Mathematical estimation for maximum flow of goods within a cross-dock to reduce inventory

Taniya Mukherjee, Isha Sangal, Biswajit Sarkar, Tamer M. Alkadash

Research output: Contribution to journalArticlepeer-review

25 Citations (Scopus)


Supply chain management has recently renovated its strategy by implementing a crossdocking scheme. Cross-docking is a calculated logistics strategy where freight emptied from inbound vehicles is handled straightforwardly onto outbound vehicles, eliminating the intermediate storage process. The cross-docking approach thrives on the minimum storage time of goods in the inventory. Most of the cross-docks avail temporary storage docks where items can be stored for up to 24 hours before being packed up for transportation. The storage capacity of the cross-dock varies depending on the nature of ownership. In the rented cross-docks center, the temporary storage docks are considered of infinite capacity. This study believes that the temporary storage facilities owned by the cross-dock center are of finite capacity, which subsequently affects the waiting time of the goods. The flow rate of goods within the cross-docks is expected to be maximum to avoid long waiting for goods in the queue. This paper uses a series of max-flow algorithms, namely Ford Fulkerson, Edmond Karp, and Dinic's, to optimize the flow of goods between the inbound port and the outbound dock and present a logical explanation to reduce the waiting time of the trucks. A numerical example is analyzed to prove the efficacity of the algorithm in finding maximum flow. The result demonstrates that Dinic's algorithm performs better than the Ford Fulkerson and Edmond Karp algorithm at addressing the problem of maximum flow at the cross-dock. The algorithm effectively provided the best result regarding iteration and time complexity. In addition, it also suggested the bottleneck paths of the network in determining the maximum flow.

Original languageEnglish
Pages (from-to)13710-13731
Number of pages22
JournalMathematical Biosciences and Engineering
Issue number12
Publication statusPublished - 2022

Bibliographical note

Publisher Copyright:
©2022 the Author(s)

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • General Agricultural and Biological Sciences
  • Computational Mathematics
  • Applied Mathematics


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