A major challenge facing manufacturing companies is working together on scheduling and maintenance activities. The machine shuts down for various reasons, which causes disturbances in production schedules. These problems are often overlooked in research. This study deals with the problem of the periodical maintenance of a single machine, which is subject to the constraints of the periodic availability of the machine. A new solution method is suggested for the problem with an ABC (Artificial Bee Colony) algorithm. As far as we know, this is the first study to address the issue of periodic maintenance of a single machine using the ABC algorithm. An operation-based sequence of sequential integers is adopted to solve it using the ABC algorithm. To update the array, the solution with the highest ordinal value is replaced by a non-dominant solution in each particular cycle. The efficiency of the ABC has been demonstrated by the use of sample sets. Altogether, 500 problems have been solved. For comparison purposes, the relative percentage difference for each sample was computed. The results of these calculations indicate that the proposed method is very satisfying.