Machine Replacement with Stochastic Costs

The machine replacement model studied assumes that, at the end of each discrete interval, the state of deterioration of a machine and the current cost of replacement become known. A decision to keep or to replace must then be made, given that future deterioration and costs are determined by a known Markovian process. A finite set of possible states of deterioration is considered, including a “failed” state at which replacement by a “new” machine must occur. The operating cost is an increasing function of the level of deterioration, and replacement cost is the difference between new machine cost and salvage value. For both a finite and infinite planning horizon, given current cost, the optimality of a “control level” policy is demonstrated. Linear programming and policy iteration methods exploiting problem structure for the calculation of optimal policies are derived.