—In this paper we propose an optimal deployment and distributed packet scheduling of multi-sink Wireless Sensors networks (WNSs). This work is devoted to computing the optimal deployment of sinks for a given maximum number of hops between nodes and sinks. We also propose an optimal distributed packet scheduling in order to estimate the minimum energy consumption. We consider the energy consumed due to reporting, forwarding and overhearing. In contrast to reporting and forwarding, the energy used in overhearing is difficult to estimate because it is dependent on the packet scheduling. In this case, we determine the lower-bound of overhearing, based on an optimal distributed packet scheduling formulation. We also propose another estimation of the lower-bound in order to simulate non interfering parallel transmissions which is more tractable in large networks. We note that overhearing largely predominates in energy consumption. A large part of the optimizations and computations carried out in this paper are obtained using ILP formalization.