We present a natural variation of the multi-depot multiple Travelling Salesman Problem (MmTSP) which considers pickup and delivery. Hence the notation of our problem: MmTSPPD. This problem must meet requests for transportation between customers and suppliers satisfying precedence. The objective is to find a solution with a minimum total travelling distance. A mixed integer programming model is presented for the MmTSPPD. To solve the MmTSPPD we propose a variable neighborhood search (VNS) that uses the variable neighborhood descent (VND) as local search procedure. We evaluate the performance of this heuristic on a data set adapted from TSPLIB instances. The results show that the VNS proposed is efficient and effective to solve MmTSPPD.