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In this paper, we propose a machine repair problem with constant retrial policy, wherein if a failed machine finds the repairman busy upon arrival, it enters into an orbit. The machines in the orbit form a single waiting line, and only the one at the head of the orbit repeats its request for repair. The failure times of operating machines and the repair times of failed machines follow exponential distributions. It is assumed that retrial times are generally distributed. We used the supplementary variable technique to obtain explicit expressions for the steady-state probabilities of the number of failed machines in the orbit. We performed sensitivity analysis of the machine availability and operative efficiency with respect to system parameters and the number of machines in operation. The analysis of the busy period and the waiting time were also presented. Finally, we developed a cost model and formulated a cost minimization problem. [ABSTRACT FROM AUTHOR]