Branch-cut-and-price for scheduling deliveries with time windows in a direct shipping network

  • Timo GschwindEmail author
  • Stefan Irnich
  • Christian Tilk
  • Simon Emde


In a direct shipping (or point-to-point) network, individual deliveries are round trips from one supplier to one customer and back to either the same or another supplier, i.e., a truck can visit only one customer at a time before it has to return to a supplier. We consider the multiple sources/multiple sinks case, where a given set of direct deliveries from a set of suppliers to a set of customers must be scheduled such that the customer time windows are not violated, the truck fleet size is minimal, and the total weighted flow time is as small as possible. Direct shipping policies are commonly employed in just-in-time logistics (e.g., in the automotive industry) and in humanitarian logistics. We present an exact branch-cut-and-price algorithm for this problem, which is shown to perform well on instances from the literature and newly generated ones. We also investigate under what circumstances bundling suppliers in so-called supplier parks actually facilitates logistics operations under a direct shipping policy.


Direct deliveries Branch-cut-and-price Weighted flow time Just-in-time logistics 


Supplementary material

10951_2019_620_MOESM1_ESM.pdf (60 kb)
Supplementary material 1 (pdf 59 KB)


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Copyright information

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Authors and Affiliations

  1. 1.Chair of Logistics Management, Gutenberg School of Management and EconomicsJohannes Gutenberg University MainzMainzGermany
  2. 2.Fachgebiet Management Science/Operations ResearchTechnische Universität DarmstadtDarmstadtGermany

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