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In this paper, we model and solve a multi-depot inventory-routing problem with split-deliveries (MDIRPSD). The problem emerges under the vendor-managed inventory paradigm when deliveries are made from multiple depots, and the customers can be served several times in the same period. The MDIRPSD integrates supply and distribution decisions and has recently been proposed in the literature. We present a new mathematical formulation, taking into account inventory holding costs, and we also introduce a new inventory policy. We have designed and implemented a new branch-and-cut that overcome a similar approach from the literature. Finally, we report comparative results between the two inventory policies considered.