The Dynamic-Demand Joint Replenishment Problem with Approximated Transportation Costs

Annelieke C. Baller*, Said Dabia, Wout E.H. Dullaert, Daniele Vigo

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review

234 Downloads (Pure)


In a vendor-managed inventory setting, a supplier determines the timing and size of replenishments for its customers. In the Dynamic-Demand Joint Replenishment Problem (DJRP), one assumes that the supplier pays a fixed fee for replenishing a customer which often occurs if the supplier outsources transportation. Hence, there is no incentive for the supplier to schedule replenishments for nearby customers in the same period. This results in higher transportation costs for the carrier, decreased vehicle utilization and increased future fees for the supplier. To lower costs for both parties, this paper extends the traditional DJRP to the DJRP with Approximated Transportation Costs (DJRP-AT) by taking transportation considerations into account. Since routing problems are difficult to solve and it is not necessary to know the sequence of the deliveries to the customers as these are outsourced, the transportation costs for a given set of customers are approximated using classical schemes. A solution approach for the DJRP-AT based on Branch-and-Cut-and-Price is validated using test instances from the literature. Results show improvements of 4% on average and up to 14.4% for individual instances compared with the DJRP. Moreover, when the DJRP-AT is compared with the DJRP on instances derived from a real-life case, similar savings are obtained. Comparing the DJRP-AT to an equivalent problem with actual routing costs, the solution values of the DJRP-AT are on average only 0.77% higher showing the value of the approximation.

Original languageEnglish
Pages (from-to)1013-1033
Number of pages21
JournalEuropean Journal of Operational Research
Issue number3
Early online date31 Jan 2019
Publication statusPublished - 1 Aug 2019


  • Branch-and-Cut-and-Price
  • Joint replenishment
  • Logistics
  • Transportation costs


Dive into the research topics of 'The Dynamic-Demand Joint Replenishment Problem with Approximated Transportation Costs'. Together they form a unique fingerprint.

Cite this