A mathematical tool for modeling the optimal set of the robotic elements at the cluster member enterprise is proposed. The necessary and sufficient conditions of the robotassisted technological equipment with the minimal resource idle time are formulated. The problem of minimizing technological downtime while robotic services a parallel working technological equipment is solved. The mathematical apparatus is proposed for calculating the duration of technological equipment servicing by robotic for proportional operations. At the stage of robotic elements design and operation the problem of organizing was solved for the clustermember enterprises. At the design stage the problem solution consists in finding the best option of the technological equipment deployment in the robotic elements sectors so that the only one robot services each element. The features of the solution problems using manipulator-type robotics are detected. At the stage of robotic elements operation, the problem solution involves the development of optimal option if the set operations for the designed elements. Algorithms for solving combinatorial problems of design and operation robotic elements are developed for a cluster-member enterprise. The computational mechanism of creating and using robotic elements allowing reduce time needed to obtain combinatorial problems solutions is proposed for a clustermember enterprise. In this mechanism, the task of splitting a given set of equipment into robotic elements is replaced by the task of sequentially extracting elements from the set of equipment in the production system of a cluster-member enterprise. The developed methods form the basis of the software package supporting solutions in the scope of robotic elements design and using for an engineering cluster enterprise.