<![CDATA[We study the selection of direct delivery / indirect delivery for LTL shipment in a two-echelon supply chain composed of a central distribution center (DC), an intermediate cross-docking center (XD) and customers, where the direct delivery is a shipment directly from the DC to customers, and the indirect delivery is a shipment to customers via the XD. We develop an optimization model that selects direct delivery / indirect delivery, taking into account the feature of volume discount. The volume discount is modeled as a nonlinear concave function and reformulated as MILP by a piecewise linearization technique. We propose a new analysis framework to account for the choice of direct / indirect delivery based on two indices, Distance-Ratio (DR), which is the ratio of the distance between direct and indirect delivery, and Demand Quantity (DQ). Based on this analysis, a heuristic solution using a support-vector-machine-based discriminant analysis model using the indices DR and DQ was proposed. In numerical experiments, the proposed heuristics were compared to the optimal solution for 100 randomly generated problem cases, and the error was shown to be within 0.8%.]]>
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