Life cycle costing with a discount rate

This article studies life cycle costing for a capability needed for the indefinite future, and specifically investigates the dependence of optimal policies on the discount rate chosen. The two costs considered are reprocurement cost and maintenance and operations (M and O) cost. The procurement price is assumed known, and the M and O costs are assumed to be a known function, in fact, a non-decreasing function, of the time since last reprocurement. The problem is to choose the optimum reprocurement time so as to minimize the quotient of the total cost over a reprocurement period divided by the period. Or one could assume a discount rate and try to minimize the total discounted costs into the indefinite future. It is shown that the optimum policy in the presence of a small discount rate hardly depends on the discount rate at all, and leads to essentially the same policy as in the case in which discounting is not considered.