Setting the length of the planning horizon in the vehicle replacement problem

In some formulations of the vehicle replacement problem, in particular those leading to repair limit type models, the alternative policies are evaluated and compared over a fixed planning horizon. Although it has been widely recognised that the optimal policies derived under these formulations depend critically on the length of the horizon, no method has been presented so far to set appropriately this parameter. In this paper, the authors describe a method which overcomes this shortcoming. Once the best policy has been derived from a given finite horizon with length H, such a policy is repeated indefinitely over time and an equivalent annual rent is computed. The parametrisation of H leads to the definition of an annual rent function with a sequence of nearly equidistant local minima. It is suggested that in practice the second local minimum of this function leads to an adequate choice of the parameter H. The method can be applied both to stochastic and deterministic cost modelling situations. The method was tested using both real data from large samples of different types of passenger vehicles and artificially generated data.