This paper addresses the flow path design issue of automated material handling systems. We concentrate on the design of unidirectional guide path for automated guided vehicle systems. We present a modelling approach to determine the optimal flow path, which takes into account the impact of empty and loaded vehicle flows on the objective function to be minimized. We suggest a branch and bound algorithm, based on a depth-first search, which gives the excellent results in a very reduced time. The presented modelling approach exploits the structure of the problem to reduce the number of constraints by contraction and subtraction. Computational performance of this algorithm is compared with a procedure developed by Kaspi and Tanchoco and Kim and Tanchoco.