We propose an exact solution method for a Logistics Service Network Design Problem (LSNDP) inspired by the management of restaurant supply chains. In this problem, a distributor seeks to source and fulfill customer orders of products (fruits, meat, napkins, etc.) through a multi-echelon distribution network consisting of supplier locations, warehouses, and customer locations in a cost-effective manner. As these products are small relative to vehicle capacity, an effective strategy for achieving low transportation costs is consolidation. Specifically, routing products so that vehicles transport multiple products at a time, with each product potentially sourced by a different supplier and destined for a different customer. As instances of this problem of sizes relevant to the operations of an industrial partner are too large for off-the-shelf optimization solvers, we propose a suite of techniques for enhancing a Benders decomposition-based algorithm, including a strengthened master problem, valid inequalities, and a heuristic. Together, these enhancements enable the resulting method to produce provably high-quality solutions to multiple variants of the problem in reasonable run-times.