Greedy Algorithms for the Freight Consolidation Problem

Authors Zuguang Gao , John R. Birge , Richard Li-Yang Chen , Maurice Cheung

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Zuguang Gao
  • The University of Chicago Booth School of Business, Chicago, IL, USA
John R. Birge
  • The University of Chicago Booth School of Business, Chicago, IL, USA
Richard Li-Yang Chen
  • Flexport, Inc., San Francisco, CA, USA
Maurice Cheung
  • Flexport, Inc., San Francisco, CA, USA

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Zuguang Gao, John R. Birge, Richard Li-Yang Chen, and Maurice Cheung. Greedy Algorithms for the Freight Consolidation Problem. In 22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2022). Open Access Series in Informatics (OASIcs), Volume 106, pp. 4:1-4:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


We define and study the (ocean) freight consolidation problem (FCP), which plays a crucial role in solving today’s supply chain crisis. Roughly speaking, every day and every hour, a freight forwarder sees a set of shipments and a set of containers at the origin port. There is a shipment cost associated with assigning each shipment to each container. If a container is assigned any shipment, there is also a procurement cost for that container. The FCP aims to minimize the total cost of fulfilling all the shipments, subject to capacity constraints of the containers. In this paper, we show that no constant factor approximation exists for FCP, and propose a series of greedy based heuristics for solving the problem. We also test our heuristics with simulated data and show that our heuristics achieve small optimality gaps.

Subject Classification

ACM Subject Classification
  • Theory of computation → Theory and algorithms for application domains
  • Freight consolidation
  • heuristics
  • greedy algorithm


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