Optimal Control of the Machine Repair Problem with Removable Repairman Subject to Working Breakdowns

摘要

This paper deals with a single removable repairman in the machine repair problem with warm standbys and working breakdowns. We assume that the repairman can be subject to working breakdowns only when there is at least one failed machine in the system. Applying the matrix-analytic method, we develop the steady-state probabilities of the number of failed machines in the system as well as several system-performance measures. We construct a cost model to compute the optimal threshold N, and the joint optimal values for the fast and slow service rates simultaneously by a two-stage optimization method whose effectiveness is proved by numerical results. Moreover, we also analyze the sensitivity with numerical illustrations based on different system parameter values.