Table 3 Summary of the fleet-size and configuration literature

Beaujon and Turnquist [56]

Fleet size and idle vehicle relocation using ICVs

Variable demand over a sequence of decision periods, OD vehicle-flow optimization to meet demand

Stochastic optimization under stochastic demand

Maximize the expected profit as the difference between the revenue and the overall costs (fleet investment, operational cost and unmet demand loss)

Frank–Wolfe algorithm embedded heuristic

Hiermann et al. [57]

Mixed fleet-size problem for vehicle-routing problem with time windows

Fixed demand, deterministic model, full-recharge policy

Mixed-integer programming

Vehicle acquisition costs and the total distance traveled

Branch and price algorithms for small instances and ALNS for large instances

Winter et al. [59]

Minimum fleet-size problem for ADRT

Fixed demand, scenario-based simulations

Simulation of ADRT vehicle dispatching and routing policy

Vehicle acquisition costs and routing costs

Iterative simulations to find the fleet size with minimal system costs

Schiffer and Walther [61]

Joint optimization of fleet size, charging station installation, and vehicle routing

EV location-routing problem with time windows and a partial-recharge policy

Mixed-integer programming and robust optimization

Vehicle routing, fleet acquisition, and charging station installation costs

ALNS

Zhang et al. [99]

Joint optimization of fleet size and charging stations for AEVs

Fixed OD demand, transport network flow, simplified routing

and relocating of AEVs

Mixed-integer programming

Annual expected investment and operational costs

Branch-and-bound

Guo et al. [62]

Robust minimization, fleet size optimization of

on-demand ride services

Door-to-door service, each vehicle can serve one customer, zone-based OD demand, routing problem is not considered

Two-stage robust optimization

Minimize the fleet size to satisfy customer demand under the worst scenarios

Cutting planes

Rezgui et al. [58]

Joint fleet-size and routing problem for EMVs

EMV routing by considering vehicle acquisition costs

Mixed-integer programming

Considers vehicle acquisition costs

VNS

Shehadeh et al. [63]

Fleet allocation of last-mile on-demand feeder service under uncertain demand

Given passenger train arrivals and the stops on last-mile vehicle routes, determine fleet allocation to meet random last-mile service demand

Two-stage stochastic/robust optimization

Minimize total waiting times and riding times of customers

Sample average approximation