Human resource allocation applications of stochastic maintenance models with super-reserve backups

This article deals with stochastic maintenance models that include a repair facility and three types of 'unreliable' machines: the main facility of working and reserve machines, and an auxiliary facility of 'super-reserve' machines. Working machines breakdown exponentially and are immediately replaced by available reserve machines. Defective machines line up for repair and refurbished machines are returned to the main facility. This system falls into the category of closed queues with hot standbys and has more options than the basic model. If the main facility is restored to its original quantity and the repair facility leaves on routine maintenance, all reserve machines are temporarily blocked and renewals come from the super-reserve group until the latter is exhausted. Explicit formulas obtained demonstrate a relatively effortless use of functional of the main stochastic characteristics, and optimization of their objective function. Human resource applications are included as optimization examples.