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Fleet Size and Mix Capacitated Vehicle Routing Problem with Time Windows for Mobile Fast Chargers

Farhang Motallebi Araghi, Armin Abdolmohammadi, Navid Mojahed, Shima Nazari

TL;DR

The paper tackles mobile fast charging for off-road heavy equipment by proposing FSMCVRPTW, a unified MILP that jointly optimizes fleet size and mix, charger specifications, routing, and service scheduling under time windows. By incorporating heterogeneous MFCV types and energy constraints, the method demonstrates how joint design-and-dispatch yields compact, well-utilized fleets capable of meeting operational windows in both urban and rural Caltrans contexts. The results reveal how demand density and geography shape optimal fleet composition, total costs, and unit costs per kWh or per client, highlighting trade-offs between scale economies and travel intensity. This framework provides a generalizable decision-support tool for context-aware, cost-efficient mobile charging and lays the groundwork for future extensions in stochastic travel times, multi-period planning, dynamic routing, and grid-aware operations.

Abstract

The electrification of off-road heavy equipment presents operational challenges for agencies serving remote sites with limited fixed charging infrastructure. Existing mobile fast charging vehicle (MFCV) planning approaches typically treat fleet design and routing as separate problems, fixing vehicle characteristics before dispatch. This paper formulates a fleet size and mix capacitated vehicle routing problem with time windows (FSMCVRPTW) for MFCV deployment, jointly optimizing fleet composition, charger specifications, routing, and scheduling within a unified mixed-integer linear program. The model incorporates heterogeneous MFCV types with varying power ratings, battery capacities, fuel range, and cost structures, minimizing total daily cost from labor, fuel, amortized capital expenditure, and energy purchase under temporal service windows, resource budgets, and energy-delivery constraints. The formulation is implemented in Python/Gurobi and applied to two case studies using California Department of Transportation wheel-loader data in Los Angeles (dense urban) and Truckee (sparse mountainous). Results show that simultaneous optimization yields compact, well-utilized fleets that meet all service windows while revealing strong sensitivity of unit cost to demand density and geography. The proposed FSMCVRPTW framework provides a generalizable decision-support methodology that co-designs fleet size, charger power, routing, and service schedules in a single optimization layer for context-aware, cost-efficient mobile fast charging.

Fleet Size and Mix Capacitated Vehicle Routing Problem with Time Windows for Mobile Fast Chargers

TL;DR

The paper tackles mobile fast charging for off-road heavy equipment by proposing FSMCVRPTW, a unified MILP that jointly optimizes fleet size and mix, charger specifications, routing, and service scheduling under time windows. By incorporating heterogeneous MFCV types and energy constraints, the method demonstrates how joint design-and-dispatch yields compact, well-utilized fleets capable of meeting operational windows in both urban and rural Caltrans contexts. The results reveal how demand density and geography shape optimal fleet composition, total costs, and unit costs per kWh or per client, highlighting trade-offs between scale economies and travel intensity. This framework provides a generalizable decision-support tool for context-aware, cost-efficient mobile charging and lays the groundwork for future extensions in stochastic travel times, multi-period planning, dynamic routing, and grid-aware operations.

Abstract

The electrification of off-road heavy equipment presents operational challenges for agencies serving remote sites with limited fixed charging infrastructure. Existing mobile fast charging vehicle (MFCV) planning approaches typically treat fleet design and routing as separate problems, fixing vehicle characteristics before dispatch. This paper formulates a fleet size and mix capacitated vehicle routing problem with time windows (FSMCVRPTW) for MFCV deployment, jointly optimizing fleet composition, charger specifications, routing, and scheduling within a unified mixed-integer linear program. The model incorporates heterogeneous MFCV types with varying power ratings, battery capacities, fuel range, and cost structures, minimizing total daily cost from labor, fuel, amortized capital expenditure, and energy purchase under temporal service windows, resource budgets, and energy-delivery constraints. The formulation is implemented in Python/Gurobi and applied to two case studies using California Department of Transportation wheel-loader data in Los Angeles (dense urban) and Truckee (sparse mountainous). Results show that simultaneous optimization yields compact, well-utilized fleets that meet all service windows while revealing strong sensitivity of unit cost to demand density and geography. The proposed FSMCVRPTW framework provides a generalizable decision-support methodology that co-designs fleet size, charger power, routing, and service schedules in a single optimization layer for context-aware, cost-efficient mobile fast charging.

Paper Structure

This paper contains 27 sections, 25 equations, 3 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Literature Review
  3. Research Gaps and Contributions
  4. Problem Formulation
  5. System Setting and Assumptions
  6. Model Assumptions
  7. Network and Index Sets
  8. Client Requirements and Service Windows
  9. Mobile Charger and Vehicle Specifications
  10. Decision Variables
  11. Cost Function Structure and Coefficients
  12. Optimization Objective Function Components
  13. Non-Optimizing Cost Component-Energy Transfer
  14. Optimization Constraints
  15. Service Coverage
  16. ...and 12 more sections

Figures (3)

  • Figure 1: Example illustration of the optimized service routes for the Los Angeles scenario, with arrows showing the direction of travel. Panel (a) shows the optimized route for the High MFCV (300 kWh, vehicle V22), and panel (b) shows the optimized route for the Mega MFCV (1000 kWh, vehicle V34). The corresponding energy delivery details for each route segment are provided in the adjacent tables.
  • Figure 2: Example illustration of the optimized service route for the Truckee scenario, with arrows indicating the direction of travel. The figure shows the optimized route for the Ultra MFCV (500 kWh), and the corresponding energy delivery information is provided in the embedded table.
  • Figure 3: Comparison of vehicle schedules and client service windows. For both (a) Los Angeles and (b) Truckee, the top panel shows vehicle schedules: depot time (gray hatching), travel (gold), waiting (purple dots), and service (green). The bottom panel compares client time windows (light gray bands) against actual service periods (green bars).