Minimization of the production cycle in the presence of loops in the robot route

In this paper we consider the problem of the production process on the robotic line (RL). Organizational and technical aspects of this problem are summarized. Main attention is paid to development of its economic and mathematical aspects, which involves choosing a target function (TF) and its optimization. Using expensive equipment on the RL calls for minimizing its downtime. Consideration of these requirements is contributed by choosing the production cycle as a CP length , which should be minimized. Construction of an optimal timetable (schedule) of the RL work is reduced by the author to finding the route of the multi-tasking robot when it is servicing the rest of the RL equipment. The novelty in this case is replacement of the traditionally considered straight route for the robot route with loops, which in many cases allows reducing duration of the production cycle. Minimizing FIT on so many robot routes demanded, as shown in the article, elaboration of an auxiliary problem, which the author names the problem of marking numbers. This particular task is still unique and highly specialized, but it can be used in other situations as well. It can be referred to the class of scheduling theory problems (i..e, discrete optimization), namely, optimization of functions that are set on combinations. The paper describes in detail the situation of this problem occurrence and its strict formulation. Its solution has not been previously shown. In this paper this gap is filled in. The solution to this problem, as well as construction of the optimal calendar schedule of the robotic line operation is illustrated by specific numerical data.