Design of single hub crossdocking networks: geometric relationships and case study

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Kittithreerapronchai, Oran
Bartholdi, John J., III
Gue, Kevin
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In the distribution network of a large retailer, shipments can either be transported by the retailer's own trucks or outsourced to third-party logistics (3PL) companies. In the former case, shipments are consolidated and transported from their origins through an intermediate facility, namely a crossdock. At a crossdock, shipments are unloaded, sorted, re-consolidated, loaded and transported to their destinations. The consolidation process offers economies of scale that reduce the transportation costs. At the same time, it increases travel distances and incurs handling costs at a crossdock. For this reason, consolidation is uneconomic for a shipment in which origin and destination are located close to one other, especially through a distant crossdock. It is cheaper to outsource transportation of such a shipment to 3PL companies. This shipping decision raises a series of questions. Should a shipment be consolidated through a crossdock or outsourced to 3PL companies? How do facility locations, the operational cost of a crossdock and mode of shipments influence the shipping decision? Can the robustness and potential growth of a crossdock be measured? How does outsourcing affect the robustness and potential growth of a crossdock? We formulate a strategic model of a retailer's distribution network as an economic trade-off between consolidated shipments through a crossdock and outsourced shipments to 3PL companies. We study the locus of facility locations where the costs of a consolidated shipment and an outsourced shipment are equal and discover that the trade-off can be modeled by classical geometric curves, particularly an ellipse, a hyperbola, a limacon and a Cartesian oval. These curves can be developed into a preliminary routing and locating tool. We also observe interesting connections between the single hub crossdocking network and other fields of geometric study, such as Voronoi diagrams and geometric inversion. In addition, the area bounded by these curves represents the likelihood in which a particular shipment is consolidated through a crossdock. We expand this concept to multiple vendor-store pairs and suggest an index that measures robustness and potential growth of a particular crossdock. This asymptotic-probability index explains economic driving factors of consolidation and outsourcing. Although the derivation of the index is limited by the dimension and spatial distribution of facilities, its numerical value can be determined by a computer simulation. Therefore, we use Monte Carlo simulation to compute the proposed index to explain the outsourcing and the interaction between TL threshold0.1 and mode of shipments. The analysis and computer simulation suggest that outsourcing may cause an adverse effect in a single hub crossdocking network, resulting in the abrupt reduction of consolidated shipments in the network. Furthermore, we propose transportation planning to alleviate this effect and compare them to the optimal allocation. The routing and locating application of the model is illustrated using the Home Depot distribution network. Our model predicts 5.5% and additional 1.0% savings in transportation cost by re-allocation of shipments and re-location of crossdocks, respectively. The empirical study shows that the adverse effect of outsourcing can be eliminated by limiting the number of crossdocks used by each store.
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