An economic replacement model with probabilistic asset utilization

Abstract

Traditional economic replacement analysis provides asset purchase and sale decisions over a given horizon based on expected purchase, operating, maintenance and salvage costs. As these costs are dependent on asset utilization, a constant or predetermined usage is generally assumed. However, due to randomness in operations, such as customer demand, these expected utilization schedules may not be realized in practice, thus invalidating the replacement schedule. This paper examines the effect of probabilistic asset utilization on replacement decisions through the use of dynamic programming. The solution determines minimum expected cost decisions for each state defined by the asset's age and cumulative utilization in each period. These decisions generalize the definition of the economic life of an asset to include age and cumulative utilization. Assumptions common to replacement analysis allow the state space to grow linearly with time, avoiding dynamic programming's `curse of dimensionality'. Examples with time invariant and variant economics are presented and compared to traditional solution procedures.