Optimal buying, running and selling policy for the private motorist: An application of capital replacement modelling

‘How old to buy a vehicle?’ and ‘how long to run it before resale?’ ought to be questions of interest for the private motorist. The paper consider a modelling approach aimed at answering these questions. A number of capital replacement models typical of that found in the Operational Research literature are considered. An equivalent rent model which assumes an infinite series of identical buying, running and selling cycles with discounting is found to be most appropriate. Extensive results are presented for a particular make and model of private car. The particular requirements of different motorists are addressed by determining optimal policy for a number of alternative annual mileage and ‘reliability’ parameter combinations. In the case considered, buying new is never optimal.