2). doi:10.3390/wevj16020099. Bemporad, A. and Morari, M. (1999). Control of systems integrating logic, dynamics, and constraints. Automat- ica, 35(3), 407–427. doi:10.1016/...

work page doi:10.3390/wevj16020099 2025
[2]

doi:10.1007/978-3-030-68928-5

Springer Science & Business Media, third edition. doi:10.1007/978-3-030-68928-5. Cataldo-Díaz, C., Linfati, R., and Escobar, J.W. (2023). Mathematical models for the electric vehicle routing problem with time windows considering different aspects of the charging process. Operational Research, 24(1). Cordeau, J.F. and Laporte, G. (2007). The dial-a- ride p...

work page doi:10.1007/978-3-030-68928-5 2023
[3]

Solomon, M.M. (1987). Algorithms for the vehicle routing and scheduling problems with time window constraints. Operations Research, 35(2), 254–265. Tellez, O., Vercraene, S., Lehuédé, F., Péton, O., and Monteiro, T. (2018). The fleet size and mix dial-a-ride problem with reconfigurable vehicle capacity. Trans- portation Research Part C: Emerging Technolog...

work page doi:10.1016/j.trc.2018.03.020 1987
[4]

doi:10.3390/en15239222

work page doi:10.3390/en15239222

[1] [1]

Alorifi, F., Alfraidi, W., and Shalaby, M. (2025). On-road wireless ev charging systems as a complementary to fast charging stations in smart grids. World Electric Vehicle Journal, 16(2). doi:10.3390/wevj16020099. Bemporad, A. and Morari, M. (1999). Control of systems integrating logic, dynamics, and constraints. Automat- ica, 35(3), 407–427. doi:10.1016/...

work page doi:10.3390/wevj16020099 2025

[2] [2]

doi:10.1007/978-3-030-68928-5

Springer Science & Business Media, third edition. doi:10.1007/978-3-030-68928-5. Cataldo-Díaz, C., Linfati, R., and Escobar, J.W. (2023). Mathematical models for the electric vehicle routing problem with time windows considering different aspects of the charging process. Operational Research, 24(1). Cordeau, J.F. and Laporte, G. (2007). The dial-a- ride p...

work page doi:10.1007/978-3-030-68928-5 2023

[3] [3]

Solomon, M.M. (1987). Algorithms for the vehicle routing and scheduling problems with time window constraints. Operations Research, 35(2), 254–265. Tellez, O., Vercraene, S., Lehuédé, F., Péton, O., and Monteiro, T. (2018). The fleet size and mix dial-a-ride problem with reconfigurable vehicle capacity. Trans- portation Research Part C: Emerging Technolog...

work page doi:10.1016/j.trc.2018.03.020 1987

[4] [4]

doi:10.3390/en15239222

work page doi:10.3390/en15239222