Evaluation of costs of ordering policies in large machine repair problems

This article examines a version of the machine repair problem where failures may be irreparable. Since the number of machines in the system keeps decreasing, we impose a fixed state-dependent ordering policy of the type often encountered in inventory models. Although the system is Markovian, the number of states becomes very large. The emphasis of the article, therefore, is on deriving computationally tractable formulas for the steady-state probabilities, the long-run average cost per unit time, and the vector of expected discounted costs. When the state space is so large that exact computations may be infeasible, we propose approximations which are relatively quick and simple to compute and which yield very accurate results for the test problems examined.