Complexity of the AGV shortest path and single-loop guide path layout problems

The guide path layout is one of the most important variables in the design of automated guided vehicle systems. Many alternative guide path configurations have been proposed in previous research. Two of the simplest are the shortest path and shortest single-loop configurations. However, the optimal solutions to these two problems have not been easy to obtain. In this paper, we show why by proving the NP-completeness of these problems using graph theoretic methods.