An important service provided by third-party logistics (3PL) firms is to manage the inbound logistics of raw materials and components from multiple suppliers to several manufacturing plants. A key challenge for these 3PL firms is to determine how to coordinate and consolidate the transportation flow, so as to get the best overall logistics performance. One tactic is to establish consolidation hubs that collect shipments from several suppliers, consolidate these shipments, and direct the consolidated shipments to the appropriate manufacturing plant. We consider the network design problem to implement this tactic, namely deciding the number, location and operation of consolidation hubs so as to minimize the total logistics costs for the network. To solve this network design problem, we define candidate shipping options for each potential hub, for which we can pre-compute the shipping quantities required from each supplier, and the incurred shipping costs and inventory holding costs. We formulate the problem as an integer linear optimization model and illustrate how to solve large instances using Lagrangian relaxation and a subgradient optimization algorithm. Our results indicate that the bounds obtained are fairly tight and are superior to the bounds obtained from the solution of the LP relaxation.
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