The Markovian two-echelon repairable item provisioning problem

A repairable-item provisioning system with two levels of repair is presented. Under the assumption that the machine time-to-failure and the repair times are exponentially distributed, a new algorithm is developed to compute the long-run average number of machines operating. Using the new algorithm the paper determines the optimal number of machines and repair channels at the two repair centres to minimize cost and meet a service-level constraint. The algorithm, whic is based on Little’s result in queueing theory and the theory of regenerative processes, is extremely efficient in terms of computer storage and execution time.