Optimal Allocation Problem in the Machine Repairman System with Heterogeneous Servers

Abstract

Abstract.A controllable repairman model consists of L machines subject to failures and two repair servers working at different speeds. The problem of optimal allocation of failed machines between the servers is examined. The optimal control policy is calculated versus cost structures. As a result the optimal policy can be of threshold type, hysteretic type or have more complicated form. It is shown that the corresponding Markov process for hysteretic control policy belongs to the class of the Quasi-Birth-and-Death processes (QBD) with three diagonal block infinitesimal matrix. The stationary characteristics in this case are derived in matrix analytic form. Some numerical results are used to illustrate a number of features of the controlled model under study.