Constant Factor Approximation Algorithms for Repetitive Routing Problems of Grasp-and-delivery Robots in Production of Printed Circuit Boards

In this paper, we consider a repetitive routing problem which we find on a printed circuit board assembly line. There are m different printed circuit boards to be processed. As an automated manipulator embeds electronic parts in a printed circuit board from above, n identical pins from underneath protect it against overbending. A dedicated pin configuration is designed for each printed circuit board so that pins do not obstruct its own circuit. A single grasp-and-delivery robot transfers the pins one by one to arrange them from a configuration to another one. Given an initial configuration of pins and a permutable set of m required configurations, our repetitive routing problem asks to find a configuration sequence, i.e., a processing order of m printed circuit boards, and a transfer route of the grasp-and-delivery robot so that the route length over all m transitions is minimized. We first design a polynomial time approximation algorithm with factor four to a restricted version of the repetitive routing problem with a non-permutable set of configurations, i.e., with a fixed processing order of m printed circuit boards. Applying the procedure, we then show that the repetitive routing problem with a permutable set of configurations admits a polynomial time approximation algorithm with factor six.