Minimum cost in a mix of new and old reusable items: an application to sizing a fleet of delivery trucks

Companies that operate a commodity delivery service, lumber for instance, often own trucks to ship from a warehouse to their customers. One of these companies may consider purchasing new trucks to reduce operation costs, when operating new trucks is cheaper than operating old ones. That is, a company can save on future operational expenditures at the cost of purchasing new trucks. Once new trucks have been bought, the fleet consists of two sub-fleets: the subfleet of new and the subfleet of old trucks. The cheaper operation [currency units/min] of new trucks makes them preferable to old trucks. Thus, old trucks start servicing orders only when all new trucks are busy. For a given time horizon, the optimal cost of the project is a trade-off between the times serviced with old trucks, new trucks, and the cost of the new trucks to be purchased. This article puts forward a method to determine the number of new trucks to purchase that maximizes the expected present value of the project that applies to full payload deliveries. It uses historical information on hour-specific expected intensities of delivery requests and delivery services. Our approach can incorporate restrictions preventing deliveries to specific customers during certain time windows.