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Finite-horizon equipment replacement analysis

The optimal solution to the infinite-horizon equipment replacement problem with stationary costs is to continually replace an asset at its economic life. The economic life is the age that minimizes the Equivalent Annual Cost (EAC), which includes purchase, operating and maintenance costs less salvage values. We explore the question of whether this is a good policy for the finite-horizon problem, which occurs when companies only require an asset for a specified length of time, usually to fulfill a specific contract. We identify cases, according to capital costs, operating costs, and the interest rate, when this policy is good and when it deviates significantly from optimal. Furthermore, we provide a bound on the minimum number of times that an asset is retained at its economic life over a finite horizon. This is facilitated through a new dynamic-programming formulation to the problem based on the integer-knapsack problem with nonlinear costs. The bound can be derived from any feasible solution, although we provide a closed-form solution for the case of convex EAC values.