Basically, simulation and approximation are used as solution
methodologies. Topaloglu and Powell (2005) solve instances with
20 locations, 200 vehicle, and up to 6000 orders, and claim that in
the deterministic version of the problem, the solutions are nearoptimal,
but in the stochastic version with random demands, centralized
decision making is slightly more effective than distributed
decision making. Topaloglu and Powell (2006) model and solve the
problem with up to 60 locations, 600 vehicles, and 4000 orders.
The hybrid value function seems to perform the best in the deterministic
case, while piecewise linear value function provides the best solutions in the stochastic case. Topaloglu and Powell (2007)
propose an approach which does not need multiple simulations
with different values of the model parameter which is an important
advantage. They decompose their dynamic program into
time-staged sub-problems and by using an iterative improvement
scheme; the value function is obtained with approximation. These
test are done on problem sets with 40 locations, 200 vehicles, and
up to 3000 orders during their planning horizon. Topaloglu and
Powell (2007) implement this procedure first for single vehicle
type and then extend it to the multiple vehicle type problem. Overall,
ADP with good approximation of value function stands strong
in solving fleet management problems with realistic sizes.