Optimization Analysis of Retrial Machine Repair Problem with Server Breakdown and Threshold Recovery Policy

Abstract

Abstract This article deals with a retrial machine repair problem, in which M operating machines and S warm standby machines are maintained by a single server. The threshold recovery policy means that the server is typically subject to unpredictable breakdowns only if there is at least one failed machine in the system, and the recovery can be performed when K (1 ≤ K ≤ N = M + S), or more failed machines are present. Employing the matrix-analytic method, the steady-state probabilities of the number of failed machines in the system are developed in this research, as well as several system performance measures. This study establishes a cost model to determine the optimal K-threshold and the joint optimal values for the service and retrial rates simultaneously by using a two-stage optimization method. To examine the effects of different parameters on the performance measures and the total expected cost function, the study carries out the sensitivity analysis with numerical illustration.