Abstract : A tandem automated guided vehicle (AGV) system deals with grouping workstations into some non-overlapping zones , and assigning exactly one AGV to each zone. This paper presents a new non-linear integer mathematical model to group n machines into N loops that minimizes both inter and intra-loop flows simultaneously. Due to computational difficulties of exact methods in solving our proposed model, a threshold accepting (TA) algorithm is proposed. To show its efficiency, a number of instances generated randomly are solved by this proposed TA and then compared with the LINGO solver package employing the branch-and-bound (B/B) method. The related computational results show that our proposed TA dominates the exact algorithm when the size of instances grows.