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

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.