A Vehicle Routing Problem for Human-Centered Electric Mobility

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.

• The paper introduces EM-DARP, a MILP formulation that integrates modular EV configurations, nonlinear battery dynamics, and adaptive request prioritization.
• It employs mixed-integer optimization to model heterogeneous fleets, configurable interiors, and selective request fulfillment in on-demand mobility.
• Numerical results demonstrate feasibility for small-scale instances while highlighting the need for scalable heuristics for larger deployments.

Formal Summary of “A Vehicle Routing Problem for Human-Centered Electric Mobility” (2604.22737)

Problem Context and Contribution

The paper defines and formalizes the Electric Mobility Dial-a-Ride Problem (EM-DARP), extending traditional EV-DARP to explicitly account for the requirements of modern, human-centered mobility services. EM-DARP integrates a heterogeneous fleet of EVs with configurable interior layouts to accommodate varying passenger needs, including elderly and disabled riders with mobility equipment. The model addresses on-demand transport operations with embedded vehicle charging logistics and prioritization of requests, advancing the practical applicability of VRP models in urban and intercity electric mobility.

Literature Context and Distinctive Features

EM-DARP represents a confluence of advances in VRP literature: PDP/VRPTW constraints, modular/configurable vehicle capacity (per Qu and Bard, 2013; Tellez et al., 2018), nonlinear charging and load-dependent battery discharge, and request prioritization. Previous works have treated either charging logistics (Schneider et al., 2014; Keskin et al., 2019; Cataldo-Díaz et al., 2023) or heterogeneous passenger/equipment needs (Tóth et al., 2024), but have not addressed the synergistic modeling of vehicle configurability in direct combination with EV operational constraints and human-centric service prioritization. This approach allows for both soft constraints on time windows and selective request fulfillment, reflecting actual operational flexibility in mobility-as-a-service systems.

Mathematical Model

EM-DARP is cast as a Mixed-Integer Linear Program (MILP) with the following characteristics:

• Network and Fleet: Directed graph formulation, multiple depots, heterogeneous EVs, each with unique capacity and battery parameters.
• Request Structure: Each customer request has associated pickup/delivery locations, passenger/equipment loads, service times, time window restrictions, and prioritization parameters.
• Vehicle Configurability: Seats can be converted to accommodate either passengers or mobility equipment, modeled via agent-specific conversion factors and upper bounds.
• Battery Modeling: Piecewise-linear approximation of nonlinear charging curves; load-dependent discharge rates; partial recharging permitted; single-agent charging station access with precedence constraints for repeated visits.
• Routing Flexibility: Supports both closed (return-to-depot) and open VRPs; selective request acceptance; soft time window penalties; prioritization incorporated directly into the objective function.

The objective function minimizes the overall mission duration, arrival time delays, time window violations, and heavily penalizes rejected or low-priority requests, enabling optimization focused on mission-critical service provision.

Solution Implementation and Numerical Results

The MILP is implemented in Pyomo and solved with Gurobi. Two illustrative scenarios are detailed:

• Small-scale selective VRP: Fleet of $K=2$ agents, $R=6$ requests. The solver achieves optimality in 4.22 seconds, demonstrating the model’s tractability for small instances. Battery discharge is artificially increased to stress charging station logistics; one request is rejected due to prioritization and operational constraints.
• Medium-scale non-selective OVRP: Fleet of $K=3$ agents, $R=8$ requests. The best solution found in 120 seconds yields a duality gap of 82%, indicating increasing computational difficulty. The scenario highlights flexible route concatenation (e.g., pickup-pickup transitions) and real-world configuration constraints.

The scenarios show that the model’s configuration logic and charging schedules ensure temporal consistency and operational feasibility. Strong numerical results are achieved in the small-scale case, while the larger instance motivates future focus on scalable heuristics/metaheuristics due to combinatorial complexity.

Implications and Future Directions

EM-DARP’s MILP formulation provides a rigorous framework for integrated scheduling in electric mobility systems, enabling fine-grained prioritization and optimizing vehicle/equipment configuration for high-throughput, human-centered service. The approach supports practical deployment scenarios involving complex battery and charging behaviors, heterogeneous fleets, and differentiated customer needs.

From a theoretical standpoint, EM-DARP extends classical VRP models to encompass modular vehicle architectures and nonlinear energy dynamics, opening avenues for future research in:

• Advanced algorithmic development (e.g., branch-and-cut, decomposition, large neighborhood search) for substantially larger instances.
• Integration with real-time dispatch systems for dynamic on-demand mobility, including stochastic travel times and battery degradation modeling.
• Policy optimization for equitable service provision, leveraging request prioritization and customizable constraints to enforce accessibility goals.

Practically, the framework can be adapted for fleet operators seeking to maximize resource utilization, minimize downtime due to charging, and deliver tailored mobility services to a diverse passenger base—all within the constraints of battery technology and urban infrastructure.

Conclusion

The paper introduces EM-DARP as a comprehensive extension of EV-DARP for human-focused electric mobility, integrating modular vehicle configurability, advanced battery logistics, and precise request prioritization into a tractable MILP formulation. Numerical experiments confirm feasibility for small-scale scenarios, while computational limitations underline the necessity of efficient heuristics for larger deployments. The model represents a solid step toward realistic, operationally actionable optimization in future electric mobility systems.