### Abstract

We consider freight consolidation problems on a single lane where cost savings can be achieved by switching from less-than-truck to full-truck loads. We first formulate the problem as an integer program and show that it is NP-hard. For the constant truck capacity case, we derive the convex hull of all solutions. In addition, if the per-truck per-day price is constant, we present a simple optimal policy and show the worst case ratio of 2 for the send-when-full policy, which is commonly used in practice. A real-world case study is carried out, which shows that the send-when-full policy can be efficient in practical situations. A two-mode transportation case, where an accelerated transportation mode is available by paying a higher cost, is also discussed. We show that several special cases of the two-mode consolidation problem are polynomially solvable.

Original language | English (US) |
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Number of pages | 37 |

State | Published - 2014 |

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## Cite this

Geng, Y., & Klabjan, D. (2014).

*Freight Consolidation on a Single Lane*.